From cdf70ba147a29404717119930015333191aaea38 Mon Sep 17 00:00:00 2001 From: toddytharmonkey Date: Tue, 18 Jun 2024 15:43:37 -0400 Subject: [PATCH 1/9] add (incomplete) maximum bound calculation --- .../qiskit/HellingerVsTime.ipynb | 224 +++++++++++++++++- 1 file changed, 221 insertions(+), 3 deletions(-) diff --git a/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb b/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb index 4a0a936c..933660b5 100644 --- a/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb +++ b/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "b5a9ab05-db97-4853-9209-4492457dbc19", "metadata": {}, "outputs": [], @@ -274,7 +274,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "id": "0e58d5a4-9d50-47a8-b181-7834aba442b4", "metadata": {}, "outputs": [], @@ -474,10 +474,228 @@ "plt.show()" ] }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "a54339c6-b484-4a6c-98e6-38bdc2dbd993", + "metadata": {}, + "source": [ + "https://arxiv.org/abs/1912.08854:\n", + "\n", + "**Proposition 15 (Tight error bound for the first-order Lie-Trotter formula).**\n", + "Let $H = \\sum_{\\gamma=1}^{\\Gamma} H_\\gamma$ be a Hamiltonian consisting of $\\Gamma$ summands and $t \\geq 0$.\n", + "Let $\\mathcal{S}_1(t) = \\prod_{\\gamma=1}^{\\Gamma} e^{-itH_\\gamma}$ be the first-order Lie-Trotter formula.\n", + "Then, the additive Trotter error can be bounded as\n", + "\n", + "$$\n", + "\\left\\| \\mathcal{S}_1(t) - e^{-itH} \\right\\| \\leq \\frac{t^2}{2} \\left\\| \\sum_{\\gamma_1=1}^{\\Gamma} \\left[ \\sum_{\\gamma_2=\\gamma_1+1}^{\\Gamma} [H_{\\gamma_2}, H_{\\gamma_1}] \\right] \\right\\|.\n", + "$$\n", + "\n", + "Given this, we can plot this error for both of our Hamiltonians and compare it to the maximum amount of error that they should be having." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "0a8cc9a9-5410-4f7b-a1a6-4e4f0df296dd", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.quantum_info import Statevector, state_fidelity, commutator\n", + "\n", + "def max_trotter_error(ham, max_time):\n", + " \"\"\"\n", + " Following the Childs et al. paper, calculate the maximum error for the order 1 Lie-Trotter trotterization. \n", + " \"\"\"\n", + "\n", + " Gamma = len(ham)\n", + "\n", + " commutators = []\n", + "\n", + " for gamma_1 in range(Gamma):\n", + " for gamma_2 in range(gamma_1+1, Gamma): \n", + "\n", + " commutators.append(commutator(ham[gamma_1], ham[gamma_2]))\n", + "\n", + " spectral_norm = np.linalg.norm(sum(commutators).to_matrix(), ord=2)\n", + "\n", + " return max_time**2 * (1/2) * spectral_norm \n", + "\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "7cc6519d-a2dd-4e8c-8efe-3903ebcd557e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0\n", + "4.472135954999579\n", + "17.888543819998315\n", + "40.24922359499621\n", + "71.55417527999326\n", + "111.80339887498947\n", + "160.99689437998484\n", + "219.13466179497937\n", + "286.21670111997304\n", + "362.24301235496586\n" + ] + } + ], + "source": [ + "for max_time in range(10):\n", + " print(max_trotter_error(construct_hamiltonian(4, \"tfim\", w, hx, hz), max_time))" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "e9b58d51-170f-4c55-8c15-4f1c2e44b437", + "metadata": {}, + "outputs": [], + "source": [ + "def HamiltonianSimulationExactVector(\n", + " n_spins: int,\n", + " t: float,\n", + " init_state: str,\n", + " hamiltonian: str,\n", + " w: float,\n", + " hx: list[float],\n", + " hz: list[float],\n", + ") -> dict:\n", + " \"\"\"\n", + " Perform exact Hamiltonian simulation using classical matrix evolution.\n", + "\n", + " Args:\n", + " n_spins (int): Number of spins (qubits).\n", + " t (float): Duration of simulation.\n", + " init_state (str): The chosen initial state. By default applies the checkerboard state, but can also be set to \"ghz\", the GHZ state.\n", + " hamiltonian (str): Which hamiltonian to run. \"heisenberg\" by default but can also choose \"TFIM\".\n", + " w (float): Strength of two-qubit interactions for heisenberg hamiltonian.\n", + " hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", + " hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", + "\n", + " Returns:\n", + " dict: The distribution of the evolved state.\n", + " \"\"\"\n", + " hamiltonian_sparse = construct_hamiltonian(n_spins, hamiltonian, w, hx, hz)\n", + " time_problem = TimeEvolutionProblem(\n", + " hamiltonian_sparse, t, initial_state=initial_state(n_spins, init_state)\n", + " )\n", + " result = SciPyRealEvolver(num_timesteps=1).evolve(time_problem)\n", + " return result.evolved_state\n", + "\n", + "def get_init_state_distribution_vector(n_spins, hamiltonian):\n", + "\n", + " if hamiltonian.lower().strip() == \"tfim\":\n", + " init_state = \"ghz\"\n", + " else:\n", + " init_state = \"checkerboard\"\n", + "\n", + " init_circ = ham.initial_state(n_spins, init_state)\n", + "\n", + " return get_vector(init_circ)\n", + "\n", + "\n", + "def get_vector_at_timestep(step, K, max_time, hamiltonian, w, hx, hz):\n", + "\n", + " if step == 0:\n", + " return get_init_state_distribution_vector(n_spins=6, hamiltonian=hamiltonian)\n", + " else:\n", + " return get_vector(\n", + " ham.HamiltonianSimulation(\n", + " n_spins=6,\n", + " K=step,\n", + " t=step * (max_time / K),\n", + " hamiltonian=hamiltonian,\n", + " w=w,\n", + " hx=hx,\n", + " hz=hz,\n", + " ).remove_final_measurements(inplace=False)\n", + " )\n", + "\n", + "def get_vector(circuit, shots=None):\n", + " \"\"\"\n", + " Generates the probability distribution of the outcomes for a given Qiskit circuit.\n", + "\n", + " Parameters:\n", + " - circuit (QuantumCircuit): The quantum circuit to simulate.\n", + " - shots (int): The number of shots for the simulation.\n", + "\n", + " Returns:\n", + " - result (dict): The probability distribution of the outcomes.\n", + " \"\"\"\n", + "\n", + " return Statevector(circuit)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "96d0ee96-3f8b-41a3-8e35-606575c7a601", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot #4: Hellinger fidelity at each time step from the classical exact to the trotterized at each time step.\n", + "\n", + "for hamiltonian, init_state in hamiltonians_initstate_pairs:\n", + " hellingers = []\n", + " times = []\n", + " initial_distribution = None\n", + "\n", + " for k_i in range(K + 1):\n", + " # note k_0 = 0\n", + " #\n", + " dist = get_vector_at_timestep(k_i, K, max_time, hamiltonian, w, hx, hz)\n", + " print(type(dist))\n", + "\n", + " exact_dist = HamiltonianSimulationExactVector(\n", + " 6,\n", + " t=k_i * (max_time / K),\n", + " init_state=init_state,\n", + " hamiltonian=\"tfim\",\n", + " w=1,\n", + " hx=hx,\n", + " hz=hz,\n", + " )\n", + "\n", + " print(type(exact_dist))\n", + "\n", + " hellingers.append(state_fidelity(exact_dist, dist))\n", + " times.append(k_i * (max_time / K))\n", + "\n", + "# plt.plot(times, hellingers, marker=\"o\")\n", + "# plt.title(\n", + "# image_label_raw\n", + "# + \"\\n\"\n", + "# + \"Hellinger fidelity of exact vs trotterized states at discrete times\"\n", + "# )\n", + "# plt.legend([\"heisenberg\", \"tfim\"])\n", + "# plt.xlabel(\"Time\")\n", + "# plt.ylabel(\"Hellinger fidelity\")\n", + "# plt.show()" + ] + }, { "cell_type": "code", "execution_count": null, - "id": "ec4301c6-5b9f-427f-8cb9-23c100f69a7d", + "id": "222723d8-cf9c-4545-8a88-3d92332bea73", "metadata": {}, "outputs": [], "source": [] From 433fce6e23fb7fa384874cb4ffbf0feb93cd71e8 Mon Sep 17 00:00:00 2001 From: toddytharmonkey Date: Wed, 19 Jun 2024 11:12:24 -0400 Subject: [PATCH 2/9] add correct l2 norm vs spectral norm comparison --- .../qiskit/HellingerVsTime.ipynb | 132 ++++++++++++------ 1 file changed, 88 insertions(+), 44 deletions(-) diff --git a/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb b/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb index 933660b5..ccdaa585 100644 --- a/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb +++ b/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 20, "id": "b5a9ab05-db97-4853-9209-4492457dbc19", "metadata": {}, "outputs": [], @@ -274,7 +274,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 21, "id": "0e58d5a4-9d50-47a8-b181-7834aba442b4", "metadata": {}, "outputs": [], @@ -432,10 +432,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, "id": "4c45e35d-42e0-49c7-bb2f-2c28e6a69743", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Plot #4: Hellinger fidelity at each time step from the classical exact to the trotterized at each time step.\n", "\n", @@ -453,7 +464,7 @@ " 6,\n", " t=k_i * (max_time / K),\n", " init_state=init_state,\n", - " hamiltonian=\"tfim\",\n", + " hamiltonian=hamiltonian,\n", " w=1,\n", " hx=hx,\n", " hz=hz,\n", @@ -496,7 +507,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 61, "id": "0a8cc9a9-5410-4f7b-a1a6-4e4f0df296dd", "metadata": {}, "outputs": [], @@ -515,7 +526,7 @@ " for gamma_1 in range(Gamma):\n", " for gamma_2 in range(gamma_1+1, Gamma): \n", "\n", - " commutators.append(commutator(ham[gamma_1], ham[gamma_2]))\n", + " commutators.append(commutator(ham[gamma_2], ham[gamma_1]))\n", "\n", " spectral_norm = np.linalg.norm(sum(commutators).to_matrix(), ord=2)\n", "\n", @@ -526,7 +537,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 63, "id": "7cc6519d-a2dd-4e8c-8efe-3903ebcd557e", "metadata": {}, "outputs": [ @@ -535,26 +546,48 @@ "output_type": "stream", "text": [ "0.0\n", - "4.472135954999579\n", - "17.888543819998315\n", - "40.24922359499621\n", - "71.55417527999326\n", - "111.80339887498947\n", - "160.99689437998484\n", - "219.13466179497937\n", - "286.21670111997304\n", - "362.24301235496586\n" + "6.987918414869866\n", + "27.951673659479464\n", + "62.891265733828796\n", + "111.80669463791786\n", + "174.69796037174666\n", + "251.56506293531518\n", + "342.4080023286234\n", + "447.22677855167143\n", + "566.0213916044592\n" ] + }, + { + "data": { + "text/plain": [ + "362.24301235496586" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ "for max_time in range(10):\n", - " print(max_trotter_error(construct_hamiltonian(4, \"tfim\", w, hx, hz), max_time))" + " print(max_trotter_error(construct_hamiltonian(6, \"tfim\", w, hx, hz), max_time))\n", + "\n", + "#0.0\n", + "4.472135954999579\n", + "17.888543819998315\n", + "40.24922359499621\n", + "71.55417527999326\n", + "111.80339887498947\n", + "160.99689437998484\n", + "219.13466179497937\n", + "286.21670111997304\n", + "362.24301235496586\n", + "\n" ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 55, "id": "e9b58d51-170f-4c55-8c15-4f1c2e44b437", "metadata": {}, "outputs": [], @@ -602,14 +635,14 @@ " return get_vector(init_circ)\n", "\n", "\n", - "def get_vector_at_timestep(step, K, max_time, hamiltonian, w, hx, hz):\n", + "def get_vector_at_timestep(n_qubits,step, K, max_time, hamiltonian, w, hx, hz):\n", "\n", " if step == 0:\n", - " return get_init_state_distribution_vector(n_spins=6, hamiltonian=hamiltonian)\n", + " return get_init_state_distribution_vector(n_spins=n_qubits, hamiltonian=hamiltonian)\n", " else:\n", " return get_vector(\n", " ham.HamiltonianSimulation(\n", - " n_spins=6,\n", + " n_spins=n_qubits,\n", " K=step,\n", " t=step * (max_time / K),\n", " hamiltonian=hamiltonian,\n", @@ -636,13 +669,13 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 60, "id": "96d0ee96-3f8b-41a3-8e35-606575c7a601", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -654,42 +687,53 @@ "source": [ "# Plot #4: Hellinger fidelity at each time step from the classical exact to the trotterized at each time step.\n", "\n", - "for hamiltonian, init_state in hamiltonians_initstate_pairs:\n", + "n_qubit = 6\n", + "\n", + "colors = ['r','b']\n", + "\n", + "for i, (hamiltonian, init_state) in enumerate(hamiltonians_initstate_pairs):\n", " hellingers = []\n", + " max_errors = []\n", " times = []\n", " initial_distribution = None\n", "\n", " for k_i in range(K + 1):\n", " # note k_0 = 0\n", - " #\n", - " dist = get_vector_at_timestep(k_i, K, max_time, hamiltonian, w, hx, hz)\n", - " print(type(dist))\n", "\n", - " exact_dist = HamiltonianSimulationExactVector(\n", - " 6,\n", + " time = \n", + " \n", + " max_error = max_trotter_error(construct_hamiltonian(n_qubit, hamiltonian, w, hx, hz), k_i * (max_time / K))\n", + " max_errors.append(max_error)\n", + " \n", + " vector = get_vector_at_timestep(n_qubit, k_i, K, max_time, hamiltonian, w, hx, hz)\n", + "\n", + " exact_vector = HamiltonianSimulationExactVector(\n", + " n_qubit,\n", " t=k_i * (max_time / K),\n", " init_state=init_state,\n", - " hamiltonian=\"tfim\",\n", + " hamiltonian=hamiltonian,\n", " w=1,\n", " hx=hx,\n", " hz=hz,\n", " )\n", "\n", - " print(type(exact_dist))\n", - "\n", - " hellingers.append(state_fidelity(exact_dist, dist))\n", + " #doing .data just gets the 1D statevectors... I think. Since these are pure states.\n", + " \n", + " hellingers.append(np.linalg.norm((vector.data- exact_vector.data), ord=2))\n", " times.append(k_i * (max_time / K))\n", "\n", - "# plt.plot(times, hellingers, marker=\"o\")\n", - "# plt.title(\n", - "# image_label_raw\n", - "# + \"\\n\"\n", - "# + \"Hellinger fidelity of exact vs trotterized states at discrete times\"\n", - "# )\n", - "# plt.legend([\"heisenberg\", \"tfim\"])\n", - "# plt.xlabel(\"Time\")\n", - "# plt.ylabel(\"Hellinger fidelity\")\n", - "# plt.show()" + " plt.plot(times, hellingers, marker=\"o\", color = colors[i])\n", + " plt.plot(times, max_errors, marker=\"_\", linestyle = '', color=colors[i])\n", + "plt.title(\n", + " image_label_raw\n", + " + \"\\n\"\n", + " + \"L2 Norm of the distance between the exact and trotterized state\"\n", + ")\n", + "plt.legend([\"heisenberg\", \"tfim\"])\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Hellinger fidelity\")\n", + "plt.yscale('log')\n", + "plt.show()" ] }, { From e3b02431f7534a2fa1306cdaec42e818b09a49c4 Mon Sep 17 00:00:00 2001 From: toddytharmonkey Date: Tue, 25 Jun 2024 17:05:44 -0400 Subject: [PATCH 3/9] seperate exact code, fix value of g to match kernel --- .../_common/hamiltonian_simulation_exact.py | 146 + .../_common/precalculated_data.ipynb | 259 +- .../_common/precalculated_data.json | 20874 ++++++++-------- 3 files changed, 10626 insertions(+), 10653 deletions(-) create mode 100644 hamiltonian-simulation/_common/hamiltonian_simulation_exact.py diff --git a/hamiltonian-simulation/_common/hamiltonian_simulation_exact.py b/hamiltonian-simulation/_common/hamiltonian_simulation_exact.py new file mode 100644 index 00000000..3c6940f7 --- /dev/null +++ b/hamiltonian-simulation/_common/hamiltonian_simulation_exact.py @@ -0,0 +1,146 @@ +import sys + +sys.path[1:1] = ["_common", "_common/qiskit"] +sys.path[1:1] = ["../../_common", "../../_common/qiskit"] +sys.path[1:1] = ["../qiskit"] +from qiskit import QuantumCircuit +from qiskit.quantum_info import SparsePauliOp +from qiskit_algorithms import TimeEvolutionProblem, SciPyRealEvolver +import numpy as np +np.random.seed(0) +import execute as ex +import metrics as metrics + +from hamiltonian_simulation_kernel import initial_state + +def construct_TFIM_hamiltonian(n_spins: int) -> SparsePauliOp: + """ + Construct the Transverse Field Ising Model (TFIM) Hamiltonian. + + Args: + n_spins (int): Number of spins (qubits). + + Returns: + SparsePauliOp: The Hamiltonian represented as a sparse Pauli operator. + """ + pauli_strings = [] + coefficients = [] + g = 1 # Strength of the transverse field + + # Pauli spin vector product terms + for i in range(n_spins): + x_term = 'I' * i + 'X' + 'I' * (n_spins - i - 1) + pauli_strings.append(x_term) + coefficients.append(g) + + identity_string = ['I'] * n_spins + + # ZZ operation on each pair of qubits in a linear chain + for j in range(2): + for i in range(j % 2, n_spins - 1, 2): + zz_term = identity_string.copy() + zz_term[i] = 'Z' + zz_term[(i + 1) % n_spins] = 'Z' + zz_term = ''.join(zz_term) + pauli_strings.append(zz_term) + coefficients.append(1.0) + + return SparsePauliOp.from_list(zip(pauli_strings, coefficients)) + +def construct_heisenberg_hamiltonian(n_spins: int, w: int, hx: list[float], hz: list[float]) -> SparsePauliOp: + """ + Construct the Heisenberg Hamiltonian with disorder. + + Args: + n_spins (int): Number of spins (qubits). + w (float): Strength of two-qubit interactions for heisenberg hamiltonian. + hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. + hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. + + Returns: + SparsePauliOp: The Hamiltonian represented as a sparse Pauli operator. + """ + + pauli_strings = [] + coefficients = [] + + # Disorder terms + for i in range(n_spins): + x_term = 'I' * i + 'X' + 'I' * (n_spins - i - 1) + z_term = 'I' * i + 'Z' + 'I' * (n_spins - i - 1) + pauli_strings.append(x_term) + coefficients.append(w * hx[i]) + pauli_strings.append(z_term) + coefficients.append(w * hz[i]) + + identity_string = ['I'] * n_spins + + # Interaction terms + for j in range(2): + for i in range(j % 2, n_spins - 1, 2): + xx_term = identity_string.copy() + yy_term = identity_string.copy() + zz_term = identity_string.copy() + + xx_term[i] = 'X' + xx_term[(i + 1) % n_spins] = 'X' + + yy_term[i] = 'Y' + yy_term[(i + 1) % n_spins] = 'Y' + + zz_term[i] = 'Z' + zz_term[(i + 1) % n_spins] = 'Z' + + pauli_strings.append(''.join(xx_term)) + coefficients.append(1.0) + pauli_strings.append(''.join(yy_term)) + coefficients.append(1.0) + pauli_strings.append(''.join(zz_term)) + coefficients.append(1.0) + + return SparsePauliOp.from_list(zip(pauli_strings, coefficients)) + +def construct_hamiltonian(n_spins: int, hamiltonian: str, w: float, hx : list[float], hz: list[float]) -> SparsePauliOp: + """ + Construct the Hamiltonian based on the specified method. + + Args: + n_spins (int): Number of spins (qubits). + hamiltonian (str): Which hamiltonian to run. "Heisenberg" by default but can also choose "TFIM". + w (float): Strength of two-qubit interactions for heisenberg hamiltonian. + hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. + hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. + + Returns: + SparsePauliOp: The constructed Hamiltonian. + """ + + hamiltonian = hamiltonian.strip().lower() + + if hamiltonian == "heisenberg": + return construct_heisenberg_hamiltonian(n_spins, w, hx, hz) + elif hamiltonian == "tfim": + return construct_TFIM_hamiltonian(n_spins) + else: + raise ValueError("Invalid Hamiltonian specification.") + +def HamiltonianSimulationExact(n_spins: int, t: float, init_state: str, hamiltonian: str, w: float, hx: list[float], hz: list[float]) -> dict: + """ + Perform exact Hamiltonian simulation using classical matrix evolution. + + Args: + n_spins (int): Number of spins (qubits). + t (float): Duration of simulation. + init_state (str): The chosen initial state. By default applies the checkerboard state, but can also be set to "ghz", the GHZ state. + hamiltonian (str): Which hamiltonian to run. "Heisenberg" by default but can also choose "TFIM". + w (float): Strength of two-qubit interactions for heisenberg hamiltonian. + hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. + hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. + + Returns: + dict: The distribution of the evolved state. + """ + hamiltonian_sparse = construct_hamiltonian(n_spins, hamiltonian, w, hx, hz) + time_problem = TimeEvolutionProblem(hamiltonian_sparse, t, initial_state=initial_state(n_spins, init_state)) + result = SciPyRealEvolver(num_timesteps=1).evolve(time_problem) + return result.evolved_state.probabilities_dict() diff --git a/hamiltonian-simulation/_common/precalculated_data.ipynb b/hamiltonian-simulation/_common/precalculated_data.ipynb index 185c4e73..14152c1c 100644 --- a/hamiltonian-simulation/_common/precalculated_data.ipynb +++ b/hamiltonian-simulation/_common/precalculated_data.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2024-05-06T16:26:36.751184Z", @@ -16,205 +16,30 @@ "sys.path[1:1] = [\"_common\", \"_common/qiskit\"]\n", "sys.path[1:1] = [\"../../_common\", \"../../_common/qiskit\"]\n", "sys.path[1:1] = [\"../qiskit\"]\n", - "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n", - "import time\n", - "import math\n", - "import numpy as np\n", - "np.random.seed(0)\n", "import execute as ex\n", "import metrics as metrics\n", - "from collections import defaultdict" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2024-05-06T16:26:37.422103Z", - "start_time": "2024-05-06T16:26:37.330344Z" - } - }, - "outputs": [], - "source": [ + "from hamiltonian_simulation_benchmark import HamiltonianSimulation\n", + "from hamiltonian_simulation_exact import HamiltonianSimulationExact\n", + "\n", + "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n", "from qiskit.quantum_info import SparsePauliOp\n", "from qiskit_algorithms import TimeEvolutionProblem, SciPyRealEvolver\n", "\n", - "# Import the hamiltonian simualtion circuit from our qiskit benchmark. \n", - "from hamiltonian_simulation_benchmark import HamiltonianSimulation" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# The functions in this cell are used to exactly simulate the hamiltonian evolution using a classical matrix evolution. \n", - "\n", - "def initial_state(n_spins: int, initial_state: str = \"checker\") -> QuantumCircuit:\n", - " \"\"\"\n", - " Initialize the quantum state.\n", - "\n", - " Dev note: This function is copy/pasted from HamiltonianSimulation.\n", - " \n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - " initial_state (str): The chosen initial state. By default applies the checkerboard state, but can also be set to \"ghz\", the GHZ state.\n", - "\n", - " Returns:\n", - " QuantumCircuit: The initialized quantum circuit.\n", - " \"\"\"\n", - " qc = QuantumCircuit(n_spins)\n", - "\n", - " if initial_state.strip().lower() == \"checkerboard\" or initial_state.strip().lower() == \"neele\":\n", - " # Checkerboard state, or \"Neele\" state\n", - " for k in range(0, n_spins, 2):\n", - " qc.x([k])\n", - " elif initial_state.strip().lower() == \"ghz\":\n", - " # GHZ state: 1/sqrt(2) (|00...> + |11...>)\n", - " qc.h(0)\n", - " for k in range(1, n_spins):\n", - " qc.cx(k-1, k)\n", - "\n", - " return qc\n", - "\n", - "def construct_TFIM_hamiltonian(n_spins: int) -> SparsePauliOp:\n", - " \"\"\"\n", - " Construct the Transverse Field Ising Model (TFIM) Hamiltonian.\n", - "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - "\n", - " Returns:\n", - " SparsePauliOp: The Hamiltonian represented as a sparse Pauli operator.\n", - " \"\"\"\n", - " pauli_strings = []\n", - " coefficients = []\n", - " g = 0.2 # Strength of the transverse field\n", - "\n", - " # Pauli spin vector product terms\n", - " for i in range(n_spins):\n", - " x_term = 'I' * i + 'X' + 'I' * (n_spins - i - 1)\n", - " pauli_strings.append(x_term)\n", - " coefficients.append(g)\n", - "\n", - " identity_string = ['I'] * n_spins\n", - "\n", - " # ZZ operation on each pair of qubits in a linear chain\n", - " for j in range(2):\n", - " for i in range(j % 2, n_spins - 1, 2):\n", - " zz_term = identity_string.copy()\n", - " zz_term[i] = 'Z'\n", - " zz_term[(i + 1) % n_spins] = 'Z'\n", - " zz_term = ''.join(zz_term)\n", - " pauli_strings.append(zz_term)\n", - " coefficients.append(1.0)\n", - "\n", - " return SparsePauliOp.from_list(zip(pauli_strings, coefficients))\n", - "\n", - "def construct_heisenberg_hamiltonian(n_spins: int, w: int, hx: list[float], hz: list[float]) -> SparsePauliOp:\n", - " \"\"\"\n", - " Construct the Heisenberg Hamiltonian with disorder.\n", - "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - " w (float): Strength of two-qubit interactions for heisenberg hamiltonian. \n", - " hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. \n", - " hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. \n", - "\n", - " Returns:\n", - " SparsePauliOp: The Hamiltonian represented as a sparse Pauli operator.\n", - " \"\"\"\n", - "\n", - " pauli_strings = []\n", - " coefficients = []\n", - "\n", - " # Disorder terms\n", - " for i in range(n_spins):\n", - " x_term = 'I' * i + 'X' + 'I' * (n_spins - i - 1)\n", - " z_term = 'I' * i + 'Z' + 'I' * (n_spins - i - 1)\n", - " pauli_strings.append(x_term)\n", - " coefficients.append(w * hx[i])\n", - " pauli_strings.append(z_term)\n", - " coefficients.append(w * hz[i])\n", - "\n", - " identity_string = ['I'] * n_spins\n", - "\n", - " # Interaction terms\n", - " for j in range(2):\n", - " for i in range(j % 2, n_spins - 1, 2):\n", - " xx_term = identity_string.copy()\n", - " yy_term = identity_string.copy()\n", - " zz_term = identity_string.copy()\n", - "\n", - " xx_term[i] = 'X'\n", - " xx_term[(i + 1) % n_spins] = 'X'\n", - "\n", - " yy_term[i] = 'Y'\n", - " yy_term[(i + 1) % n_spins] = 'Y'\n", - "\n", - " zz_term[i] = 'Z'\n", - " zz_term[(i + 1) % n_spins] = 'Z'\n", - "\n", - " pauli_strings.append(''.join(xx_term))\n", - " coefficients.append(1.0)\n", - " pauli_strings.append(''.join(yy_term))\n", - " coefficients.append(1.0)\n", - " pauli_strings.append(''.join(zz_term))\n", - " coefficients.append(1.0)\n", - "\n", - " return SparsePauliOp.from_list(zip(pauli_strings, coefficients))\n", - "\n", - "def construct_hamiltonian(n_spins: int, hamiltonian: str, w: float, hx : list[float], hz: list[float]) -> SparsePauliOp:\n", - " \"\"\"\n", - " Construct the Hamiltonian based on the specified method.\n", - "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - " hamiltonian (str): Which hamiltonian to run. \"Heisenberg\" by default but can also choose \"TFIM\". \n", - " w (float): Strength of two-qubit interactions for heisenberg hamiltonian. \n", - " hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. \n", - " hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. \n", - "\n", - " Returns:\n", - " SparsePauliOp: The constructed Hamiltonian.\n", - " \"\"\"\n", - "\n", - " hamiltonian = hamiltonian.strip().lower()\n", - "\n", - " if hamiltonian == \"heisenberg\":\n", - " return construct_heisenberg_hamiltonian(n_spins, w, hx, hz)\n", - " elif hamiltonian == \"tfim\":\n", - " return construct_TFIM_hamiltonian(n_spins)\n", - " else:\n", - " raise ValueError(\"Invalid Hamiltonian specification.\")\n", + "import time\n", + "import math\n", + "import numpy as np\n", "\n", - "def HamiltonianSimulationExact(n_spins: int, t: float, init_state: str, hamiltonian: str, w: float, hx: list[float], hz: list[float]) -> dict:\n", - " \"\"\"\n", - " Perform exact Hamiltonian simulation using classical matrix evolution.\n", + "import execute as ex\n", + "import metrics as metrics\n", "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - " t (float): Duration of simulation.\n", - " init_state (str): The chosen initial state. By default applies the checkerboard state, but can also be set to \"ghz\", the GHZ state.\n", - " hamiltonian (str): Which hamiltonian to run. \"Heisenberg\" by default but can also choose \"TFIM\". \n", - " w (float): Strength of two-qubit interactions for heisenberg hamiltonian. \n", - " hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. \n", - " hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian. \n", + "from collections import defaultdict\n", "\n", - " Returns:\n", - " dict: The distribution of the evolved state.\n", - " \"\"\"\n", - " hamiltonian_sparse = construct_hamiltonian(n_spins, hamiltonian, w, hx, hz)\n", - " time_problem = TimeEvolutionProblem(hamiltonian_sparse, t, initial_state=initial_state(n_spins, init_state))\n", - " result = SciPyRealEvolver(num_timesteps=1).evolve(time_problem)\n", - " return result.evolved_state.probabilities_dict()" + "np.random.seed(0)" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2024-05-06T16:39:58.644353Z", @@ -222,12 +47,31 @@ }, "tags": [] }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Now running n_spins 2\n", + "Now running n_spins 3\n", + "Now running n_spins 4\n", + "Now running n_spins 5\n", + "Now running n_spins 6\n", + "Now running n_spins 7\n", + "Now running n_spins 8\n", + "Now running n_spins 9\n", + "Now running n_spins 10\n", + "Now running n_spins 11\n", + "Now running n_spins 12\n" + ] + } + ], "source": [ "import json\n", "from qiskit_aer import Aer\n", "from qiskit import transpile\n", "\n", + "# Parameters for the Heisenberg Hamiltonian simulation\n", "w = 1 \n", "k = 5\n", "t = .2 # Heisenberg state evolves \"just\" enough \n", @@ -235,8 +79,10 @@ "min_qubits = 2\n", "max_qubits = 12\n", "\n", + "# Backend for simulation\n", "backend = Aer.get_backend(\"qasm_simulator\")\n", "\n", + "# Dictionary to store precalculated data\n", "precalculated_data = {}\n", "\n", "# store parameters in precalculated data\n", @@ -250,8 +96,10 @@ "np.random.seed(75)\n", "precalculated_data['hz'] = list(2 * np.random.random(20) - 1) # random numbers between [-1, 1]\n", "\n", + "# Number of shots for the (close to) perfect circuit simulation\n", "num_shots = 100000\n", "\n", + "# Generate precalculated data for each number of qubits\n", "for n_spins in range(min_qubits, max_qubits+1):\n", "\n", " print(f\"Now running n_spins {n_spins}\")\n", @@ -259,36 +107,40 @@ " hx = precalculated_data['hx'][:n_spins]\n", " hz = precalculated_data['hz'][:n_spins]\n", "\n", + " # Initialize the Hamiltonian simulation circuits\n", " qc = HamiltonianSimulation(n_spins, k, t, hamiltonian=\"heisenberg\", w=w, hx = hx, hz = hz)\n", + " qc2 = HamiltonianSimulation(n_spins, k, t, hamiltonian=\"tfim\", w=w, hx = hx, hz = hz)\n", "\n", - " qc3 = HamiltonianSimulation(n_spins, k, t, hamiltonian=\"tfim\", w=w, hx = hx, hz = hz)\n", - "\n", + " # Transpile and run the circuits\n", " transpiled_qc = transpile(qc, backend, optimization_level=0)\n", " job = backend.run(transpiled_qc, shots=num_shots)\n", " result = job.result()\n", " counts = result.get_counts(qc)\n", "\n", - " transpiled_qc3 = transpile(qc3, backend, optimization_level=0)\n", - " job3 = backend.run(transpiled_qc3, shots=num_shots)\n", - " result3 = job3.result()\n", - " counts3 = result3.get_counts()\n", + " transpiled_qc2 = transpile(qc2, backend, optimization_level=0)\n", + " job2 = backend.run(transpiled_qc2, shots=num_shots)\n", + " result2 = job2.result()\n", + " counts2 = result2.get_counts()\n", "\n", + " # Normalize probabilities for Heisenberg model circuit \n", " dist = {}\n", " for key in counts.keys():\n", " prob = counts[key] / num_shots\n", " dist[key] = prob\n", "\n", - " dist3 = {}\n", - " for key in counts3.keys():\n", - " prob = counts3[key] / num_shots\n", - " dist3[key] = prob\n", + " # Normalize probabilities for TFIM model circuit\n", + " dist2 = {}\n", + " for key in counts2.keys():\n", + " prob = counts2[key] / num_shots\n", + " dist2[key] = prob\n", "\n", " # add dist values to precalculated data for use in fidelity calculation\n", " precalculated_data[f\"Heisenberg - Qubits{n_spins}\"] = dist \n", " precalculated_data[f\"Exact Heisenberg - Qubits{n_spins}\"] = HamiltonianSimulationExact(n_spins, t=t, init_state = \"checkerboard\", hamiltonian=\"heisenberg\", w=w, hx = hx, hz = hz)\n", - " precalculated_data[f\"TFIM - Qubits{n_spins}\"] = dist3 \n", + " precalculated_data[f\"TFIM - Qubits{n_spins}\"] = dist2\n", " precalculated_data[f\"Exact TFIM - Qubits{n_spins}\"] = HamiltonianSimulationExact(n_spins, t=t, init_state = \"ghz\", hamiltonian=\"tfim\", w=w, hx = hx, hz = hz) \n", "\n", + "# Save precalculated data to a JSON file\n", "# https://stackoverflow.com/questions/36021332/how-to-prettyprint-human-readably-print-a-python-dict-in-json-format-double-q\n", "with open('precalculated_data.json', 'w') as f:\n", " f.write(json.dumps(\n", @@ -298,6 +150,13 @@ " separators=(',', ': ')\n", " ))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/hamiltonian-simulation/_common/precalculated_data.json b/hamiltonian-simulation/_common/precalculated_data.json index 102fc734..e856e406 100644 --- a/hamiltonian-simulation/_common/precalculated_data.json +++ b/hamiltonian-simulation/_common/precalculated_data.json @@ -8210,10815 +8210,10783 @@ "111111111": 7.078551780234473e-14 }, "Exact TFIM - Qubits10": { - "0000000000": 0.4924121375146698, - "0000000001": 0.0007781709310813996, - "0000000010": 0.0007473621649840448, - "0000000011": 1.2352928374832666e-06, - "0000000100": 0.0007473317308040635, - "0000000101": 1.1810779929222402e-06, - "0000000110": 1.2187425826518359e-06, - "0000000111": 1.957426361344795e-09, - "0000001000": 0.0007473317332281632, - "0000001001": 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"11111111": 0.49151 + "01111111": 0.00066, + "10000000": 0.00071, + "10111011": 1e-05, + "10111111": 0.00067, + "11000000": 1e-05, + "11011111": 0.00061, + "11101111": 0.00071, + "11110111": 0.00085, + "11111011": 0.00067, + "11111101": 0.00066, + "11111110": 0.00061, + "11111111": 0.49378 }, "TFIM - Qubits9": { - "000000000": 0.49263, - "000000001": 0.00088, - "000000010": 0.00063, - "000000011": 1e-05, - "000000100": 0.00076, - "000001000": 0.00056, + "000000000": 0.49556, + "000000001": 0.00077, + "000000010": 0.00059, + "000000100": 0.00068, + "000001000": 0.00073, + "000001001": 1e-05, "000010000": 0.00073, - "000100000": 0.00073, - "000100001": 1e-05, - "001000000": 0.00076, - "001010000": 1e-05, - "001111111": 1e-05, - "010000000": 0.00066, - "010111111": 1e-05, - "011111111": 0.00091, - "100000000": 0.00087, - "100000001": 1e-05, - "101110111": 1e-05, - "101111111": 0.00068, - "110011111": 1e-05, - "110111111": 0.00064, - "111010111": 2e-05, - "111011111": 0.00084, - "111101011": 1e-05, - "111101111": 0.0007, - "111110011": 1e-05, - "111110110": 1e-05, + "000100000": 0.00062, + "001000000": 0.00065, + "001000001": 2e-05, + "001000010": 2e-05, + "010000000": 0.00067, + "010000001": 1e-05, + "011111111": 0.00081, + "100000000": 0.00089, + "100111111": 1e-05, + "101111011": 1e-05, + "101111110": 1e-05, + "101111111": 0.00066, + "110110111": 1e-05, + "110111111": 0.00075, + "111011111": 0.00073, + "111101111": 0.00062, "111110111": 0.00068, - "111111011": 0.00059, - "111111101": 0.00079, - "111111110": 0.00068, - "111111111": 0.49415 + "111111011": 0.00086, + "111111101": 0.00073, + "111111110": 0.00079, + "111111111": 0.49138 }, "hx": [ -0.3841300947500583, From 077427fafe11ae4d20ba6ccb1867047ed04c9bc4 Mon Sep 17 00:00:00 2001 From: toddytharmonkey Date: Tue, 25 Jun 2024 17:11:24 -0400 Subject: [PATCH 4/9] seperate from exact calc, add documentation --- .../qiskit/HellingerVsTime.ipynb | 623 +++--------------- 1 file changed, 86 insertions(+), 537 deletions(-) diff --git a/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb b/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb index ccdaa585..b31f4ca5 100644 --- a/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb +++ b/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb @@ -2,219 +2,26 @@ "cells": [ { "cell_type": "code", - "execution_count": 20, + "execution_count": null, "id": "b5a9ab05-db97-4853-9209-4492457dbc19", "metadata": {}, "outputs": [], "source": [ "import sys\n", - "\n", "import numpy as np\n", "from qiskit_aer import Aer\n", "from qiskit_aer.noise import NoiseModel, depolarizing_error\n", + "from qiskit_aer.primitives import Sampler\n", "from qiskit_algorithms import SciPyRealEvolver, TimeEvolutionProblem\n", - "\n", - "import hamiltonian_simulation_kernel as ham\n", "from qiskit import QuantumCircuit, transpile\n", "from qiskit.quantum_info import SparsePauliOp, hellinger_distance, hellinger_fidelity\n", - "\n", - "import matplotlib.pyplot as plt\n", - "from qiskit_aer.primitives import Sampler\n", "from qiskit.visualization import plot_distribution\n", + "import matplotlib.pyplot as plt\n", "\n", - "def initial_state(n_spins: int, initial_state: str = \"checker\") -> QuantumCircuit:\n", - " \"\"\"\n", - " Initialize the quantum state.\n", - "\n", - " Dev note: This function is copy/pasted from HamiltonianSimulation.\n", - "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - " initial_state (str): The chosen initial state. By default applies the checkerboard state, but can also be set to \"ghz\", the GHZ state.\n", - "\n", - " Returns:\n", - " QuantumCircuit: The initialized quantum circuit.\n", - " \"\"\"\n", - " qc = QuantumCircuit(n_spins)\n", - "\n", - " if (\n", - " initial_state.strip().lower() == \"checkerboard\"\n", - " or initial_state.strip().lower() == \"neele\"\n", - " ):\n", - " # Checkerboard state, or \"Neele\" state\n", - " for k in range(0, n_spins, 2):\n", - " qc.x([k])\n", - " elif initial_state.strip().lower() == \"ghz\":\n", - " # GHZ state: 1/sqrt(2) (|00...> + |11...>)\n", - " qc.h(0)\n", - " for k in range(1, n_spins):\n", - " qc.cx(k - 1, k)\n", - "\n", - " return qc\n", - "\n", - "\n", - "def construct_TFIM_hamiltonian(n_spins: int) -> SparsePauliOp:\n", - " \"\"\"\n", - " Construct the Transverse Field Ising Model (TFIM) Hamiltonian.\n", - "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - "\n", - " Returns:\n", - " SparsePauliOp: The Hamiltonian represented as a sparse Pauli operator.\n", - " \"\"\"\n", - " pauli_strings = []\n", - " coefficients = []\n", - " g = 1 # Strength of the transverse field\n", - "\n", - " # Pauli spin vector product terms\n", - " for i in range(n_spins):\n", - " x_term = \"I\" * i + \"X\" + \"I\" * (n_spins - i - 1)\n", - " pauli_strings.append(x_term)\n", - " coefficients.append(g)\n", - "\n", - " identity_string = [\"I\"] * n_spins\n", - "\n", - " # ZZ operation on each pair of qubits in a linear chain\n", - " for j in range(2):\n", - " for i in range(j % 2, n_spins - 1, 2):\n", - " zz_term = identity_string.copy()\n", - " zz_term[i] = \"Z\"\n", - " zz_term[(i + 1) % n_spins] = \"Z\"\n", - " zz_term = \"\".join(zz_term)\n", - " pauli_strings.append(zz_term)\n", - " coefficients.append(1.0)\n", - "\n", - " return SparsePauliOp.from_list(zip(pauli_strings, coefficients))\n", - "\n", - "\n", - "def construct_heisenberg_hamiltonian(\n", - " n_spins: int, w: int, hx: list[float], hz: list[float]\n", - ") -> SparsePauliOp:\n", - " \"\"\"\n", - " Construct the Heisenberg Hamiltonian with disorder.\n", - "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - " w (float): Strength of two-qubit interactions for heisenberg hamiltonian.\n", - " hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", - " hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", - "\n", - " Returns:\n", - " SparsePauliOp: The Hamiltonian represented as a sparse Pauli operator.\n", - " \"\"\"\n", - "\n", - " pauli_strings = []\n", - " coefficients = []\n", - "\n", - " # Disorder terms\n", - " for i in range(n_spins):\n", - " x_term = \"I\" * i + \"X\" + \"I\" * (n_spins - i - 1)\n", - " z_term = \"I\" * i + \"Z\" + \"I\" * (n_spins - i - 1)\n", - " pauli_strings.append(x_term)\n", - " coefficients.append(w * hx[i])\n", - " pauli_strings.append(z_term)\n", - " coefficients.append(w * hz[i])\n", - "\n", - " identity_string = [\"I\"] * n_spins\n", - "\n", - " # Interaction terms\n", - " for j in range(2):\n", - " for i in range(j % 2, n_spins - 1, 2):\n", - " xx_term = identity_string.copy()\n", - " yy_term = identity_string.copy()\n", - " zz_term = identity_string.copy()\n", - "\n", - " xx_term[i] = \"X\"\n", - " xx_term[(i + 1) % n_spins] = \"X\"\n", - "\n", - " yy_term[i] = \"Y\"\n", - " yy_term[(i + 1) % n_spins] = \"Y\"\n", - "\n", - " zz_term[i] = \"Z\"\n", - " zz_term[(i + 1) % n_spins] = \"Z\"\n", - "\n", - " pauli_strings.append(\"\".join(xx_term))\n", - " coefficients.append(1.0)\n", - " pauli_strings.append(\"\".join(yy_term))\n", - " coefficients.append(1.0)\n", - " pauli_strings.append(\"\".join(zz_term))\n", - " coefficients.append(1.0)\n", - "\n", - " return SparsePauliOp.from_list(zip(pauli_strings, coefficients))\n", - "\n", - "\n", - "def construct_hamiltonian(\n", - " n_spins: int, hamiltonian: str, w: float, hx: list[float], hz: list[float]\n", - ") -> SparsePauliOp:\n", - " \"\"\"\n", - " Construct the Hamiltonian based on the specified method.\n", - "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - " hamiltonian (str): Which hamiltonian to run. \"heisenberg\" by default but can also choose \"TFIM\".\n", - " w (float): Strength of two-qubit interactions for heisenberg hamiltonian.\n", - " hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", - " hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", - "\n", - " Returns:\n", - " SparsePauliOp: The constructed Hamiltonian.\n", - " \"\"\"\n", - "\n", - " hamiltonian = hamiltonian.strip().lower()\n", - "\n", - " if hamiltonian == \"heisenberg\":\n", - " return construct_heisenberg_hamiltonian(n_spins, w, hx, hz)\n", - " elif hamiltonian == \"tfim\":\n", - " return construct_TFIM_hamiltonian(n_spins)\n", - " else:\n", - " raise ValueError(\"Invalid Hamiltonian specification.\")\n", - "\n", - "\n", - "def HamiltonianSimulationExact(\n", - " n_spins: int,\n", - " t: float,\n", - " init_state: str,\n", - " hamiltonian: str,\n", - " w: float,\n", - " hx: list[float],\n", - " hz: list[float],\n", - ") -> dict:\n", - " \"\"\"\n", - " Perform exact Hamiltonian simulation using classical matrix evolution.\n", - "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - " t (float): Duration of simulation.\n", - " init_state (str): The chosen initial state. By default applies the checkerboard state, but can also be set to \"ghz\", the GHZ state.\n", - " hamiltonian (str): Which hamiltonian to run. \"heisenberg\" by default but can also choose \"TFIM\".\n", - " w (float): Strength of two-qubit interactions for heisenberg hamiltonian.\n", - " hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", - " hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", - "\n", - " Returns:\n", - " dict: The distribution of the evolved state.\n", - " \"\"\"\n", - " hamiltonian_sparse = construct_hamiltonian(n_spins, hamiltonian, w, hx, hz)\n", - " time_problem = TimeEvolutionProblem(\n", - " hamiltonian_sparse, t, initial_state=initial_state(n_spins, init_state)\n", - " )\n", - " result = SciPyRealEvolver(num_timesteps=1).evolve(time_problem)\n", - " return result.evolved_state.probabilities_dict()\n", - "\n", - "\n", - "def create_noise_model(fidelity):\n", - "\n", - " if fidelity == 1:\n", - " return None\n", - " else:\n", - " p = 15 / 4 * (1 - fidelity)\n", - " noise_model = NoiseModel()\n", - " depolarizing_err = depolarizing_error(p, 2) # 2-qubit depolarizing error\n", - " noise_model.add_all_qubit_quantum_error(\n", - " depolarizing_err, [\"cx\"]\n", - " ) # Apply to CNOT gates\n", - " return noise_model\n", + "# Adjusting the path for custom imports\n", + "sys.path[1:1] = [\"../_common\", \"../../_common/qiskit\"]\n", + "import hamiltonian_simulation_kernel as ham\n", + "from hamiltonian_simulation_exact import HamiltonianSimulationExact\n", "\n", "\n", "\n", @@ -241,7 +48,16 @@ "\n", "\n", "def get_init_state_distribution(n_spins, hamiltonian):\n", + " \"\"\"\n", + " Generates the initial state probability distribution based on the Hamiltonian.\n", + "\n", + " Parameters:\n", + " - n_spins (int): Number of spins (qubits) in the system.\n", + " - hamiltonian (str): Type of Hamiltonian (e.g., \"tfim\" for Transverse Field Ising Model).\n", "\n", + " Returns:\n", + " - dict: The probability distribution of the initial state.\n", + " \"\"\"\n", " if hamiltonian.lower().strip() == \"tfim\":\n", " init_state = \"ghz\"\n", " else:\n", @@ -255,7 +71,19 @@ "\n", "\n", "def get_dist_at_timestep(step, K, max_time, hamiltonian, w, hx, hz):\n", + " \"\"\"\n", + " Generates the probability distribution at a specific time step during the simulation.\n", "\n", + " Parameters:\n", + " - step (int): Current time step in the simulation.\n", + " - K (int): Total number of time steps.\n", + " - max_time (float): Maximum simulation time.\n", + " - hamiltonian (str): Type of Hamiltonian (e.g., \"tfim\" for Transverse Field Ising Model).\n", + " - w, hx, hz (float): Parameters for the Hamiltonian.\n", + "\n", + " Returns:\n", + " - dict: The probability distribution at the given time step.\n", + " \"\"\"\n", " if step == 0:\n", " return get_init_state_distribution(n_spins=6, hamiltonian=hamiltonian)\n", " else:\n", @@ -274,33 +102,74 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": null, "id": "0e58d5a4-9d50-47a8-b181-7834aba442b4", "metadata": {}, "outputs": [], "source": [ "# produce four plots.\n", "#\n", - "# Plot #1: Hellinger distance from initial state using quantum trotterization steps.\n", - "# Plot #2: Hellinger distance from initial state using exact classical calculation (can use many more little time steps.)\n", - "# Plot #3: Combine plots #1 and #2 onto the same axis.\n", - "# Plot #4: Hellinger fidelity at each time step from the classical exact to the trotterized at each time step.\n", + "# Plot #1: Hellinger fidelity at each time step from the classical exact to the trotterized at each time step.\n", + "# Plot #2: Hellinger distance from initial state using quantum trotterization steps.\n", + "# Plot #3: Hellinger distance from initial state using exact classical calculation (can use many more little time steps.)\n", + "# Plot #4: Combine plots #1 and #2 onto the same axis.\n", "# All four of these plots will be saved onto the computer into the working directory.\n", "\n", + "# These parameters define Heisenberg model variables.\n", "np.random.seed(26)\n", "hx = list(2 * np.random.random(20) - 1) # random numbers between [-1, 1]\n", "np.random.seed(75)\n", "hz = list(2 * np.random.random(20) - 1) # random numbers between [-1, 1]\n", "w = 1\n", + "\n", + "\n", + "# Number of trotter steps \n", "K = 10\n", "\n", + "# Hamiltonians, along with a desired initial state. \n", "hamiltonians_initstate_pairs = [(\"heisenberg\", \"checkerboard\"), (\"tfim\", \"ghz\")]\n", "\n", - "# add switching bewteen different total times in the future?\n", - "max_time = 0.4\n", + "# The total amount of time to split into K trotter steps of size max_time / K. \n", + "max_time = 0.4" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4c45e35d-42e0-49c7-bb2f-2c28e6a69743", + "metadata": {}, + "outputs": [], + "source": [ + "# Plot #1: Hellinger fidelity at each time step from the classical exact to the trotterized at each time step.\n", + "\n", + "for hamiltonian, init_state in hamiltonians_initstate_pairs:\n", + " hellingers = []\n", + " times = []\n", + " initial_distribution = None\n", + "\n", + " for k_i in range(K + 1):\n", + " # note k_0 = 0\n", + " dist = get_dist_at_timestep(k_i, K, max_time, hamiltonian, w, hx, hz)\n", + "\n", + " exact_dist = HamiltonianSimulationExact(\n", + " 6,\n", + " t=k_i * (max_time / K),\n", + " init_state=init_state,\n", + " hamiltonian=hamiltonian,\n", + " w=w,\n", + " hx=hx,\n", + " hz=hz,\n", + " )\n", + "\n", + " hellingers.append(hellinger_fidelity(exact_dist, dist))\n", + " times.append(k_i * (max_time / K))\n", "\n", - "image_label_raw = f\"maxtime {max_time}\"\n", - "image_label = image_label_raw.replace(\".\", \"dot\").replace(\" \", \"_\")" + " plt.plot(times, hellingers, marker=\"o\")\n", + "plt.title(\"Hellinger fidelity of exact vs trotterized states at discrete times\")\n", + "plt.legend([\"heisenberg\", \"tfim\"])\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Hellinger fidelity\")\n", + "plt.show()" ] }, { @@ -310,7 +179,7 @@ "metadata": {}, "outputs": [], "source": [ - "# Plot #1: Hellinger distance from initial state using quantum trotterization steps.\n", + "# Plot #2: Hellinger distance from initial state using quantum trotterization steps.\n", "\n", "for hamiltonian, init_state in hamiltonians_initstate_pairs:\n", "\n", @@ -330,9 +199,7 @@ " times.append(k_i * (max_time / K))\n", "\n", " plt.plot(times, hellingers, marker=\"o\")\n", - "plt.title(\n", - " \"Hellinger distance from initial state VS time for quantum trotterization steps\"\n", - ")\n", + "plt.title(\"Hellinger distance from initial state VS time for quantum trotterization steps\")\n", "plt.legend([\"trotterized heisenberg\", \"trotterized tfim\"])\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Hellinger distance\")\n", @@ -346,7 +213,7 @@ "metadata": {}, "outputs": [], "source": [ - "# Plot #2: Hellinger distance from initial state using exact classical calculation (can use many more little time steps.)\n", + "# Plot #3: Hellinger distance from initial state using exact classical calculation (can use many more little time steps.)\n", "\n", "for hamiltonian, init_state in hamiltonians_initstate_pairs:\n", " hellinger_list = []\n", @@ -355,7 +222,7 @@ " for t in np.linspace(0, max_time, 100):\n", "\n", " exact_dist = HamiltonianSimulationExact(\n", - " 6, t, init_state=init_state, hamiltonian=hamiltonian, w=1, hx=hx, hz=hz\n", + " 6, t, init_state=init_state, hamiltonian=hamiltonian, w=w, hx=hx, hz=hz\n", " )\n", "\n", " if t == 0:\n", @@ -365,11 +232,7 @@ " hellinger_list.append(dist)\n", "\n", " plt.plot([t for t in np.linspace(0, max_time, 100)], hellinger_list)\n", - "plt.title(\n", - " image_label_raw\n", - " + \"\\n\"\n", - " + \"Hellinger distance from initial state for exact evolution VS time\"\n", - ")\n", + "plt.title(\"Hellinger distance from initial state for exact evolution VS time\")\n", "plt.legend([\"exact heisenberg\", \"exact tfim\"])\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Hellinger distance\")\n", @@ -383,7 +246,7 @@ "metadata": {}, "outputs": [], "source": [ - "# Plot #3: Combine plots #1 and #2 onto the same axis.\n", + "# Plot #4: Combine plots #1 and #2 onto the same axis.\n", "\n", "for hamiltonian, init_state in hamiltonians_initstate_pairs:\n", "\n", @@ -411,7 +274,7 @@ " for t in np.linspace(0, max_time, 100):\n", "\n", " exact_dist = HamiltonianSimulationExact(\n", - " 6, t, init_state=init_state, hamiltonian=hamiltonian, w=1, hx=hx, hz=hz\n", + " 6, t, init_state=init_state, hamiltonian=hamiltonian, w=w, hx=hx, hz=hz\n", " )\n", "\n", " if t == 0:\n", @@ -421,7 +284,7 @@ " hellinger_list.append(dist)\n", "\n", " plt.plot([t for t in np.linspace(0, max_time, 100)], hellinger_list)\n", - "plt.title(image_label_raw + \"\\n\" + \"Hellinger distance from initial state VS time\")\n", + "plt.title(\"Hellinger distance from initial state VS time\")\n", "plt.legend(\n", " [\"trotterized heisenberg\", \"trotterized tfim\", \"exact heisenberg\", \"exact tfim\"]\n", ")\n", @@ -429,320 +292,6 @@ "plt.ylabel(\"Hellinger distance\")\n", "plt.show()" ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "4c45e35d-42e0-49c7-bb2f-2c28e6a69743", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot #4: Hellinger fidelity at each time step from the classical exact to the trotterized at each time step.\n", - "\n", - "for hamiltonian, init_state in hamiltonians_initstate_pairs:\n", - " hellingers = []\n", - " times = []\n", - " initial_distribution = None\n", - "\n", - " for k_i in range(K + 1):\n", - " # note k_0 = 0\n", - " #\n", - " dist = get_dist_at_timestep(k_i, K, max_time, hamiltonian, w, hx, hz)\n", - "\n", - " exact_dist = HamiltonianSimulationExact(\n", - " 6,\n", - " t=k_i * (max_time / K),\n", - " init_state=init_state,\n", - " hamiltonian=hamiltonian,\n", - " w=1,\n", - " hx=hx,\n", - " hz=hz,\n", - " )\n", - "\n", - " hellingers.append(hellinger_fidelity(exact_dist, dist))\n", - " times.append(k_i * (max_time / K))\n", - "\n", - " plt.plot(times, hellingers, marker=\"o\")\n", - "plt.title(\n", - " image_label_raw\n", - " + \"\\n\"\n", - " + \"Hellinger fidelity of exact vs trotterized states at discrete times\"\n", - ")\n", - "plt.legend([\"heisenberg\", \"tfim\"])\n", - "plt.xlabel(\"Time\")\n", - "plt.ylabel(\"Hellinger fidelity\")\n", - "plt.show()" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "a54339c6-b484-4a6c-98e6-38bdc2dbd993", - "metadata": {}, - "source": [ - "https://arxiv.org/abs/1912.08854:\n", - "\n", - "**Proposition 15 (Tight error bound for the first-order Lie-Trotter formula).**\n", - "Let $H = \\sum_{\\gamma=1}^{\\Gamma} H_\\gamma$ be a Hamiltonian consisting of $\\Gamma$ summands and $t \\geq 0$.\n", - "Let $\\mathcal{S}_1(t) = \\prod_{\\gamma=1}^{\\Gamma} e^{-itH_\\gamma}$ be the first-order Lie-Trotter formula.\n", - "Then, the additive Trotter error can be bounded as\n", - "\n", - "$$\n", - "\\left\\| \\mathcal{S}_1(t) - e^{-itH} \\right\\| \\leq \\frac{t^2}{2} \\left\\| \\sum_{\\gamma_1=1}^{\\Gamma} \\left[ \\sum_{\\gamma_2=\\gamma_1+1}^{\\Gamma} [H_{\\gamma_2}, H_{\\gamma_1}] \\right] \\right\\|.\n", - "$$\n", - "\n", - "Given this, we can plot this error for both of our Hamiltonians and compare it to the maximum amount of error that they should be having." - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "id": "0a8cc9a9-5410-4f7b-a1a6-4e4f0df296dd", - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit.quantum_info import Statevector, state_fidelity, commutator\n", - "\n", - "def max_trotter_error(ham, max_time):\n", - " \"\"\"\n", - " Following the Childs et al. paper, calculate the maximum error for the order 1 Lie-Trotter trotterization. \n", - " \"\"\"\n", - "\n", - " Gamma = len(ham)\n", - "\n", - " commutators = []\n", - "\n", - " for gamma_1 in range(Gamma):\n", - " for gamma_2 in range(gamma_1+1, Gamma): \n", - "\n", - " commutators.append(commutator(ham[gamma_2], ham[gamma_1]))\n", - "\n", - " spectral_norm = np.linalg.norm(sum(commutators).to_matrix(), ord=2)\n", - "\n", - " return max_time**2 * (1/2) * spectral_norm \n", - "\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "id": "7cc6519d-a2dd-4e8c-8efe-3903ebcd557e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0\n", - "6.987918414869866\n", - "27.951673659479464\n", - "62.891265733828796\n", - "111.80669463791786\n", - "174.69796037174666\n", - "251.56506293531518\n", - "342.4080023286234\n", - "447.22677855167143\n", - "566.0213916044592\n" - ] - }, - { - "data": { - "text/plain": [ - "362.24301235496586" - ] - }, - "execution_count": 63, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "for max_time in range(10):\n", - " print(max_trotter_error(construct_hamiltonian(6, \"tfim\", w, hx, hz), max_time))\n", - "\n", - "#0.0\n", - "4.472135954999579\n", - "17.888543819998315\n", - "40.24922359499621\n", - "71.55417527999326\n", - "111.80339887498947\n", - "160.99689437998484\n", - "219.13466179497937\n", - "286.21670111997304\n", - "362.24301235496586\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "id": "e9b58d51-170f-4c55-8c15-4f1c2e44b437", - "metadata": {}, - "outputs": [], - "source": [ - "def HamiltonianSimulationExactVector(\n", - " n_spins: int,\n", - " t: float,\n", - " init_state: str,\n", - " hamiltonian: str,\n", - " w: float,\n", - " hx: list[float],\n", - " hz: list[float],\n", - ") -> dict:\n", - " \"\"\"\n", - " Perform exact Hamiltonian simulation using classical matrix evolution.\n", - "\n", - " Args:\n", - " n_spins (int): Number of spins (qubits).\n", - " t (float): Duration of simulation.\n", - " init_state (str): The chosen initial state. By default applies the checkerboard state, but can also be set to \"ghz\", the GHZ state.\n", - " hamiltonian (str): Which hamiltonian to run. \"heisenberg\" by default but can also choose \"TFIM\".\n", - " w (float): Strength of two-qubit interactions for heisenberg hamiltonian.\n", - " hx (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", - " hz (list[float]): Strength of internal disorder parameter for heisenberg hamiltonian.\n", - "\n", - " Returns:\n", - " dict: The distribution of the evolved state.\n", - " \"\"\"\n", - " hamiltonian_sparse = construct_hamiltonian(n_spins, hamiltonian, w, hx, hz)\n", - " time_problem = TimeEvolutionProblem(\n", - " hamiltonian_sparse, t, initial_state=initial_state(n_spins, init_state)\n", - " )\n", - " result = SciPyRealEvolver(num_timesteps=1).evolve(time_problem)\n", - " return result.evolved_state\n", - "\n", - "def get_init_state_distribution_vector(n_spins, hamiltonian):\n", - "\n", - " if hamiltonian.lower().strip() == \"tfim\":\n", - " init_state = \"ghz\"\n", - " else:\n", - " init_state = \"checkerboard\"\n", - "\n", - " init_circ = ham.initial_state(n_spins, init_state)\n", - "\n", - " return get_vector(init_circ)\n", - "\n", - "\n", - "def get_vector_at_timestep(n_qubits,step, K, max_time, hamiltonian, w, hx, hz):\n", - "\n", - " if step == 0:\n", - " return get_init_state_distribution_vector(n_spins=n_qubits, hamiltonian=hamiltonian)\n", - " else:\n", - " return get_vector(\n", - " ham.HamiltonianSimulation(\n", - " n_spins=n_qubits,\n", - " K=step,\n", - " t=step * (max_time / K),\n", - " hamiltonian=hamiltonian,\n", - " w=w,\n", - " hx=hx,\n", - " hz=hz,\n", - " ).remove_final_measurements(inplace=False)\n", - " )\n", - "\n", - "def get_vector(circuit, shots=None):\n", - " \"\"\"\n", - " Generates the probability distribution of the outcomes for a given Qiskit circuit.\n", - "\n", - " Parameters:\n", - " - circuit (QuantumCircuit): The quantum circuit to simulate.\n", - " - shots (int): The number of shots for the simulation.\n", - "\n", - " Returns:\n", - " - result (dict): The probability distribution of the outcomes.\n", - " \"\"\"\n", - "\n", - " return Statevector(circuit)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "id": "96d0ee96-3f8b-41a3-8e35-606575c7a601", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot #4: Hellinger fidelity at each time step from the classical exact to the trotterized at each time step.\n", - "\n", - "n_qubit = 6\n", - "\n", - "colors = ['r','b']\n", - "\n", - "for i, (hamiltonian, init_state) in enumerate(hamiltonians_initstate_pairs):\n", - " hellingers = []\n", - " max_errors = []\n", - " times = []\n", - " initial_distribution = None\n", - "\n", - " for k_i in range(K + 1):\n", - " # note k_0 = 0\n", - "\n", - " time = \n", - " \n", - " max_error = max_trotter_error(construct_hamiltonian(n_qubit, hamiltonian, w, hx, hz), k_i * (max_time / K))\n", - " max_errors.append(max_error)\n", - " \n", - " vector = get_vector_at_timestep(n_qubit, k_i, K, max_time, hamiltonian, w, hx, hz)\n", - "\n", - " exact_vector = HamiltonianSimulationExactVector(\n", - " n_qubit,\n", - " t=k_i * (max_time / K),\n", - " init_state=init_state,\n", - " hamiltonian=hamiltonian,\n", - " w=1,\n", - " hx=hx,\n", - " hz=hz,\n", - " )\n", - "\n", - " #doing .data just gets the 1D statevectors... I think. Since these are pure states.\n", - " \n", - " hellingers.append(np.linalg.norm((vector.data- exact_vector.data), ord=2))\n", - " times.append(k_i * (max_time / K))\n", - "\n", - " plt.plot(times, hellingers, marker=\"o\", color = colors[i])\n", - " plt.plot(times, max_errors, marker=\"_\", linestyle = '', color=colors[i])\n", - "plt.title(\n", - " image_label_raw\n", - " + \"\\n\"\n", - " + \"L2 Norm of the distance between the exact and trotterized state\"\n", - ")\n", - "plt.legend([\"heisenberg\", \"tfim\"])\n", - "plt.xlabel(\"Time\")\n", - "plt.ylabel(\"Hellinger fidelity\")\n", - "plt.yscale('log')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "222723d8-cf9c-4545-8a88-3d92332bea73", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { From 0617fb6bc182bec2a2eb80229825b6b99c1685ac Mon Sep 17 00:00:00 2001 From: Sonny Rappaport <84343879+toddytharmonkey@users.noreply.github.com> Date: Wed, 26 Jun 2024 11:07:07 -0400 Subject: [PATCH 5/9] Update README.md --- hamiltonian-simulation/README.md | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/hamiltonian-simulation/README.md b/hamiltonian-simulation/README.md index f43ff7b6..88e183dd 100644 --- a/hamiltonian-simulation/README.md +++ b/hamiltonian-simulation/README.md @@ -1,6 +1,8 @@ # Hamiltonian Simulation - Prototype Benchmark Program -Simulation of quantum systems is one of the most promising applications for quantum computers [[1]](#references). In the current version of this benchmark, we compare the quantum simulation against a classical simultion of the same circuit in order to report our fidelity. This works well for small circuit sizes, but is not scalable past a certain number of qubits. Additionally, we can now only run specific circuits, rather than random ones, limiting the ability of this benchmark to completely characterize real uses cases of the Hamiltonian simulation algorithm. We have some suggested modifications to this benchmark which we outline and explain why we did not chose to use them at this time in the section [Proposed Improvements](#Proposed-Improvements). +Simulation of quantum systems is one of the most promising applications for quantum computers [[1]](#references). In the current version of this benchmark, we compare the quantum simulation against a classical simultion of the same circuit in order to report our fidelity. This works well for small circuit sizes, but is not scalable past a certain number of qubits. We also compare the quantum simulation + +Additionally, we can now only run specific circuits, rather than random ones, limiting the ability of this benchmark to completely characterize real uses cases of the Hamiltonian simulation algorithm. We have some suggested modifications to this benchmark which we outline and explain why we did not chose to use them at this time in the section [Proposed Improvements](#Proposed-Improvements). ## Problem outline @@ -37,7 +39,7 @@ $$ Where is the coupling strength between neighboring spins, and is the strength of the transverse field. -In our benchmarks, currently both $J=1$ and $h=.2$. +In our benchmarks, currently both $J=1$ and $h=1$. ## Benchmarking The Hamiltonian Simulation algorithm is benchmarked by running **just a single circuit**. This circuit is repeated a number of times denoted by `num_shots`. We then run the algorithm circuit for numbers of qubits between `min_qubits` and `max_qubits`, inclusive. The test returns the averages of the circuit creation times, average execution times, fidelities, and circuit depths, like all of the other algorithms. @@ -48,7 +50,7 @@ In either case, we compare the resultant distribution using our [noise-normalize We calculate these expected distributions in the jupyter notebook `precalculated_data.ipynb`, which stores the results for up to 20 qubits in the `precalculated_data.json` data file. The python code then imports the distributions from the `json` file. This is a less than ideal fidelity calculation as it does not scale to any size of qubits. It requires the classical simulation of matrix products, which requires resources exponential in number of qubits. -In the `precalculated_data.ipnyb`, we set the trotterization steps (k) to 5 and the time to .2. For the Heisenberg Hamiltonian, $w$ is set to 1 but $J$ is hard-coded to 1. For TFIM, the Hamiltonian variables are both hard-coded to $J=1$ and $h=.2$ respectively. +In the `precalculated_data.ipnyb`, we set the trotterization steps (k) to 5 and the time to .2. For the Heisenberg Hamiltonian, $w$ is set to 1 but $J$ is hard-coded to 1. For TFIM, the Hamiltonian variables are both hard-coded to $J=1$ and $h=1$ respectively. ## Classical algorithm From 9473547da10321430e7debdf7989428521c5423b Mon Sep 17 00:00:00 2001 From: toddytharmonkey Date: Wed, 26 Jun 2024 12:44:01 -0400 Subject: [PATCH 6/9] update readme to mention method = 3 (mirror) --- hamiltonian-simulation/README.md | 30 +++++++++++++++++------------- 1 file changed, 17 insertions(+), 13 deletions(-) diff --git a/hamiltonian-simulation/README.md b/hamiltonian-simulation/README.md index 88e183dd..d787a46a 100644 --- a/hamiltonian-simulation/README.md +++ b/hamiltonian-simulation/README.md @@ -1,8 +1,12 @@ # Hamiltonian Simulation - Prototype Benchmark Program -Simulation of quantum systems is one of the most promising applications for quantum computers [[1]](#references). In the current version of this benchmark, we compare the quantum simulation against a classical simultion of the same circuit in order to report our fidelity. This works well for small circuit sizes, but is not scalable past a certain number of qubits. We also compare the quantum simulation +Simulation of quantum systems is one of the most promising applications for quantum computers [1](#references). In the current version of this benchmark, we have two main strategies for calculating fidelities. -Additionally, we can now only run specific circuits, rather than random ones, limiting the ability of this benchmark to completely characterize real uses cases of the Hamiltonian simulation algorithm. We have some suggested modifications to this benchmark which we outline and explain why we did not chose to use them at this time in the section [Proposed Improvements](#Proposed-Improvements). +In the first strategy, we compare the quantum simulation against a classical simultion in order to report our fidelity. This works well for small circuit sizes, but is not scalable past a certain number of qubits. + +In the second strategy, we use the mirror circuits method developed by Sandia Labratories [2](#references). This is scalable to all qubit sizes. + +We can now only run specific circuits, rather than random ones, limiting the ability of this benchmark to completely characterize real uses cases of the Hamiltonian simulation algorithm. We have some suggested modifications to this benchmark which we outline and explain why we did not chose to use them at this time in the section [Proposed Improvements](#Proposed-Improvements). ## Problem outline @@ -44,14 +48,20 @@ In our benchmarks, currently both $J=1$ and $h=1$. ## Benchmarking The Hamiltonian Simulation algorithm is benchmarked by running **just a single circuit**. This circuit is repeated a number of times denoted by `num_shots`. We then run the algorithm circuit for numbers of qubits between `min_qubits` and `max_qubits`, inclusive. The test returns the averages of the circuit creation times, average execution times, fidelities, and circuit depths, like all of the other algorithms. -After running the Hamiltonian Simulation circuit, there are two options for how to produce the fidelity metric, both of which use a precalculated distribution to compare to the Hamiltonian Simulation results. Method = 1 uses a distribution from a noiseless simulation of the trotterized quantum circuit. For this method, if the benchmark is also run on a noiseless simulation, with a high number of shots, the fidelity should be high. Method = 2 uses a classical matrix technique to simulate the evolution of the hamiltonian directly. Wheras method = 1 more directly tests the hardware, method = 2 also tests the accuracy of the hamiltonian simulation algorithm itself. +There are currently three methods for how to produce the fidelity metric. All three methods evolve a state, and create a metric based on how well the state evolved. -In either case, we compare the resultant distribution using our [noise-normalized fidelity calculation](../_doc/POLARIZATION_FIDELITY.md). +The first two methods evolve an initial state a time $t$, and compare the final state against a precalculated distribution. Method = 1 creates the precalculated distribution from a noiseless simulation of the Hamiltonian Simulation quantum circuit. Method = 2 uses a classical matrix technique to simulate the evolution of the hamiltonian directly. Wheras method = 1 only tests the performance of the hardware, method = 2 also tests the accuracy of the Hamiltonian simulation itself. -We calculate these expected distributions in the jupyter notebook `precalculated_data.ipynb`, which stores the results for up to 20 qubits in the `precalculated_data.json` data file. The python code then imports the distributions from the `json` file. This is a less than ideal fidelity calculation as it does not scale to any size of qubits. It requires the classical simulation of matrix products, which requires resources exponential in number of qubits. +We calculate these precalculated distributions in the jupyter notebook `precalculated_data.ipynb`, which stores the results for up to 20 qubits in the `precalculated_data.json` data file. The python code then imports the distributions from the `json` file. This is a less than ideal fidelity calculation as it does not scale to any size of qubits. It requires the classical simulation of matrix products, which requires resources exponential in number of qubits. In the `precalculated_data.ipnyb`, we set the trotterization steps (k) to 5 and the time to .2. For the Heisenberg Hamiltonian, $w$ is set to 1 but $J$ is hard-coded to 1. For TFIM, the Hamiltonian variables are both hard-coded to $J=1$ and $h=1$ respectively. +Method = 3 uses a mirror circuit based off of the Hamiltonian Simulation circuit, designed so that the target distribution is trivial. It evolves an initial state forwards a time $t$, then backwards in time $t$, so that the final state should be the (trivial) initial state. Because this doesn't utilize classical resources to generate a comparison metric, this scales to any size of qubits. + + +In all cases, we compare the resultant distribution using our [noise-normalized fidelity calculation](../_doc/POLARIZATION_FIDELITY.md). + + ## Classical algorithm Much effort has been done in the field of many-body physics to understand the approximate behaviors of Hamiltonians like the ones we have here. However, to calculate the evolution of an excited state through exact diagonalization scales approximately as for qubits, quite poor scaling [[2]](#references). This quickly becomes intractible even utilizing extremely powerful classical supercomputers. @@ -127,19 +137,13 @@ There are two options of circuit creation for this simulation:

*Fig 6. Naive gate.* - -## Proposed Improvements - -Our suggested method of modifying this benchmark involves a topic taken from condensed matter called *many-body localization* [[2]](#references) [[5]](#references). The essence of this phenomenon is that for certain closed quantum systems, some excited states fail to thermalize as expected. - -The parameters that we use for the current Hamiltonian simulation benchmark already put us in the many-body localization regime. After evolving the system for a suitibly long time, with , we can then take a look at a parameter called *imbalance* to characterize this property. The imbalance compares the percentage of measured 1's on the even versus odd sites. We see that for our Heisenberg Hamiltonian, when averaging over many random choices for and , the imbalance will converge to a constant value for increasing circuit width. We could then set our fidelity calculation as the deviation from the expected imbalance value. This benchmark is outlined in the `mbl_benchmark.py` file in the qiskit `WIP_benchmarks` folder. - -While we have already coded this benchmark, we are not using it as a benchmark because some of the parameters required are not feasible on current computers. Because of our comparatively large value of , we need to have a large number of Trotter steps so our simulation is close to the actual evolution of the Hamiltonian. This results in circuits that are thousands of gates long. Then, because the imbalance converging is a feature that occurs *on average*, we need to average over more than 100 different circuits for the fidelity calculation to capture just the hardware error, not the algorithmic error. All of these factors make it such that running the benchmark is difficult on simulators, and exceedingly expensive and/or time-intensive to run on hardware. In the future, when hardware is more accessible, these downsides might not be as big of an issue, and many-body-localization can be utilized as an effective benchmark. ## References [1] Feynman, RP. (1982) Simulating physics with computers. Int J Theor Phys 21:467–488. +[2] Proctor, T., Rudinger, K., Young, K. et al. Measuring the capabilities of quantum computers. Nat. Phys. 18, 75–79 (2022). https://doi.org/10.1038/s41567-021-01409-7 + [2] Andrew M. Childs, Dmitri Maslov, Yunseong Nam, Neil J. Ross, Yuan Su. (2017). Toward the first quantum simulation with quantum speedup. [`arXiv:1711.10980`](https://arxiv.org/pdf/1711.10980.pdf) From 38be849fb5371ecb582575b55e95734bd50523fa Mon Sep 17 00:00:00 2001 From: toddytharmonkey Date: Wed, 26 Jun 2024 15:11:06 -0400 Subject: [PATCH 7/9] add parameter documentation in readme.md --- hamiltonian-simulation/README.md | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) diff --git a/hamiltonian-simulation/README.md b/hamiltonian-simulation/README.md index d787a46a..0a886f58 100644 --- a/hamiltonian-simulation/README.md +++ b/hamiltonian-simulation/README.md @@ -61,6 +61,22 @@ Method = 3 uses a mirror circuit based off of the Hamiltonian Simulation circuit In all cases, we compare the resultant distribution using our [noise-normalized fidelity calculation](../_doc/POLARIZATION_FIDELITY.md). +In the run() method for the benchmark, there are a number of optional arguments that can be specified. Some of the key arguments are as follows: + +``` +Parameters +---- + + min_qubits (int): Minimum number of qubits (smallest circuit is 2 qubits). + max_qubits (int): Maximum number of qubits. + max_circuits (int): Maximum number of circuits to execute per group. + num_shots (int): Number of shots for each circuit execution. + hamiltonian (str): Which hamiltonian to run. "heisenberg" by default but can also choose "TFIM". + method (int): Method for fidelity checking (1 for noiseless trotterized quantum, 2 for exact classical, 3 for mirror circuit.) + use_XX_YY_ZZ_gates (bool): Flag to use unoptimized XX, YY, ZZ gates. + random_pauli_flag (bool): Flag to activate more sophisticated mirror circuit formation that utilizes a layer of random paulis seperating the mirror circuits in addition to using a quasi-inverse rather than an inverse. + init_state (str): The desired initial state. Choices are "checkerboard" or "ghz". +``` ## Classical algorithm From 186ee8c5bad06c2ca6ab722bd9a1939c2c4e9b18 Mon Sep 17 00:00:00 2001 From: toddytharmonkey Date: Wed, 26 Jun 2024 15:53:33 -0400 Subject: [PATCH 8/9] clear cell outputs, add markdown docuemntation --- .../qiskit/HellingerVsTime.ipynb | 31 +++++++++++++++++++ 1 file changed, 31 insertions(+) diff --git a/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb b/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb index b31f4ca5..3604b289 100644 --- a/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb +++ b/hamiltonian-simulation/qiskit/HellingerVsTime.ipynb @@ -1,5 +1,28 @@ { "cells": [ + { + "cell_type": "markdown", + "id": "7007f489-1d8c-4864-9a32-69bd8d7409df", + "metadata": {}, + "source": [ + "# Hellinger Fidelity and Distance Analysis\n", + "\n", + "This notebook performs an analysis of Hellinger fidelity and distance for the Transverse Field Ising Model (TFIM) and Heisenberg Hamiltonians. The analysis leverages both classical exact calculations and quantum trotterization steps.\n", + "\n", + "**To run the notebook correctly, run the cells in order from top-to-bottom.** \n", + "\n", + "The notebook produces four main plots:\n", + "\n", + "1. **Hellinger Fidelity at Each Time Step**: Comparing the classical exact simulation to the trotterized simulation.\n", + "2. **Hellinger Distance from Initial State (Quantum Trotterization)**: Tracking the distance using quantum trotterization steps.\n", + "3. **Hellinger Distance from Initial State (Classical Calculation)**: Utilizing many small time steps for precise calculations.\n", + "4. **Combined Plot**: Overlaying the results from the quantum trotterization and classical calculations on the same axis for comparison.\n", + "\n", + "Note that only plot 1 is directly relevant to benchmarking and is similar to method 2 in the primary benchmarking code.\n", + "\n", + "Plots 2-4, while offering insight into state evolution, are not intended to serve as performance metrics. Instead, they are an example of a simple way to track state evolution against time. " + ] + }, { "cell_type": "code", "execution_count": null, @@ -292,6 +315,14 @@ "plt.ylabel(\"Hellinger distance\")\n", "plt.show()" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4d31ad0e-742a-4248-9c44-9ddbab2f3c5d", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { From 659cf970285ec5a05f72b42d181110badc1e20b7 Mon Sep 17 00:00:00 2001 From: toddytharmonkey Date: Wed, 26 Jun 2024 16:04:49 -0400 Subject: [PATCH 9/9] run precalculated data again, remove cell output --- .../_common/precalculated_data.ipynb | 24 +- .../_common/precalculated_data.json | 4497 +++++++++-------- 2 files changed, 2268 insertions(+), 2253 deletions(-) diff --git a/hamiltonian-simulation/_common/precalculated_data.ipynb b/hamiltonian-simulation/_common/precalculated_data.ipynb index 14152c1c..6b21ac69 100644 --- a/hamiltonian-simulation/_common/precalculated_data.ipynb +++ b/hamiltonian-simulation/_common/precalculated_data.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2024-05-06T16:26:36.751184Z", @@ -39,7 +39,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2024-05-06T16:39:58.644353Z", @@ -47,25 +47,7 @@ }, "tags": [] }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Now running n_spins 2\n", - "Now running n_spins 3\n", - "Now running n_spins 4\n", - "Now running n_spins 5\n", - "Now running n_spins 6\n", - "Now running n_spins 7\n", - "Now running n_spins 8\n", - "Now running n_spins 9\n", - "Now running n_spins 10\n", - "Now running n_spins 11\n", - "Now running n_spins 12\n" - ] - } - ], + "outputs": [], "source": [ "import json\n", "from qiskit_aer import Aer\n", diff --git a/hamiltonian-simulation/_common/precalculated_data.json b/hamiltonian-simulation/_common/precalculated_data.json index e856e406..ee4ad01d 100644 --- a/hamiltonian-simulation/_common/precalculated_data.json +++ b/hamiltonian-simulation/_common/precalculated_data.json @@ -16420,2573 +16420,2606 @@ "111111111": 0.353795949398561 }, "Heisenberg - Qubits10": { - "0000001101": 1e-05, + "0000001101": 2e-05, "0000010011": 1e-05, - "0000010101": 2e-05, "0000011001": 4e-05, - "0000100101": 1e-05, - "0000101001": 2e-05, - "0000101011": 0.00015, - "0000101101": 0.00037, - "0000110001": 1e-05, - "0000110011": 0.0002, - "0000110101": 0.00056, - "0000111001": 0.00039, - "0000111101": 2e-05, - "0001000101": 1e-05, - "0001000111": 1e-05, - "0001001001": 0.00012, - "0001001011": 0.00026, - "0001001101": 0.00061, - "0001001110": 2e-05, - "0001010001": 2e-05, - "0001010011": 0.00035, - "0001010101": 0.00099, - "0001010111": 1e-05, - "0001011001": 0.00081, - "0001011011": 2e-05, - "0001011101": 4e-05, - "0001100011": 0.00012, - "0001100101": 0.00031, - "0001101001": 0.00015, - "0001101011": 0.0002, - "0001101101": 0.00044, - "0001110001": 9e-05, - "0001110011": 0.00029, - "0001110101": 0.0008, - "0001111001": 0.00069, - "0001111011": 3e-05, - "0001111101": 4e-05, - "0010001001": 1e-05, - "0010001011": 2e-05, - "0010001101": 5e-05, - "0010010011": 7e-05, - "0010010101": 5e-05, + "0000011101": 1e-05, + "0000100111": 1e-05, + "0000101011": 0.00017, + "0000101101": 0.00038, + "0000101110": 2e-05, + "0000110011": 0.00033, + "0000110101": 0.00075, + "0000111001": 0.00049, + "0000111011": 1e-05, + "0000111101": 3e-05, + "0001000011": 2e-05, + "0001000101": 2e-05, + "0001000111": 2e-05, + "0001001001": 7e-05, + "0001001011": 0.00027, + "0001001101": 0.00063, + "0001010001": 1e-05, + "0001010011": 0.0004, + "0001010101": 0.00101, + "0001010110": 1e-05, + "0001011001": 0.00055, + "0001011010": 1e-05, + "0001011011": 1e-05, + "0001100001": 1e-05, + "0001100011": 0.0002, + "0001100101": 0.00051, + "0001101001": 0.00028, + "0001101010": 2e-05, + "0001101011": 0.00014, + "0001101101": 0.0006, + "0001110001": 5e-05, + "0001110011": 0.00028, + "0001110101": 0.00076, + "0001111001": 0.00065, + "0001111010": 1e-05, + "0001111011": 2e-05, + "0001111101": 3e-05, + "0010001011": 1e-05, + "0010001101": 9e-05, + "0010010011": 3e-05, + "0010010101": 9e-05, "0010011001": 4e-05, - 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