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": [
+ "
*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": {
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+ "0000001101": 2e-05,
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- "0000101001": 2e-05,
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- "0000110011": 0.0002,
- "0000110101": 0.00056,
- "0000111001": 0.00039,
- "0000111101": 2e-05,
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+ "0000110011": 0.00033,
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