From 5380c7a940ad4976a3fee745bfc3809ac4cbe3af Mon Sep 17 00:00:00 2001 From: Maxwell Kapral Date: Thu, 27 Apr 2023 03:57:50 -0700 Subject: [PATCH] ibm headache --- data/init.ipynb | 257 +++++++++++++++++++++++++++++++++++++---------- requirements.txt | 3 + 2 files changed, 206 insertions(+), 54 deletions(-) diff --git a/data/init.ipynb b/data/init.ipynb index 0e721a2..0353621 100644 --- a/data/init.ipynb +++ b/data/init.ipynb @@ -1,7 +1,6 @@ { "cells": [ { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -9,7 +8,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -17,7 +15,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -26,7 +23,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -34,11 +30,10 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "### Get Token" + "### Imports" ] }, { @@ -47,17 +42,26 @@ "metadata": {}, "outputs": [], "source": [ - "token = None\n", - "with open('token.txt', 'r') as f:\n", - " token = f.read().strip()" + "import math\n", + "from qiskit import execute, QuantumCircuit\n", + "from qiskit.circuit import Qubit\n", + "from qiskit.compiler import transpile\n", + "from qiskit.visualization import plot_histogram\n", + "from qiskit_ibm_provider import IBMBackend, IBMProvider, least_busy" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "### Imports" + "### Globals" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Manually Managed Variables" ] }, { @@ -66,17 +70,21 @@ "metadata": {}, "outputs": [], "source": [ - "import math\n", - "from qiskit import QuantumCircuit\n", - "from qiskit.circuit import Qubit" + "# number of qubits\n", + "N = 8\n", + "\n", + "# use simulator\n", + "use_sim = True\n", + "\n", + "# shots\n", + "shots = 1024" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "### Generate Linear Time Complexity Circuits for $|\\text{GHZ}_N\\rangle$" + "#### Automanaged Variables" ] }, { @@ -84,6 +92,50 @@ "execution_count": 3, "metadata": {}, "outputs": [], + "source": [ + "# IBM token\n", + "token = None\n", + "\n", + "# linear complexity GHZ circuit\n", + "linear_complexity_circuit = None\n", + "\n", + "# linear complexity mapped circuit\n", + "linear_complexity_mapped_circuit = None\n", + "\n", + "# linear complexity job\n", + "linear_complexity_job = None\n", + "\n", + "# linear complexity result\n", + "linear_complexity_result = None\n", + "\n", + "# logarithmic complexity GHZ circuit\n", + "log_complexity_circuit = None\n", + "\n", + "# log complexity mapped circuit\n", + "log_complexity_mapped_circuit = None\n", + "\n", + "# log complexity job\n", + "log_complexity_job = None\n", + "\n", + "# log complexity result\n", + "log_complexity_result = None\n", + "\n", + "# IBMBackend\n", + "backend = None\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Generate Linear Time Complexity Circuits for $|\\text{GHZ}_N\\rangle$" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], "source": [ "def linear_complexity_GHZ(N: int) -> QuantumCircuit:\n", " if not isinstance(N, int):\n", @@ -92,7 +144,8 @@ " raise ValueError(\"There must be one or more qubits.\")\n", "\n", " c = QuantumCircuit(N)\n", - " c.reset([i for i in range(N)])\n", + " for i in range(N):\n", + " c.reset(i)\n", " c.h(0)\n", " for i in range(1, N):\n", " c.cx(i-1, i)\n", @@ -101,7 +154,28 @@ ] }, { - "attachments": {}, + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "linear_complexity_circuit = linear_complexity_GHZ(N)\n", + "linear_complexity_circuit.draw(output='mpl')" + ] + }, + { "cell_type": "markdown", "metadata": {}, "source": [ @@ -110,7 +184,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -135,7 +209,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -144,7 +217,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -168,68 +241,145 @@ ] }, { - "attachments": {}, + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "log_complexity_circuit = log_complexity_GHZ(N)\n", + "log_complexity_circuit.draw(output='mpl')" + ] + }, + { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Get Token" + ] + }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ - "N=5" + "with open('token.txt', 'r') as f:\n", + " token = f.read().strip()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Setup IBM Machine" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "backend = least_busy(IBMProvider(token).backends(min_num_qubits=N, simulator=use_sim, operational=True))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Transpile Circuits" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```python\n", + "linear_complexity_mapped_circuit = transpile(linear_complexity_circuit, backend=backend)\n", + "log_complexity_mapped_circuit = transpile(log_complexity_circuit, backend=backend)\n", + "```" + ] + }, + { + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], "source": [ - "linear_complexity_GHZ(N=N).draw(output='mpl')" + "### Run Circuits" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 11, "metadata": {}, "outputs": [ { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" + "ename": "TranspilerError", + "evalue": "\"The number of qubits for Instruction(name='cx', num_qubits=2, num_clbits=0, params=[]) does not match the number of qubits in the properties dictionary: (0,)\"", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTranspilerError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[11], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m linear_complexity_job \u001b[39m=\u001b[39m execute(linear_complexity_circuit, backend\u001b[39m=\u001b[39;49mbackend, shots\u001b[39m=\u001b[39;49mshots)\n\u001b[1;32m 2\u001b[0m log_complexity_job \u001b[39m=\u001b[39m execute(log_complexity_circuit, backend\u001b[39m=\u001b[39mbackend, shots\u001b[39m=\u001b[39mshots)\n", + "File \u001b[0;32m/usr/local/lib/python3.8/site-packages/qiskit/execute_function.py:302\u001b[0m, in \u001b[0;36mexecute\u001b[0;34m(experiments, backend, basis_gates, coupling_map, backend_properties, initial_layout, seed_transpiler, optimization_level, pass_manager, qobj_id, qobj_header, shots, memory, max_credits, seed_simulator, default_qubit_los, default_meas_los, qubit_lo_range, meas_lo_range, schedule_los, meas_level, meas_return, memory_slots, memory_slot_size, rep_time, rep_delay, parameter_binds, schedule_circuit, inst_map, meas_map, scheduling_method, init_qubits, **run_config)\u001b[0m\n\u001b[1;32m 299\u001b[0m experiments \u001b[39m=\u001b[39m pass_manager\u001b[39m.\u001b[39mrun(experiments)\n\u001b[1;32m 300\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[1;32m 301\u001b[0m \u001b[39m# transpiling the circuits using given transpile options\u001b[39;00m\n\u001b[0;32m--> 302\u001b[0m experiments \u001b[39m=\u001b[39m transpile(\n\u001b[1;32m 303\u001b[0m experiments,\n\u001b[1;32m 304\u001b[0m basis_gates\u001b[39m=\u001b[39;49mbasis_gates,\n\u001b[1;32m 305\u001b[0m coupling_map\u001b[39m=\u001b[39;49mcoupling_map,\n\u001b[1;32m 306\u001b[0m backend_properties\u001b[39m=\u001b[39;49mbackend_properties,\n\u001b[1;32m 307\u001b[0m initial_layout\u001b[39m=\u001b[39;49minitial_layout,\n\u001b[1;32m 308\u001b[0m seed_transpiler\u001b[39m=\u001b[39;49mseed_transpiler,\n\u001b[1;32m 309\u001b[0m optimization_level\u001b[39m=\u001b[39;49moptimization_level,\n\u001b[1;32m 310\u001b[0m backend\u001b[39m=\u001b[39;49mbackend,\n\u001b[1;32m 311\u001b[0m )\n\u001b[1;32m 313\u001b[0m \u001b[39mif\u001b[39;00m schedule_circuit:\n\u001b[1;32m 314\u001b[0m experiments \u001b[39m=\u001b[39m schedule(\n\u001b[1;32m 315\u001b[0m circuits\u001b[39m=\u001b[39mexperiments,\n\u001b[1;32m 316\u001b[0m backend\u001b[39m=\u001b[39mbackend,\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 319\u001b[0m method\u001b[39m=\u001b[39mscheduling_method,\n\u001b[1;32m 320\u001b[0m )\n", + "File \u001b[0;32m/usr/local/lib/python3.8/site-packages/qiskit/compiler/transpiler.py:326\u001b[0m, in \u001b[0;36mtranspile\u001b[0;34m(circuits, backend, basis_gates, inst_map, coupling_map, backend_properties, initial_layout, layout_method, routing_method, translation_method, scheduling_method, instruction_durations, dt, approximation_degree, timing_constraints, seed_transpiler, optimization_level, callback, output_name, unitary_synthesis_method, unitary_synthesis_plugin_config, target, hls_config, init_method, optimization_method, ignore_backend_supplied_default_methods)\u001b[0m\n\u001b[1;32m 314\u001b[0m \u001b[39mif\u001b[39;00m (\n\u001b[1;32m 315\u001b[0m scheduling_method \u001b[39mis\u001b[39;00m \u001b[39mnot\u001b[39;00m \u001b[39mNone\u001b[39;00m\n\u001b[1;32m 316\u001b[0m \u001b[39mand\u001b[39;00m backend \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m\n\u001b[1;32m 317\u001b[0m \u001b[39mand\u001b[39;00m target \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m\n\u001b[1;32m 318\u001b[0m \u001b[39mand\u001b[39;00m \u001b[39mnot\u001b[39;00m instruction_durations\n\u001b[1;32m 319\u001b[0m ):\n\u001b[1;32m 320\u001b[0m warnings\u001b[39m.\u001b[39mwarn(\n\u001b[1;32m 321\u001b[0m \u001b[39m\"\u001b[39m\u001b[39mWhen scheduling circuits without backend,\u001b[39m\u001b[39m\"\u001b[39m\n\u001b[1;32m 322\u001b[0m \u001b[39m\"\u001b[39m\u001b[39m \u001b[39m\u001b[39m'\u001b[39m\u001b[39minstruction_durations\u001b[39m\u001b[39m'\u001b[39m\u001b[39m should be usually provided.\u001b[39m\u001b[39m\"\u001b[39m,\n\u001b[1;32m 323\u001b[0m \u001b[39mUserWarning\u001b[39;00m,\n\u001b[1;32m 324\u001b[0m )\n\u001b[0;32m--> 326\u001b[0m unique_transpile_args, shared_args \u001b[39m=\u001b[39m _parse_transpile_args(\n\u001b[1;32m 327\u001b[0m circuits,\n\u001b[1;32m 328\u001b[0m backend,\n\u001b[1;32m 329\u001b[0m basis_gates,\n\u001b[1;32m 330\u001b[0m inst_map,\n\u001b[1;32m 331\u001b[0m coupling_map,\n\u001b[1;32m 332\u001b[0m backend_properties,\n\u001b[1;32m 333\u001b[0m initial_layout,\n\u001b[1;32m 334\u001b[0m layout_method,\n\u001b[1;32m 335\u001b[0m routing_method,\n\u001b[1;32m 336\u001b[0m translation_method,\n\u001b[1;32m 337\u001b[0m scheduling_method,\n\u001b[1;32m 338\u001b[0m instruction_durations,\n\u001b[1;32m 339\u001b[0m dt,\n\u001b[1;32m 340\u001b[0m approximation_degree,\n\u001b[1;32m 341\u001b[0m seed_transpiler,\n\u001b[1;32m 342\u001b[0m optimization_level,\n\u001b[1;32m 343\u001b[0m callback,\n\u001b[1;32m 344\u001b[0m output_name,\n\u001b[1;32m 345\u001b[0m timing_constraints,\n\u001b[1;32m 346\u001b[0m unitary_synthesis_method,\n\u001b[1;32m 347\u001b[0m unitary_synthesis_plugin_config,\n\u001b[1;32m 348\u001b[0m target,\n\u001b[1;32m 349\u001b[0m hls_config,\n\u001b[1;32m 350\u001b[0m init_method,\n\u001b[1;32m 351\u001b[0m optimization_method,\n\u001b[1;32m 352\u001b[0m ignore_backend_supplied_default_methods,\n\u001b[1;32m 353\u001b[0m )\n\u001b[1;32m 354\u001b[0m \u001b[39m# Get transpile_args to configure the circuit transpilation job(s)\u001b[39;00m\n\u001b[1;32m 355\u001b[0m \u001b[39mif\u001b[39;00m coupling_map \u001b[39min\u001b[39;00m unique_transpile_args:\n", + "File \u001b[0;32m/usr/local/lib/python3.8/site-packages/qiskit/compiler/transpiler.py:652\u001b[0m, in \u001b[0;36m_parse_transpile_args\u001b[0;34m(circuits, backend, basis_gates, inst_map, coupling_map, backend_properties, initial_layout, layout_method, routing_method, translation_method, scheduling_method, instruction_durations, dt, approximation_degree, seed_transpiler, optimization_level, callback, output_name, timing_constraints, unitary_synthesis_method, unitary_synthesis_plugin_config, target, hls_config, init_method, optimization_method, ignore_backend_supplied_default_methods)\u001b[0m\n\u001b[1;32m 648\u001b[0m \u001b[39m# If target is not specified and any hardware constraint object is\u001b[39;00m\n\u001b[1;32m 649\u001b[0m \u001b[39m# manually specified then do not use the target from the backend as\u001b[39;00m\n\u001b[1;32m 650\u001b[0m \u001b[39m# it is invalidated by a custom basis gate list or a custom coupling map\u001b[39;00m\n\u001b[1;32m 651\u001b[0m \u001b[39melif\u001b[39;00m basis_gates \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m \u001b[39mand\u001b[39;00m coupling_map \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m--> 652\u001b[0m target \u001b[39m=\u001b[39m _parse_target(backend, target)\n\u001b[1;32m 654\u001b[0m basis_gates \u001b[39m=\u001b[39m _parse_basis_gates(basis_gates, backend)\n\u001b[1;32m 655\u001b[0m initial_layout \u001b[39m=\u001b[39m _parse_initial_layout(initial_layout, circuits)\n", + "File \u001b[0;32m/usr/local/lib/python3.8/site-packages/qiskit/compiler/transpiler.py:1004\u001b[0m, in \u001b[0;36m_parse_target\u001b[0;34m(backend, target)\u001b[0m\n\u001b[1;32m 1003\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39m_parse_target\u001b[39m(backend, target):\n\u001b[0;32m-> 1004\u001b[0m backend_target \u001b[39m=\u001b[39m \u001b[39mgetattr\u001b[39;49m(backend, \u001b[39m\"\u001b[39;49m\u001b[39mtarget\u001b[39;49m\u001b[39m\"\u001b[39;49m, \u001b[39mNone\u001b[39;49;00m)\n\u001b[1;32m 1005\u001b[0m \u001b[39mif\u001b[39;00m target \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[1;32m 1006\u001b[0m target \u001b[39m=\u001b[39m backend_target\n", + "File \u001b[0;32m/usr/local/lib/python3.8/site-packages/qiskit_ibm_provider/ibm_backend.py:329\u001b[0m, in \u001b[0;36mIBMBackend.target\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 327\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_get_properties()\n\u001b[1;32m 328\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_get_defaults()\n\u001b[0;32m--> 329\u001b[0m \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_convert_to_target()\n\u001b[1;32m 330\u001b[0m \u001b[39mreturn\u001b[39;00m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_target\n", + "File \u001b[0;32m/usr/local/lib/python3.8/site-packages/qiskit_ibm_provider/ibm_backend.py:284\u001b[0m, in \u001b[0;36mIBMBackend._convert_to_target\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 282\u001b[0m \u001b[39m\u001b[39m\u001b[39m\"\"\"Converts backend configuration, properties and defaults to Target object\"\"\"\u001b[39;00m\n\u001b[1;32m 283\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_target:\n\u001b[0;32m--> 284\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_target \u001b[39m=\u001b[39m convert_to_target(\n\u001b[1;32m 285\u001b[0m configuration\u001b[39m=\u001b[39;49m\u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_configuration,\n\u001b[1;32m 286\u001b[0m properties\u001b[39m=\u001b[39;49m\u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_properties,\n\u001b[1;32m 287\u001b[0m defaults\u001b[39m=\u001b[39;49m\u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_defaults,\n\u001b[1;32m 288\u001b[0m )\n", + "File \u001b[0;32m/usr/local/lib/python3.8/site-packages/qiskit_ibm_provider/utils/backend_converter.py:120\u001b[0m, in \u001b[0;36mconvert_to_target\u001b[0;34m(configuration, properties, defaults)\u001b[0m\n\u001b[1;32m 118\u001b[0m gate_len \u001b[39m=\u001b[39m \u001b[39mlen\u001b[39m(gate\u001b[39m.\u001b[39mcoupling_map[\u001b[39m0\u001b[39m]) \u001b[39mif\u001b[39;00m \u001b[39mhasattr\u001b[39m(gate, \u001b[39m\"\u001b[39m\u001b[39mcoupling_map\u001b[39m\u001b[39m\"\u001b[39m) \u001b[39melse\u001b[39;00m \u001b[39m0\u001b[39m\n\u001b[1;32m 119\u001b[0m \u001b[39mif\u001b[39;00m name \u001b[39min\u001b[39;00m name_mapping:\n\u001b[0;32m--> 120\u001b[0m target\u001b[39m.\u001b[39;49madd_instruction(name_mapping[name], gate_props)\n\u001b[1;32m 121\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[1;32m 122\u001b[0m custom_gate \u001b[39m=\u001b[39m Gate(name, gate_len, [])\n", + "File \u001b[0;32m/usr/local/lib/python3.8/site-packages/qiskit/transpiler/target.py:381\u001b[0m, in \u001b[0;36mTarget.add_instruction\u001b[0;34m(self, instruction, properties, name)\u001b[0m\n\u001b[1;32m 379\u001b[0m \u001b[39mfor\u001b[39;00m qarg \u001b[39min\u001b[39;00m properties:\n\u001b[1;32m 380\u001b[0m \u001b[39mif\u001b[39;00m qarg \u001b[39mis\u001b[39;00m \u001b[39mnot\u001b[39;00m \u001b[39mNone\u001b[39;00m \u001b[39mand\u001b[39;00m \u001b[39mlen\u001b[39m(qarg) \u001b[39m!=\u001b[39m instruction\u001b[39m.\u001b[39mnum_qubits:\n\u001b[0;32m--> 381\u001b[0m \u001b[39mraise\u001b[39;00m TranspilerError(\n\u001b[1;32m 382\u001b[0m \u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mThe number of qubits for \u001b[39m\u001b[39m{\u001b[39;00minstruction\u001b[39m}\u001b[39;00m\u001b[39m does not match the number \u001b[39m\u001b[39m\"\u001b[39m\n\u001b[1;32m 383\u001b[0m \u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mof qubits in the properties dictionary: \u001b[39m\u001b[39m{\u001b[39;00mqarg\u001b[39m}\u001b[39;00m\u001b[39m\"\u001b[39m\n\u001b[1;32m 384\u001b[0m )\n\u001b[1;32m 385\u001b[0m \u001b[39mif\u001b[39;00m qarg \u001b[39mis\u001b[39;00m \u001b[39mnot\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[1;32m 386\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mnum_qubits \u001b[39m=\u001b[39m \u001b[39mmax\u001b[39m(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39mnum_qubits, \u001b[39mmax\u001b[39m(qarg) \u001b[39m+\u001b[39m \u001b[39m1\u001b[39m)\n", + "\u001b[0;31mTranspilerError\u001b[0m: \"The number of qubits for Instruction(name='cx', num_qubits=2, num_clbits=0, params=[]) does not match the number of qubits in the properties dictionary: (0,)\"" + ] } ], "source": [ - "log_complexity_GHZ(N=N).draw(output='mpl')" + "linear_complexity_job = execute(linear_complexity_circuit, backend=backend, shots=shots)\n", + "log_complexity_job = execute(log_complexity_circuit, backend=backend, shots=shots)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Results" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "linear_complexity_result = linear_complexity_job.result()\n", + "log_complexity_result = log_complexity_job.result()" ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -244,9 +394,8 @@ "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.16" - }, - "orig_nbformat": 4 + } }, "nbformat": 4, - "nbformat_minor": 2 + "nbformat_minor": 4 } diff --git a/requirements.txt b/requirements.txt index 296cd2b..27bc6cc 100644 --- a/requirements.txt +++ b/requirements.txt @@ -3,3 +3,6 @@ qiskit-ibm-provider==0.5.2 matplotlib==3.7.1 jupyterlab==3.6.3 pylatexenc==2.10 +# ipywidgets==8.0.6 +# ipyvuetify==1.8.10 +# pyperclip==1.8.2