446 lines
277 KiB
Plaintext
446 lines
277 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "9857bace",
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"metadata": {},
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"source": [
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"# Grover's algorithm\n",
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"*Usage estimate: under 1 minute on IBM Nairobi (NOTE: This is an estimate only. Your runtime may vary.)*"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9f72eb0a",
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"metadata": {},
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"source": [
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"## Background\n",
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"\n",
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"Amplitude amplification is a general purpose quantum algorithm, or subroutine, that can be used to obtain a quadratic speedup over a handful of classical algorithms. [Grover’s algorithm](https://arxiv.org/abs/quant-ph/9605043) was the first to demonstrate this speedup on unstructured search problems. Formulating a Grover's search problem requires an oracle function that marks one or more computational basis states as the states we are interested in finding, and an amplification circuit that increases the amplitude of marked states, consequently suppressing the remaining states.\n",
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"\n",
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"Here, we demonstrate how to construct Grover oracles and use the [`grover_operator()`](/api/qiskit/qiskit.circuit.library.grover_operator) from the Qiskit circuit library to easily set up a Grover's search instance. The runtime `Sampler` primitive allows seamless execution of Grover circuits."
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]
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},
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{
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"cell_type": "markdown",
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"id": "152c479f",
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"metadata": {},
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"source": [
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"## Requirements\n",
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"\n",
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"Before starting this tutorial, ensure that you have the following installed:\n",
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"\n",
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"* Qiskit SDK 1.4 or later, with visualization support (`pip install 'qiskit[visualization]'`)\n",
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"* Qiskit Runtime (`pip install qiskit-ibm-runtime`) 0.36 or later"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"id": "54602708",
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"metadata": {},
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"source": [
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"## Setup"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "e2cb0472",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Built-in modules\n",
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"import math\n",
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"\n",
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"# Imports from Qiskit\n",
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"from qiskit import QuantumCircuit\n",
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"from qiskit.circuit.library import grover_operator, MCMTGate, ZGate\n",
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"from qiskit.visualization import plot_distribution\n",
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"from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
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"\n",
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"# Imports from Qiskit Runtime\n",
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"from qiskit_ibm_runtime import QiskitRuntimeService\n",
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"from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
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"\n",
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"\n",
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"def grover_oracle(marked_states):\n",
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" \"\"\"Build a Grover oracle for multiple marked states\n",
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"\n",
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" Here we assume all input marked states have the same number of bits\n",
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"\n",
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" Parameters:\n",
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" marked_states (str or list): Marked states of oracle\n",
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"\n",
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" Returns:\n",
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" QuantumCircuit: Quantum circuit representing Grover oracle\n",
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" \"\"\"\n",
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" if not isinstance(marked_states, list):\n",
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" marked_states = [marked_states]\n",
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" # Compute the number of qubits in circuit\n",
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" num_qubits = len(marked_states[0])\n",
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"\n",
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" qc = QuantumCircuit(num_qubits)\n",
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" # Mark each target state in the input list\n",
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" for target in marked_states:\n",
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" # Flip target bit-string to match Qiskit bit-ordering\n",
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" rev_target = target[::-1]\n",
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" # Find the indices of all the '0' elements in bit-string\n",
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" zero_inds = [\n",
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" ind\n",
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" for ind in range(num_qubits)\n",
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" if rev_target.startswith(\"0\", ind)\n",
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" ]\n",
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" # Add a multi-controlled Z-gate with pre- and post-applied X-gates (open-controls)\n",
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" # where the target bit-string has a '0' entry\n",
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" qc.x(zero_inds)\n",
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" qc.compose(MCMTGate(ZGate(), num_qubits - 1, 1), inplace=True)\n",
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" qc.x(zero_inds)\n",
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" return qc"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"id": "d4845f4d",
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"metadata": {},
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"source": [
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"## Step 1: Map classical inputs to a quantum problem\n",
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"\n",
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"Grover's algorithm requires an [oracle](https://learning.quantum-computing.ibm.com/course/fundamentals-of-quantum-algorithms/grovers-algorithm) that specifies one or more marked computational basis states, where \"marked\" means a state with a phase of -1. A controlled-Z gate, or its multi-controlled generalization over $N$ qubits, marks the $2^{N}-1$ state (`'1'`*$N$ bit-string). Marking basis states with one or more `'0'` in the binary representation requires applying X-gates on the corresponding qubits before and after the controlled-Z gate; equivalent to having an open-control on that qubit. In the following code, we define an oracle that does just that, marking one or more input basis states defined through their bit-string representation. The `MCMT` gate is used to implement the multi-controlled Z-gate."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8668ab00",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'ibm_kyoto'"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# To run on hardware, select the backend with the fewest number of jobs in the queue\n",
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"service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
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"backend = service.least_busy(\n",
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" operational=True, simulator=False, min_num_qubits=127\n",
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")\n",
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"backend.name"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"id": "cde40906",
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"metadata": {},
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"source": [
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"## Step 1: Map classical inputs to a quantum problem\n",
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"\n",
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"Grover's algorithm requires an [oracle](https://learning.quantum-computing.ibm.com/course/fundamentals-of-quantum-algorithms/grovers-algorithm) that specifies one or more marked computational basis states, where \"marked\" means a state with a phase of -1. A controlled-Z gate, or its multi-controlled generalization over $N$ qubits, marks the $2^{N}-1$ state (`'1'`*$N$ bit-string). Marking basis states with one or more `'0'` in the binary representation requires applying X-gates on the corresponding qubits before and after the controlled-Z gate; equivalent to having an open-control on that qubit. In the following code, we define an oracle that does just that, marking one or more input basis states defined through their bit-string representation. The `MCMT` gate is used to implement the multi-controlled Z-gate."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "6e419a8a",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'ibm_cusco'"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# To run on hardware, select the backend with the fewest number of jobs in the queue\n",
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"service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
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"backend = service.least_busy(\n",
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" operational=True, simulator=False, min_num_qubits=127\n",
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")\n",
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"backend.name"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"id": "bca14740",
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"metadata": {},
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"source": [
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"### Specific Grover's instance\n",
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"\n",
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"Now that we have the oracle function, we can define a specific instance of Grover search. In this example we will mark two computational states out of the eight available in a three-qubit computational space:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "c150298f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 538.33x284.278 with 1 Axes>"
|
||
]
|
||
},
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"marked_states = [\"011\", \"100\"]\n",
|
||
"\n",
|
||
"oracle = grover_oracle(marked_states)\n",
|
||
"oracle.draw(output=\"mpl\", style=\"iqp\")"
|
||
]
|
||
},
|
||
{
|
||
"attachments": {},
|
||
"cell_type": "markdown",
|
||
"id": "25487b93",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Grover operator\n",
|
||
"\n",
|
||
"The built-in Qiskit `grover_operator()` takes an oracle circuit and returns a circuit that is composed of the oracle circuit itself and a circuit that amplifies the states marked by the oracle. Here, we use the `decompose()` method the circuit to see the gates within the operator:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "283d5265",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 2126.94x284.278 with 1 Axes>"
|
||
]
|
||
},
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"grover_op = grover_operator(oracle)\n",
|
||
"grover_op.decompose().draw(output=\"mpl\", style=\"iqp\")"
|
||
]
|
||
},
|
||
{
|
||
"attachments": {},
|
||
"cell_type": "markdown",
|
||
"id": "83c34dc9",
|
||
"metadata": {},
|
||
"source": [
|
||
"Repeated applications of this `grover_op` circuit amplify the marked states, making them the most probable bit-strings in the output distribution from the circuit. There is an optimal number of such applications that is determined by the ratio of marked states to total number of possible computational states:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "f4c3d4b5",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"optimal_num_iterations = math.floor(\n",
|
||
" math.pi\n",
|
||
" / (4 * math.asin(math.sqrt(len(marked_states) / 2**grover_op.num_qubits)))\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"attachments": {},
|
||
"cell_type": "markdown",
|
||
"id": "e06c8238",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Full Grover circuit\n",
|
||
"\n",
|
||
"A complete Grover experiment starts with a Hadamard gate on each qubit; creating an even superposition of all computational basis states, followed the Grover operator (`grover_op`) repeated the optimal number of times. Here we make use of the `QuantumCircuit.power(INT)` method to repeatedly apply the Grover operator."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "4933ae44",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 663.998x367.889 with 1 Axes>"
|
||
]
|
||
},
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"qc = QuantumCircuit(grover_op.num_qubits)\n",
|
||
"# Create even superposition of all basis states\n",
|
||
"qc.h(range(grover_op.num_qubits))\n",
|
||
"# Apply Grover operator the optimal number of times\n",
|
||
"qc.compose(grover_op.power(optimal_num_iterations), inplace=True)\n",
|
||
"# Measure all qubits\n",
|
||
"qc.measure_all()\n",
|
||
"qc.draw(output=\"mpl\", style=\"iqp\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "97eb3019",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 2: Optimize problem for quantum hardware execution"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "c9a3020e",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 2263.23x2458.17 with 1 Axes>"
|
||
]
|
||
},
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"target = backend.target\n",
|
||
"pm = generate_preset_pass_manager(target=target, optimization_level=3)\n",
|
||
"\n",
|
||
"circuit_isa = pm.run(qc)\n",
|
||
"circuit_isa.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")"
|
||
]
|
||
},
|
||
{
|
||
"attachments": {},
|
||
"cell_type": "markdown",
|
||
"id": "c5edec73",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 3: Execute using Qiskit primitives\n",
|
||
"\n",
|
||
"Amplitude amplification is a sampling problem that is suitable for execution with the [`Sampler`](/api/qiskit-ibm-runtime/sampler-v2) runtime primitive.\n",
|
||
"\n",
|
||
"Note that the `run()` method of [Qiskit Runtime `SamplerV2`](/api/qiskit-ibm-runtime/sampler-v2) takes an iterable of `primitive unified blocks (PUBs)`. For sampler, each PUB is an iterable in the format `(circuit, parameter_values)`. However, at a minimum, it takes a list of quantum circuit(s)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "0eb154d4",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# To run on local simulator:\n",
|
||
"# 1. Use the StatevectorSampler from qiskit.primitives instead\n",
|
||
"sampler = Sampler(mode=backend)\n",
|
||
"sampler.options.default_shots = 10_000\n",
|
||
"result = sampler.run([circuit_isa]).result()\n",
|
||
"dist = result[0].data.meas.get_counts()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "87484abf",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Step 4: Post-process and return result in desired classical format"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "a5ef9913",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 700x500 with 1 Axes>"
|
||
]
|
||
},
|
||
"execution_count": 9,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"plot_distribution(dist)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2bdde144",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Tutorial survey\n",
|
||
"\n",
|
||
"Please take one minute to provide feedback on this tutorial. Your insights will help us improve our content offerings and user experience.\n",
|
||
"\n",
|
||
"[Link to survey](https://your.feedback.ibm.com/jfe/form/SV_0j1SlLPkooyeFJY)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fd6d2f21",
|
||
"metadata": {},
|
||
"source": [
|
||
"© IBM Corp. 2023"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"description": "Learn the basics of quantum computing, and how to use IBM Quantum services and systems to solve real-world problems.",
|
||
"kernelspec": {
|
||
"display_name": "Python 3",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3"
|
||
},
|
||
"platform": "cloud",
|
||
"title": "Grover's algorithm"
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|