qiskit的grover算法demo

01 资源

01.01 vscode的qiskt插件

01.02 qiskit的demo

02 grover算法demo

grover_algorithm.py代码如下:

import numpy as np import matplotlib.pyplot as plt #%matplotlib inline # importing Qiskit from qiskit import Aer, IBMQ from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister from qiskit import available_backends, execute, register, get_backend, compile from qiskit.tools import visualization from qiskit.tools.visualization import circuit_drawer q = QuantumRegister(6) qc = QuantumCircuit(q) qc.x(q[2]) qc.cx(q[1], q[5]) qc.cx(q[2], q[5]) qc.cx(q[3], q[5]) qc.ccx(q[1], q[2], q[4]) qc.ccx(q[3], q[4], q[5]) qc.ccx(q[1], q[2], q[4]) qc.x(q[2]) circuit_drawer(qc) def black_box_u_f(circuit, f_in, f_out, aux, n, exactly_1_3_sat_formula): """Circuit that computes the black-box function from f_in to f_out. Create a circuit that verifies whether a given exactly-1 3-SAT formula is satisfied by the input. The exactly-1 version requires exactly one literal out of every clause to be satisfied. """ num_clauses = len(exactly_1_3_sat_formula) for (k, clause) in enumerate(exactly_1_3_sat_formula): # This loop ensures aux[k] is 1 if an odd number of literals # are true for literal in clause: if literal > 0: circuit.cx(f_in[literal-1], aux[k]) else: circuit.x(f_in[-literal-1]) circuit.cx(f_in[-literal-1], aux[k]) # Flip aux[k] if all literals are true, using auxiliary qubit # (ancilla) aux[num_clauses] circuit.ccx(f_in[0], f_in[1], aux[num_clauses]) circuit.ccx(f_in[2], aux[num_clauses], aux[k]) # Flip back to reverse state of negative literals and ancilla circuit.ccx(f_in[0], f_in[1], aux[num_clauses]) for literal in clause: if literal < 0: circuit.x(f_in[-literal-1]) # The formula is satisfied if and only if all auxiliary qubits # except aux[num_clauses] are 1 if (num_clauses == 1): circuit.cx(aux[0], f_out[0]) elif (num_clauses == 2): circuit.ccx(aux[0], aux[1], f_out[0]) elif (num_clauses == 3): circuit.ccx(aux[0], aux[1], aux[num_clauses]) circuit.ccx(aux[2], aux[num_clauses], f_out[0]) circuit.ccx(aux[0], aux[1], aux[num_clauses]) else: raise ValueError('We only allow at most 3 clauses') # Flip back any auxiliary qubits to make sure state is consistent # for future executions of this routine; same loop as above. for (k, clause) in enumerate(exactly_1_3_sat_formula): for literal in clause: if literal > 0: circuit.cx(f_in[literal-1], aux[k]) else: circuit.x(f_in[-literal-1]) circuit.cx(f_in[-literal-1], aux[k]) circuit.ccx(f_in[0], f_in[1], aux[num_clauses]) circuit.ccx(f_in[2], aux[num_clauses], aux[k]) circuit.ccx(f_in[0], f_in[1], aux[num_clauses]) for literal in clause: if literal < 0: circuit.x(f_in[-literal-1]) # -- end function def n_controlled_Z(circuit, controls, target): """Implement a Z gate with multiple controls""" if (len(controls) > 2): raise ValueError('The controlled Z with more than 2 ' + 'controls is not implemented') elif (len(controls) == 1): circuit.h(target) circuit.cx(controls[0], target) circuit.h(target) elif (len(controls) == 2): circuit.h(target) circuit.ccx(controls[0], controls[1], target) circuit.h(target) # -- end function def inversion_about_average(circuit, f_in, n): """Apply inversion about the average step of Grover's algorithm.""" # Hadamards everywhere for j in range(n): circuit.h(f_in[j]) # D matrix: flips the sign of the state |000> only for j in range(n): circuit.x(f_in[j]) n_controlled_Z(circuit, [f_in[j] for j in range(n-1)], f_in[n-1]) for j in range(n): circuit.x(f_in[j]) # Hadamards everywhere again for j in range(n): circuit.h(f_in[j]) # -- end function qr = QuantumRegister(3) qInvAvg = QuantumCircuit(qr) inversion_about_average(qInvAvg, qr, 3) circuit_drawer(qInvAvg) """ Grover search implemented in Qiskit. This module contains the code necessary to run Grover search on 3 qubits, both with a simulator and with a real quantum computing device. This code is the companion for the paper "An introduction to quantum computing, without the physics", Giacomo Nannicini, https://arxiv.org/abs/1708.03684. """ def input_state(circuit, f_in, f_out, n): """(n+1)-qubit input state for Grover search.""" for j in range(n): circuit.h(f_in[j]) circuit.x(f_out) circuit.h(f_out) # -- end function # Make a quantum program for the n-bit Grover search. n = 3 # Exactly-1 3-SAT formula to be satisfied, in conjunctive # normal form. We represent literals with integers, positive or # negative, to indicate a Boolean variable or its negation. exactly_1_3_sat_formula = [[1, 2, -3], [-1, -2, -3], [-1, 2, 3]] # Define three quantum registers: 'f_in' is the search space (input # to the function f), 'f_out' is bit used for the output of function # f, aux are the auxiliary bits used by f to perform its # computation. f_in = QuantumRegister(n) f_out = QuantumRegister(1) aux = QuantumRegister(len(exactly_1_3_sat_formula) + 1) # Define classical register for algorithm result ans = ClassicalRegister(n) # Define quantum circuit with above registers grover = QuantumCircuit() grover.add(f_in) grover.add(f_out) grover.add(aux) grover.add(ans) input_state(grover, f_in, f_out, n) T = 2 for t in range(T): # Apply T full iterations black_box_u_f(grover, f_in, f_out, aux, n, exactly_1_3_sat_formula) inversion_about_average(grover, f_in, n) # Measure the output register in the computational basis for j in range(n): grover.measure(f_in[j], ans[j]) # Execute circuit backend = Aer.get_backend('qasm_simulator') job = execute([grover], backend=backend, shots=1000) result = job.result() # Get counts and plot histogram counts = result.get_counts(grover) visualization.plot_histogram(counts) # 下面需要有IBMQ的账号在本地磁盘的配置 IBMQ.load_accounts() # get ibmq_16_rueschlikon configuration and coupling map backend = IBMQ.get_backend('ibmq_16_melbourne') backend_config = backend.configuration() backend_coupling = backend_config['coupling_map'] # compile the circuit for ibmq_16_rueschlikon grover_compiled = compile(grover, backend=backend, coupling_map=backend_coupling, seed=1) grover_compiled_qasm = grover_compiled.experiments[0].header.compiled_circuit_qasm print("Number of gates for", backend.name(), "is", len(grover_compiled_qasm.split("\n")) - 4) circuit_drawer(grover) 

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