I would like to discuss the discrepancies between what we see in the simulator versus what we see in the actual running of the code on any IBMQ machine for any qubits at 5 or above. I am doing a final project on grover's algorithm, and the premise would require an extremely large number of qubits. I have tested my theory on the simulators up to 26 qubits (took 6 hours), and they are ~100% accurate. When I went to test the theory using the exact same circuit, I couldn't get a circuit of 4 qubits to even deviate from statistical random distrubution.
First of all, I have used Qiskit and Q# to create the exact same algorithm. If you could provide me with a methodology that would allow for easier work / do the work for the transpiler on qiskit, or the ability to utilize a real quantum computer in Q#, I would appreciate it.
Currently the transpiler in qiskit / IBMQ for grover's algorithm is limited to around 6-7 qubits. I don't like that I don't have more gates available. Regardless of this issue, I get garbage results for an oracle / ancilla at or larger than 4 qubits total. Why is is that the transpiler / decoherance that is occuring within the circuit is so terrible that I cannot construct Grover's algorithm using gates at or larger than 4 qubits? The probabilties of the simulators themselves are upwards of 99%, but even after a two qubit Grover's algorithm, it shows as only 40ish %?
When I go to three qubits, the entire algorithm is garbage, and I cannot provide ANY accuracy other than a random distribution, and when I tabulated it the accuracy was actually less than the statistical random distrubution. I'm not happy with what is going on here, as I cannot feasibly run anything of meaning on any IBMQ machine. I don't understand why the transpiler is inserting such a ludicrous range in the possible number of gates (about a hundred different possible gate configurations for 5 qubit Grover's algorithm)
Is this an issue with the transpiler? Is this just an issue with general decoherance? I don't understand why the quantum computer can't peform a grover's algorithm of 5 or more.
Please help me to understand what I am not getting here. Are the physical devices that far off from where I felt the technology was? I was hoping that a 15 qubit machine would be able to actually perform better, esp. in the 5 qubit realm.
#initialization import matplotlib.pyplot as plt import math import numpy as np # importing Qiskit from qiskit import ClassicalRegister, QuantumRegister from qiskit.providers.ibmq import least_busy from qiskit.quantum_info import Statevector from qiskit.providers.aer import QasmSimulator # import basic plot tools from qiskit.visualization import plot_histogram def initialize_s(qc,qubits): """Apply a H-gate to 'qubits' in qc""" for q in qubits: qc.h(q) return qc def numberofiterations(nqubits): temp = 2 ** nqubits; squareRoot = math.sqrt(temp) iterations = round(squareRoot) return iterations def oracle(nqubits): q = QuantumRegister(nqubits) qc = QuantumCircuit(q) #set the oracle's 0 bits qc.x(q[1]) qc.x(q[2]) #qc.x(q[5]) #qc.x(q[7]) #qc.x(q[8]) #qc.x(q[12]) #qc.x(q[13]) #qc.x(q[15]) #qc.x(q[19]) #qc.x(q[20]) #qc.x(q[21]) #qc.x(q[22]) #qc.x(q[24]) qc.h(q[nqubits-1]) #[0,3,4,6,9,10,11,14,16,17,18,23,26,27],30,ancilla_qubits=None, mode='noancilla') #qc.mcx([0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],q[25],ancilla_qubits=None, mode='noancilla') #qc.cx([0],[1]) qc.mcx([0,1,2],q[nqubits-1],ancilla_qubits=None, mode='noancilla') qc.x(q[1]) qc.x(q[2]) #qc.x(q[5]) #qc.x(q[7]) #qc.x(q[8]) #qc.x(q[12]) #qc.x(q[13]) #qc.x(q[15]) #qc.x(q[19]) #qc.x(q[20]) #qc.x(q[21]) #qc.x(q[22]) #qc.x(q[24]) qc.h(q[nqubits-1]) #return the oracle as a gate. oracle = qc.to_gate() oracle.name = "U$_\omega$" return oracle def diffuser(nqubits): qc = QuantumCircuit(nqubits) # Apply transformation |s> -> |00..0> (H-gates) for qubit in range(nqubits): qc.h(qubit) # Apply transformation |00..0> -> |11..1> (X-gates) for qubit in range(nqubits): qc.x(qubit) # Do multi-controlled-Z gate qc.h(nqubits-1) qc.mcx(list(range(nqubits-1)), nqubits-1) # multi-controlled-toffoli #qc.cx([0],[1]) qc.h(nqubits-1) # Apply transformation |11..1> -> |00..0> for qubit in range(nqubits): qc.x(qubit) # Apply transformation |00..0> -> |s> for qubit in range(nqubits): qc.h(qubit) # We will return the diffuser as a gate U_s = qc.to_gate() U_s.name = "$U_s$" return U_s n = 4 qr = QuantumRegister(n-1, 'register') anc = QuantumRegister(1, 'ancilla') cr = ClassicalRegister(n-1, 'classical') grover_circuit = QuantumCircuit(qr,anc) grover_circuit = initialize_s(grover_circuit, list(range(n))) iterations = numberofiterations(n-1) for j in range(iterations ): grover_circuit.append(oracle(n), list(range(n))) grover_circuit.append(diffuser(n), list(range(n))) measure_circuit = QuantumCircuit(qr,cr) measure_circuit.measure(qr,cr) ``` 