Random Numbers Generation

Generating random numbers on a quantum computer is not difficult because the unpredictability of measure of a qubit in a state of superposition it is in fact a form of natural randomness. Translating this idea into code is relatively simple: taking n qubits (therefore the random number obtained from each execution will be an integer from 0 to 2ⁿ - 1) with initial state equals to $|0\rangle$, the quantum Hadamard gate is applied to each of the n qubits and finally the measurement is performed. The quantum Hadamard gate applied to a qubit in $|0\rangle$ state brings it in superposition state: $$\frac{|0\rangle + |1\rangle}{\sqrt{2}}$$ and this means that the measure will have the probability of 50% to be equal to 0 and 50% to be equal to 1.

Circuit diagram

Considering that a quantum computer with 5 qubits is available, the circuit diagram that achieves the above is the following:

QASM code

The following program is the translation in QASM language of the circuit illustrated above; this program has been tested both on IBM's quantum computer 'ibmq_london' and on the IBM 'qasm_simulator' simulator.

OPENQASM 2.0;
include "qelib1.inc";

qreg q[5];
creg c[5];

h q[0];
h q[1];
h q[2];
h q[3];
h q[4];

measure q[0] -> c[0];
measure q[1] -> c[1];
measure q[2] -> c[2];
measure q[3] -> c[3];
measure q[4] -> c[4];

Python with Qiskit code

The following program is the translation in Python with Qiskit of the circuit shown above; this program was tested inside a Jupyter Notebook using as backend both IBM's quantum computer 'ibmq_london' and IBM's 'qasm_simulator' simulator.

q = QuantumRegister(5, 'q')
c = ClassicalRegister(5, 'c')
circuit = QuantumCircuit(q, c)

circuit.h(q[0])
circuit.h(q[1])
circuit.h(q[2])
circuit.h(q[3])
circuit.h(q[4])

circuit.measure(q, c)

Microsoft Q# .NET Core code for quantum simulator

The following program is the Microsoft Q# translation of the circuit shown above; this program has been tested on a Linux with .NET Core, Q# runtime and Microsoft quantum simulator installed.

namespace ComputationalMindset.QuantumExperiments

    open Microsoft.Quantum.Intrinsic;
    open Microsoft.Quantum.Canon;
    open Microsoft.Quantum.Measurement;

    operation RandomNumberGenerator() : (Result, Result, Result, Result, Result)
    {
        using (q = Qubit[5])
        {
            H(q[0]);
            H(q[1]);
            H(q[2]);
            H(q[3]);
            H(q[4]);

            let result = (M(q[0]), M(q[1]), M(q[2]), M(q[3]), M(q[4]));

            ResetAll(q);
            return result;
        }
    }

Results on IBM Q Experience

Both programs for IBM Q Experience were executed with a number of shots equals to 8192 both on the IBM's simulator 'qasm_simulator' and on the real computer IBM's 'ibmq_london' obtaining the expected result, ie a uniform distribution of all 5-bit combinations. The imperfect uniformity shown in the case of real quantum computers compared to simulators is due to noise.
Note: Given the stochastic nature of this code, your specific reults may vary. Consider running the example a few times.

Results on Microsoft simulator

The execution of the Q# program for .NET Core produced the expected result, namely a uniform distribution of all 5 bits combinations.
Note: Given the stochastic nature of this code, your specific results may vary. Consider running the example a few times.

Media

Download of the complete code

The complete code is available at GitHub.
These materials are distributed under MIT license; feel free to use, share, fork and adapt these materials as you see fit.
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