Random measurement of qubits

Question

from qiskit import *
def qrng(bit_num, backend):
    bitstring = ""
    qrng_circuit = QuantumCircuit(5, 5)
    qrng_circuit.h(4)
    qrng_circuit.measure(4, 4)
    for _ in range(bit_num):
        counts = execute(qrng_circuit, backend, shots=8192).result().get_counts()
        bit = list(counts.keys())[0]  
        bitstring += bit
    return bitstring

backend = BasicAer.get_backend('qasm_simulator')

print(qrng(1024, backend))

For the above code is supposed to generate a random sequence by measurement of some specific qubits. For example if i have a quantum circuit with 10 qubits which are all put in superposition using Hadamard gate but I want that the measurement method would be random (to be able to select say 2, 3, 5, 7, 8th qubit) leading to random bitstring being generated.

Answer 1

To add some information to KAJ226 answer.

To generate random bit string having uniform distribution with quantum computer, you do not need to perform random measurement. Lets say you want to generate bit string of length $n$. Then simply put Hadamard gate on each qubit, then apply measurement and send your circuit to quantum computer with one shot as proposed by KAJ226. Repeat this $m$ times. In the end, you will have $m$ uniformly distributed random bit strings with length $n$. The reason why this works is that Hadamard gate prepares equally distributed superposition.

Answer 2

I am not sure exactly what you are trying to do by doing this but this does what you are looking for:

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
from numpy import pi
from numpy.random import randint
from numpy.random import shuffle

num_qubits  = 10
qreg_q = QuantumRegister(num_qubits, 'q')
creg_c = ClassicalRegister(num_qubits, 'c')
circuit = QuantumCircuit(qreg_q, creg_c)
for i in range(num_qubits):
    circuit.h(qreg_q[i])
    
sequence = [i for i in range(num_qubits)]
shuffle(sequence)


num_measurements = 6
for i in range(num_measurements):
    circuit.measure(qreg_q[sequence[i] ], creg_c[sequence[i] ])

circuit.draw( ) 

This will create a layer of Hadamard gate on n-qubits then you can select the number of measurements you want to execute. It will then place those measurement randomly on different qubits. Thus, if you run the above code, you might generate a circuit something like:

      ┌───┐                  
 q_0: ┤ H ├──────────────────
      ├───┤            ┌─┐   
 q_1: ┤ H ├────────────┤M├───
      ├───┤            └╥┘   
 q_2: ┤ H ├─────────────╫────
      ├───┤             ║    
 q_3: ┤ H ├─────────────╫────
      ├───┤         ┌─┐ ║    
 q_4: ┤ H ├─────────┤M├─╫────
      ├───┤         └╥┘ ║    
 q_5: ┤ H ├──────────╫──╫────
      ├───┤   ┌─┐    ║  ║    
 q_6: ┤ H ├───┤M├────╫──╫────
      ├───┤   └╥┘    ║  ║ ┌─┐
 q_7: ┤ H ├────╫─────╫──╫─┤M├
      ├───┤┌─┐ ║     ║  ║ └╥┘
 q_8: ┤ H ├┤M├─╫─────╫──╫──╫─
      ├───┤└╥┘ ║ ┌─┐ ║  ║  ║ 
 q_9: ┤ H ├─╫──╫─┤M├─╫──╫──╫─
      └───┘ ║  ║ └╥┘ ║  ║  ║ 
c: 10/══════╩══╩══╩══╩══╩══╩═
            8  6  9  4  1  7 

Updated: So now, if we want to read-out the random bitstring, we can do:

backend = BasicAer.get_backend('qasm_simulator')
counts = execute(circuit, backend, shots=1).result().get_counts()
bit_strings = list(counts.keys())[0]  
print('random bit_strings:', bit_strings)

which would output:

random bit_strings: 0011010010