A quantum program to validate the provided errors with an experiment on the real backend.

measurement_error_validation.py

import Qconfig
import qiskit
import numpy as np

qiskit.register(Qconfig.APItoken, Qconfig.config["url"])

ibmqx4 = qiskit.get_backend('ibmqx4')
qubit_number = ibmqx4.configuration['n_qubits']
shot_number = 8192


## 1. Computing experimental probabilities.

Q_SPECS = {
    "name": "Measurement_errors",
    "circuits": [
        {
            "name": "measurement",
            "quantum_registers": [
                {
                    "name": "q",
                    "size": qubit_number
                },
            ],
            "classical_registers": [
                {
                    "name": "c",
                    "size": qubit_number
                }
            ]
        }
    ],
}

Q_program = qiskit.QuantumProgram(specs=Q_SPECS)

circuit = Q_program.get_circuit("measurement")
q = Q_program.get_quantum_register("q")
c = Q_program.get_classical_register("c")

circuit.measure(q, c)

print("Executing...")
result = qiskit.execute(circuit, ibmqx4, shots=shot_number, max_credits=5).result()
print("Done!")

counts = result.get_counts('measurement')
experimental_probabilities = np.array([counts.get(bin(n)[2:].zfill(qubit_number), 0) / shot_number
                                       for n in range(2**qubit_number)])

## 2. Computing theoretical probabilities
readout_errors = np.array([qubit_data['readoutError']['value'] for qubit_data in ibmqx4.calibration['qubits']])
N = np.arange(2**qubit_number)
theoretical_probabilities = []
for n in N:
    mask = np.array([((n & (1<<i)) != 0) for i in range(5)])
    theoretical_probabilities.append(np.prod(readout_errors[mask]) * np.prod(1 - readout_errors[np.logical_not(mask)]))

theoretical_probabilities = np.array(theoretical_probabilities)

## 3. Printing the error probabilities
print("Experimental errors:\n{}".format(experimental_probabilities))
print("Theoretical errors:\n{}".format(theoretical_probabilities))
print("Error on errors: {}".format(np.linalg.norm(experimental_probabilities - theoretical_probabilities)))