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How can you measure qubits in QuTiP?

As far as I have seen you can define a Hamiltonian and let it evolve in time. It is also possible to define a quantum circuit, however, measuring and running it is not possible.

Does anyone know how to do this?

A simple circuit could be

H q[0]
CNOT q[0],q[1]
Measure q[0], q[1]
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QuTiP is not really meant for this I think. As said on the home page :

QuTiP is open-source software for simulating the dynamics of open quantum systems.

Simulating dynamics of open quantum systems by definition means you are interested in the quantum state as a result of your algorithm.

I tried looking at the Notebook examples provided in this Github but could not find measurement examples somewhere. You have a possibility to get expectation values though (see this notebook).

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Main purpose of Qutip is to explore dynamics of quantum systems and therefore density matrices are the tool to use. According to this answer on Quantum computing, we can model a measurement operator Pi on a density matrix. In the case of the measurement of a single qubit in the computational basis, you have $$P_0=|0\rangle\langle 0|\qquad P_1=|1\rangle\langle 1|$$

If you want to talk about n qubits where you measure just the first one, then you use the measurement operators

$$P_0=|0\rangle\langle 0|\otimes\mathbb{I}^{\otimes(n-1)}\qquad P_1=|1\rangle\langle 1|\otimes\mathbb{I}^{\otimes(n-1)}$$

Implementation with the Qutip dag method. First we set up a two level quantum system with the basis method use a vector v0 for the zero vector and v1 for one vector.

v0 = qp.basis(2, 0)

Calculate outer product with the dag method this will give a density operator

P0 = v0 * v0.dag()

expand for multiqubit gate

M0 = qp.gate_expand_1toN(P0, self.activeQubits, qubitNum)

Also

v1 = qp.basis(2, 1)

You can find a basic qubit quantum simulator running on Qutip in the SimulaQron software.

SimulaQron crudeSimulator

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Here. Scroll down to the stochastic solver, and you'll find an attribute for storing measurements.

It's certainly not the emphasis of the package, as cnada pointed out, but it's there.

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If you really want to simulate measurement, that's how I would do it.

A function that finds probability amplitude associated to each eigenstate.

import numpy as np
import itertools

from qutip import basis, tensor, snot

def prepareMeasurement(N, psi):
    # all the spin configurations
    confs = list(itertools.product([0, 1], repeat=N))
    # probability distribution
    P = []
    for conf in confs:
        # particular outcome as quantum object
        psi_ref = tensor([basis(2, m) for m in conf])
        # probability of this outcome
        p = np.abs(psi.overlap(psi_ref))**2.
        # append to the distribution
        P.append(p)
    return confs, np.array(P)

Then a function that given this amplitude takes n random measurements.

def simulateMeasurement(confs, P, n):
    return np.random.choice(range(len(confs)), n, p=P)

We can test it on a little example, let's create an even superposition of all the eigenstates. They should all have same amplitudes.

psi0 = tensor([basis(2, 0), basis(2, 0), basis(2, 0)])
psif = snot(N=3, target=0)*psi0
psif = snot(N=3, target=1)*psif
psif = snot(N=3, target=2)*psif

And this is how we apply our measurement simulation, let's perform 10000 measurements. Let's also calculate counts.

confs, P = prepareMeasurement(3, psif)
measurements = simulateMeasurement(confs, P, 10000)
unique, counts = np.unique(measurements, return_counts=True)

Visualize the data in histogram-like form.

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
ax.bar(unique, height=counts)
plt.xticks(unique, ["|{0}>".format(format(m, '03b')) for m in unique])
ax.set_title('Testing measurement simulation with QuTip')
ax.set_ylabel('Count')
ax.set_xlabel('Measurement')
plt.show()

This is what we're getting

histogram

I included everything in this public gist repository. Hope it helps!

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