Mid-Circuit Measurements Tutorial

We are excited to announce that mid-circuit measurements are now available on IBM Quantum systems.

Info: As of January 8th, 2021, only some of the IBM Q Network devices are enabled with this functionality. These features will be rolled out to open users at a later date.

Up until now, IBM Quantum backends only allowed a single measurement per circuit. This measurement was further restricted to the final instruction in the circuit. This was sufficient for early use cases, but is a significant barrier as we seek to implement real-time computation between classical and quantum systems.

Now, IBM Quantum users can perform multiple measurements in a circuit and at any point throughout the circuit. This enables immediate use cases such as heralding and monitoring qubit evolution. Together with conditional reset, this provides a powerful initial framework for real-time compute.

This notebook provides a number of examples demonstrating how to perform mid-circuit measurements on IBM Quantum backends. We show a simple circuit, mixing of reset and mid-circuit measurements, and a GHZ to Bell state example.

Coming soon: At present, real-time conditionals (i.e., if statements) are not enabled on backends. Equivalent behavior can be produced by inserting a mid-circuit measurement and post selecting results of interest.

We are presently working on adding this functionality in conjunction with other real-time functionality as outlined in the OpenQasm3 specification.

import sys
import warnings

import matplotlib.pyplot as plt

import qiskit
from qiskit import IBMQ, QuantumCircuit, execute,  Aer
from qiskit.result import marginal_counts
from qiskit.providers.ibmq.job import job_monitor
from qiskit.tools.visualization import plot_histogram

# Fill in your hub/group/provider
provider = IBMQ.get_provider(hub='your_hub', group='your_group', project='your_provider')
# ibmq_manhattan supports mid-circuit measurements
backend = provider.get_backend('ibmq_manhattan')

config = backend.configuration()
n_qubits = config.n_qubits

Here config is the backend.configuration() that will be referenced throughout this tutorial.

Info: These features require qiskit>0.22.0 as they rely on qiskit-terra>0.16.0. If required, you can install the latest version of qiskit by uncommenting and running the line below.

#!pip install qiskit -U
import qiskit.tools.jupyter

Version Information

Qiskit SoftwareVersion
IBM Q Provider0.11.1
System information
Python3.7.9 (default, Aug 31 2020, 07:22:35) [Clang 10.0.0 ]
Memory (Gb)16.0
Thu Jan 07 12:05:09 2021 EST

Checking the backend

We begin by checking if this backend supports mid-circuit measurements. A boolean flag is provided in config, multi_meas_enabled, which defines whether this feature is supported. If the flag is False, the old restrictions of a single, final measurement apply.


Simple circuit

The first circuit is a simple sequence of single-qubit operations: x(0) -> measure(0,1) -> barrier(0,1) -> x(1) -> measure(0,1). It is given below.

qc_simp = QuantumCircuit(2,4)
qc_simp.measure([0,1], [0,1])
qc_simp.barrier([0, 1])
qc_simp.measure([0,1], [2,3])
<qiskit.circuit.instructionset.InstructionSet at 0x7f9f4e3325d0>

NOTE: In order to store the different measurement results, we must allocate additional memory slots. The Qiskit measure command has the syntax measure(qubits, mem_slots). In the above circuit, the first measurement is on qubits [0,1] and results are stored in memory slots [0,1]. The second measurement is on qubits [0,1] as well, but the results are stored in memory slots [2,3].

If new memory slots are not provided, the old result will be overwritten.

We expect that state |01\rangle after the first measurement since x(0) flips qubit 0 to the |1\rangle state (recall, Qiskit uses little endian bit ordering). We then expect |11\rangle after the second measuremement as x(1) flips qubit 1 to the |1\rangle state.

Info: The backend will attempt to merge measures on separate qubits following standard commutation rules. This provides significant speedups as the number of measurements scale.

simp_job = execute(qc_simp, backend=backend)
Job Status: job has successfully run
simp_counts1 = marginal_counts(simp_job.result(), indices=[0,1]).get_counts()
simp_counts2 = marginal_counts(simp_job.result(), indices=[2,3]).get_counts()
print("Meas 1 result: ", simp_counts1)
print("Meas 2 result: ", simp_counts2)
Meas 1 result:  {'00': 51, '01': 970, '11': 3}
Meas 2 result:  {'00': 2, '01': 28, '10': 148, '11': 846}
plot_histogram([simp_counts1, simp_counts2],
               legend=['x(0); meas(0,1)', 'x(0); meas(0,1); x(1); meas(0,1)'],

Single-qubit circuit with reset

Next we combine the ability to reset qubits with mid-circuit measurements. This enables qubit reuse and is a first step in providing control flow in the future.

Before reading this section, make sure you are familiar with conditional reset on IBM Quantum systems.

In order to use reset, we must verify that the backend supports it by checking supported_instructions.

assert hasattr(config, 'supported_instructions'), 'Reset is not supported by this backend.'
assert 'reset' in config.supported_instructions, 'Reset is not supported by this backend.'

We perform the sequence h(0) -> measure(0) -> reset(0) [n times] -> x(0) -> measure(0). Without reset, we expect 50/50 0s and 1s after both the first measurement and the second measurement.

However, when the reset is included, the superposition prepared by the Hadamard gate is reset to |0\rangle . The X gate then flips the state, so after the second measurement we expect all 1s rather than an even distribution.

In this example, note that we “reuse” the qubit after the first measurement via the reset instruction. This provides flexibility in more advanced algorithms.

def h_reset_x_circ(n_resets, qubit=0):
    """Do h, then n_resets reset instructions, then x.

    Two measurements are done--one after the hadamard
    and one at the end of the circuit.
    Measurement 0 is in memory slot 0. Measurement1 is in
    memory slot 1.
    qc = QuantumCircuit(n_qubits, 2)
    qc.measure(qubit, [0])
    qc.measure(qubit, [1])
    return qc

We run this experiment on qubits 0, with 0, 1, and 3 resets. We see clear improvement after a single reset and further improvement with 3 resets.

circs_1q = [h_reset_x_circ(0), h_reset_x_circ(1), h_reset_x_circ(3)]
job_1q = execute(circs_1q, backend=backend, optimization_level=0)
Job Status: job has successfully run
counts_1q_1 = marginal_counts(job_1q.result(), indices=[0]).get_counts()
counts_1q_2 = marginal_counts(job_1q.result(), indices=[1]).get_counts()
print("Meas 1 result: ", counts_1q_1)
print("Meas 2 result: ", counts_1q_2)
Meas 1 result:  [{'0': 497, '1': 527}, {'0': 504, '1': 520}, {'0': 573, '1': 451}]
Meas 2 result:  [{'0': 504, '1': 520}, {'0': 101, '1': 923}, {'0': 38, '1': 986}]

After the first measurement, all counts are an equal distribution, as expected.

plot_histogram(counts_1q_1, legend=['h(0); meas(0)', 'h(0); meas(0)', 'h(0); meas(0)'],

After the second measurement, however, we observe that the reset pushes the counts to all 1s.

               legend=['h(0); meas(0); x(0); meas(0);',
                       'h(0); meas(0); reset(0); x(0); meas(0)',
                       'h(0); meas(0); 3x reset(0); x(0); meas(0)'],

Multi-qubit circuit with reset

This next experiment combines multi-qubit operations with reset and mid-circuit measurements. A complex circuit is considered with the possiblity of multiple resets in the middle. The expected result is given by the Aer qasm simulator (it can also be verified analytically).

Without any resets, we expect the result of the first measurement to be all 50/50 0s and 1s. We expect the result of the second measurement to give nearly equal counts in all 8 possible states.

With reset added, we expect all 1s after the first measurement and 50/50 counts for the states 010 and 110 after the second measurement.

We run the circuit with 0, 1 and 3 resets. We see an improvement for 1 reset and further improvement for 3 resets.

def multiq_custom_circ(n_resets):
    """Custom multiq circuit w/ many resets."""
    qc = QuantumCircuit(n_qubits, 4)
    qc.measure(0, 0)
    qc.cx(0, 2)
    qc.measure([0, 1, 2], [1,2,3])
    return qc
circs_multiq = [multiq_custom_circ(0), multiq_custom_circ(1), multiq_custom_circ(3)]

First we run on the simulator to verify our expected output.

# verify expected output via Aer qasm simulator
sim_job_multiq = execute(circs_multiq, backend=Aer.get_backend('qasm_simulator'), optimization_level=0)
sim_counts_multiq_1 = marginal_counts(sim_job_multiq.result(), indices=[0]).get_counts()
sim_counts_multiq_2 = marginal_counts(sim_job_multiq.result(), indices=[1,2,3]).get_counts()
print("Meas 1 sim result: ", sim_counts_multiq_1)
print("Meas 2 sim result: ", sim_counts_multiq_2)
Meas 1 sim result:  [{'0': 536, '1': 488}, {'0': 1024}, {'0': 1024}]
Meas 2 sim result:  [{'000': 141, '001': 119, '010': 116, '011': 104, '100': 137, '101': 141, '110': 142, '111': 124}, {'010': 518, '110': 506}, {'010': 493, '110': 531}]
legend_multiq_1 = ['h(0,1,2); meas(0);',
                   'h(0,1,2); reset(0); meas(0);',
                   'h(0,1,2); 3x reset(0); meas(0);']
legend_multiq_2 = ['h(0,1,2); meas(0); cx(0,2); x(1); meas(0,1,2);',
                   'h(0,1,2); reset(0); meas(0); cx(0,2); reset(1); x(1); meas(0,1,2);',
                   'h(0,1,2); 3x reset(0); meas(0); cx(0,2); 3x reset(1); x(1); meas(0,1,2);']
               title="QASM simulator")
               title="QASM simulator")

Now we run on a real backend.

job_multiq = execute(circs_multiq, backend=backend, optimization_level=0)
Job Status: job has successfully run
counts_multiq_1 = marginal_counts(job_multiq.result(), indices=[0]).get_counts()
counts_multiq_2 = marginal_counts(job_multiq.result(), indices=[1,2,3]).get_counts()
print("Meas 1 result: ", counts_multiq_1)
print("Meas 2 result: ", counts_multiq_2)
Meas 1 result:  [{'0': 470, '1': 554}, {'0': 939, '1': 85}, {'0': 991, '1': 33}]
Meas 2 result:  [{'000': 146, '001': 118, '010': 143, '011': 138, '100': 113, '101': 119, '110': 128, '111': 119}, {'000': 54, '001': 2, '010': 440, '011': 43, '100': 36, '101': 6, '110': 411, '111': 32}, {'000': 45, '010': 444, '011': 24, '100': 24, '101': 1, '110': 472, '111': 14}]

GHZ to Bell State

This example uses mid-circuit measurement to demonstrate how to convert GHZ states to Bell states. It also demonstrates how mid-circuit measurements alter the behavior of the quantum state.

Consider the canonical three-qubit GHZ gate: \frac{1}{\sqrt{2}}\left(|000\rangle + |111\rangle\right) . If one attempts to blindly measure one of the three qubits in the computational (z) basis, then the remaining two qubits are left in an unentangled state. However, by noting that a GHZ state can be written as (ignoring normalization constants):

|000\rangle + |111\rangle = \left[|00\rangle + |11\rangle\right] \otimes \left(|0\rangle+|1\rangle\right) + \left[|00\rangle - |11\rangle\right] \otimes \left(|0\rangle-|1\rangle\right) = \left[|00\rangle + |11\rangle\right] \otimes |+x\rangle + \left[|00\rangle - |11\rangle\right] \otimes |-x\rangle,

we can see that if we make a measurement of any one of the three qubits in the x-basis, then the state of the two remaining qubits is in one of two possible Bell states; that is, the two remaining qubits are still maximally entangled. Given this, it is possible to use interference to transform these Bell states back into the computational basis. The circuit below does this, mapping \left[|00\rangle + |11\rangle\right] \rightarrow |00\rangle and \left[|00\rangle - |11\rangle\right] \rightarrow |10\rangle . To explicitly show that measurement is done in the middle, we will flip the flag qubit used to record the result of the x-basis measurement and re-measure. We write the results to different classical bits so both can be displayed.

We use qubit 0 as the flag qubit in our example. For the first measurement, we expect a 50/50 distribution of 0 and 1 (on qubit 0). For the second measurement, we expect a 50/50 distribution of 001 and 100 states (with little endian ordering).

qc_ghz_bell = QuantumCircuit(3, 4)
qc_ghz_bell.cx([2,1], [1,0])
qc_ghz_bell.measure(0, 0)  # w/ h(0) gives meas in x basis
qc_ghz_bell.cx(2, 1)
qc_ghz_bell.measure([0, 1, 2], [1, 2, 3])

First, simulate to verify that we built the circuit correctly.

sim = Aer.get_backend('qasm_simulator')
sim_job_ghz_bell = execute(qc_ghz_bell, sim)
sim_counts_ghz_bell_1 = marginal_counts(sim_job_ghz_bell.result(), indices=[0]).get_counts()
sim_counts_ghz_bell_2 = marginal_counts(sim_job_ghz_bell.result(), indices=[1,2,3]).get_counts()
print("Sim meas 1 result: ", sim_counts_ghz_bell_1)
print("Sim meas 2 result: ", sim_counts_ghz_bell_2)
Sim meas 1 result:  {'0': 508, '1': 516}
Sim meas 2 result:  {'001': 508, '100': 516}

Now we try on real hardware:

job_ghz_bell = execute(qc_ghz_bell, backend, initial_layout=[1,2,3])
Job Status: job has successfully run
counts_ghz_bell_1 = marginal_counts(job_ghz_bell.result(), indices=[0]).get_counts()
counts_ghz_bell_2 = marginal_counts(job_ghz_bell.result(), indices=[1,2,3]).get_counts()
print("Meas 1 result: ", counts_ghz_bell_1)
print("Meas 2 result: ", counts_ghz_bell_2)
Meas 1 result:  {'0': 561, '1': 463}
Meas 2 result:  {'000': 155, '001': 201, '010': 23, '011': 41, '100': 156, '101': 379, '110': 30, '111': 39}
plot_histogram([counts_ghz_bell_2, sim_counts_ghz_bell_2],
               legend=['ibmq_manhattan', 'QASM simulator'],
               title='X-basis measurement of GHZ state')

Now let’s see what happens if we do the first measurement in the computational basis rather than the x basis, destroying the entanglement. Given that the state after the measurement is no longer a Bell pair, we would expect our transformation back to the computational basis to yield a different result.

qc_ghz2 = QuantumCircuit(3, 4)
qc_ghz2.cx([2,1], [1,0])
qc_ghz2.measure(0, 0)  # measure in z, not x basis
qc_ghz2.cx(2, 1)
qc_ghz2.measure([0, 1, 2], [1, 2, 3])
sim_job_ghz2 = execute(qc_ghz2, sim)
sim_counts_ghz2 = marginal_counts(sim_job_ghz2.result(), indices=[1,2,3]).get_counts()
print("Sim meas result: ", sim_counts_ghz2)
Sim meas result:  {'000': 262, '001': 260, '100': 254, '101': 248}
job_ghz2 = execute(qc_ghz2, backend, initial_layout=[1,2,3])
Job Status: job has successfully run
counts_ghz2 = marginal_counts(job_ghz2.result(), indices=[1,2,3]).get_counts()
print("Meas result: ", counts_ghz2)
Meas result:  {'000': 190, '001': 277, '010': 48, '011': 17, '100': 175, '101': 256, '110': 45, '111': 16}
plot_histogram([counts_ghz2, sim_counts_ghz2],
               legend=['ibmq_manhattan', 'QASM simulator'],
               title='Computational (z) basis measurement of GHZ state')

This code is a part of Qiskit

© Copyright IBM 2017, 2021.

This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.

Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.

[ ]: