How to measure a qubit and depending on measurement outcome act with a gate (cirq)

Question

Is there a way on cirq that I can make a measurement on a qubit, and depending on the outcome of that measurement act with another gate on that qubit. So, I want to measure a qubit (in the computational basis) and then apply a gate (say the Y gate) on that qubit if the measurement outcome was $|1\rangle$. Is this possible?

Answer 1

Use cirq.Operation.with_classical_controls.

import cirq
q = cirq.LineQubit(0)
c = cirq.Circuit(
    cirq.H(q),
    cirq.measure(q, key="before"),
    cirq.X(q).with_classical_controls("before"),
    cirq.measure(q, key="after"),
)
print(c)
print(cirq.Simulator().sample(c, repetitions=10))

0: ────────H───M───X───M('after')───
               ║   ║
before: ═══════@═══^════════════════

   before  after
0       0      0
1       1      0
2       1      0
3       1      0
4       0      0
5       0      0
6       1      0
7       0      0
8       0      0
9       0      0

Answer 2

The term you're looking for is "classical control" - see Cirq classical control documentation here. You will need to store the measurement result and then apply a classically-controlled operation based on the measurement value. The first example on the page is shown below, which applies an H gate on q1 when q0 is measured to be 1.

q0, q1 = cirq.LineQubit.range(2)
circuit = cirq.Circuit(
    cirq.H(q0),
    cirq.measure(q0, key='a'),
    cirq.H(q1).with_classical_controls('a'),
    cirq.measure(q1, key='b'),
)