Classical feedforward and control flow

• Package versions

  The code on this page was developed using the following requirements. We recommend using these versions or newer.

  qiskit[all]~=2.3.1
  

Dynamic circuits are powerful tools with which you can measure qubits in the middle of a quantum circuit execution and then perform classical logic operations within the circuit, based on the outcome of those mid-circuit measurements. This process is also known as classical feedforward. While these are early days of understanding how best to take advantage of dynamic circuits, the quantum research community has already identified a number of use cases, such as the following:

• Efficient quantum state preparation, such as GHZ state, W-state (for more information about W-state, also refer to "State preparation by shallow circuits using feed forward"), and a broad class of matrix product states
• Efficient long-range entanglement between qubits on the same chip by using shallow circuits
• Efficient sampling of IQP-like circuits

if statement

The if statement is used to conditionally perform operations based on the value of a classical bit or register.

In the example below, we apply a Hadamard gate to a qubit and measure it. If the result is 1, then we apply an X gate on the qubit, which has the effect of flipping it back to the 0 state. We then measure the qubit again. The resulting measurement outcome should be 0 with 100% probability.

from qiskit.circuit import QuantumCircuit, QuantumRegister, ClassicalRegister

qubits = QuantumRegister(1)
clbits = ClassicalRegister(1)
circuit = QuantumCircuit(qubits, clbits)
(q0,) = qubits
(c0,) = clbits

circuit.h(q0)
# Use MidCircuitMeasure() if it's supported by the backend.
# circuit.append(MidCircuitMeasure(), [q0], [c0])
circuit.measure(q0, c0)
with circuit.if_test((c0, 1)):
    circuit.x(q0)
circuit.measure(q0, c0)
circuit.draw("mpl")

# example output counts: {'0': 1024}

Output:

The with statement can be given an assignment target which is itself a context manager that can be stored and subsequently used to create an else block, which is executed whenever the contents of the if block are not executed.

In the example below, we initialize registers with two qubits and two classical bits. We apply a Hadamard gate to the first qubit and measure it. If the result is 1, then we apply a Hadamard gate on the second qubit; otherwise, we apply an X gate on the second qubit. Finally, we measure the second qubit as well.

qubits = QuantumRegister(2)
clbits = ClassicalRegister(2)
circuit = QuantumCircuit(qubits, clbits)
(q0, q1) = qubits
(c0, c1) = clbits

circuit.h(q0)
circuit.measure(q0, c0)
with circuit.if_test((c0, 1)) as else_:
    circuit.h(q1)
with else_:
    circuit.x(q1)
circuit.measure(q1, c1)

circuit.draw("mpl")

# example output counts: {'01': 260, '11': 272, '10': 492}

Output:

In addition to conditioning on a single classical bit, it's also possible to condition on the value of a classical register composed of multiple bits.

In the example below, we apply Hadamard gates to two qubits and measure them. If the result is 01, that is, the first qubit is 1 and the second qubit is 0, then we apply an X gate to a third qubit. Finally, we measure the third qubit. Note that for clarity, we chose to specify the state of the third classical bit, which is 0, in the if condition. In the circuit drawing, the condition is indicated by the circles on the classical bits being conditioned on. A solid circle indicates conditioning on 1, while an outlined circle indicates conditioning on 0.

qubits = QuantumRegister(3)
clbits = ClassicalRegister(3)
circuit = QuantumCircuit(qubits, clbits)
(q0, q1, q2) = qubits
(c0, c1, c2) = clbits

circuit.h([q0, q1])
circuit.measure(q0, c0)
circuit.measure(q1, c1)
with circuit.if_test((clbits, 0b001)):
    circuit.x(q2)
circuit.measure(q2, c2)

circuit.draw("mpl")

# example output counts: {'101': 269, '011': 260, '000': 252, '010': 243}

Output:

Classical expressions

The Qiskit classical expression module qiskit.circuit.classical contains an exploratory representation of runtime operations on classical values during circuit execution. Due to hardware limitations, only QuantumCircuit.if_test() conditions are currently supported.

The following example shows that you can use the calculation of the parity to create an n-qubit GHZ state using dynamic circuits. First, generate $n/2$ Bell pairs on adjacent qubits. Then, glue these pairs together using a layer of CNOT gates in between pairs. You then measure the target qubit of all prior CNOT gates and reset each measured qubit to the state $\vert 0 \rangle$. You apply $X$ to every unmeasured site for which the parity of all preceding bits is odd. Finally, CNOT gates are applied to the measured qubits to re-establish the entanglement lost in the measurement.

In the parity calculation, the first element of the constructed expression involves lifting the Python object mr[0] to a Value node (lift is used to turn arbitrary objects into classical expressions). This is not necessary for mr[1] and the possible following classical register, as they are inputs to expr.bit_xor, and any necessary lifting is done automatically in these cases. Such expressions can be built up in loops and other constructs.

from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.circuit.classical import expr

num_qubits = 8
if num_qubits % 2 or num_qubits < 4:
    raise ValueError("num_qubits must be an even integer ≥ 4")
meas_qubits = list(range(2, num_qubits, 2))  # qubits to measure and reset

qr = QuantumRegister(num_qubits, "qr")
mr = ClassicalRegister(len(meas_qubits), "m")
qc = QuantumCircuit(qr, mr)

# Create local Bell pairs
qc.reset(qr)
qc.h(qr[::2])
for ctrl in range(0, num_qubits, 2):
    qc.cx(qr[ctrl], qr[ctrl + 1])

# Glue neighboring pairs
for ctrl in range(1, num_qubits - 1, 2):
    qc.cx(qr[ctrl], qr[ctrl + 1])

# Measure boundary qubits between pairs,reset to 0
for k, q in enumerate(meas_qubits):
    qc.measure(qr[q], mr[k])
    qc.reset(qr[q])

# Parity-conditioned X corrections
# Each non-measured qubit gets flipped iff the parity (XOR) of all
# preceding measurement bits is 1
for tgt in range(num_qubits):
    if tgt in meas_qubits:  # skip measured qubits
        continue
    # all measurement registers whose physical qubit index < tgt
    left_bits = [k for k, q in enumerate(meas_qubits) if q < tgt]
    if not left_bits:  # skip if list empty
        continue

    # build XOR-parity expression
    parity = expr.lift(
        mr[left_bits[0]]
    )  # lift the first bit to Value so it will be treated like a boolean.
    for k in left_bits[1:]:
        parity = expr.bit_xor(
            mr[k], parity
        )  # calculate parity with all other bits
    with qc.if_test(parity):  # Add X if parity is 1
        qc.x(qr[tgt])

# Re-entangle measured qubits
for ctrl in range(1, num_qubits - 1, 2):
    qc.cx(qr[ctrl], qr[ctrl + 1])

qc.draw(output="mpl", style="iqp", idle_wires=False, fold=-1)

Output:

Next steps