Single-qubit gates merger
All single-qubit gates appearing in a circuit can be merged by using the single-qubit gates merging pass
(SingleQubitGatesMerger).
Note that multi-qubit gates remain untouched and single-qubit gates are not merged across any multi-qubit gates.
Single-qubit gates are also not merged across non-unitary instructions, e.g. init, reset, and measure,
and control instructions, e.g., wait, and barrier.
Merging single-qubit gates may lead to a significant reduction in circuit depth, i.e.,
the number of operations required to execute the circuit.
OpenSquirrel will try to recognize whether the resulting gate is a known gate, e.g., if two consecutive X90 gates are merged, OpenSquirrel will recognize it as a single X gate. Nevertheless, the gate that results from the merger of multiple single-qubit gates will, in general, be an arbitrary rotation. Accordingly, to be able to run the circuit on a particular backend that supports a given primitive gate set, it is often required to perform a decomposition pass after merging the single-qubit gates.
Note
Depending on the circuit and chosen decomposition, the circuit depth might actually increase,
even though a merging pass has been applied.
For instance, if the merging of two single-qubit gates leads to an arbitrary single-qubit rotation gate
and the McKayDecomposer is used, then the two initial gates may
ultimately result in five single-qubit rotation gates.
This is demonstrated in the final example below.
The example below shows how the single-qubit gates merging pass can be used to merge the single-qubit gates in the
circuit.
Note that the SingleQubitGatesMerger pass does not require any input arguments.
Check the circuit builder on how to generate a circuit.
from opensquirrel import CircuitBuilder
from opensquirrel.passes.merger import SingleQubitGatesMerger
from math import pi # not necessary for using the SingleQubitGatesMerger
builder = CircuitBuilder(1)
for _ in range(4):
builder.Rx(0, pi / 4)
circuit = builder.to_circuit()
circuit.merge(merger=SingleQubitGatesMerger())
The above example shows how four consecutive Rx rotations over \(\pi/4\), are merged into a single Rx rotation over \(\pi\).
The following example shows that the merging of single-qubit gates does not occur across multi-qubit gates, non-unitary instructions, and control instructions.
builder = CircuitBuilder(2, 2)
builder.Ry(0, pi / 2).X(0).CNOT(0, 1).H(0).X(1)
builder.barrier(1)
builder.H(0).X(1).measure(0, 0).H(0).X(1)
circuit = builder.to_circuit()
circuit.merge(merger=SingleQubitGatesMerger())
print(circuit)
Note
In the above example, note that even though the barrier is placed on qubit at index 1,
that the Hadamards (H) on qubit at index 0 on either side of that barrier are not merged.
Barriers are unique in this regard; no merging of single-qubit gates occurs across barriers
regardless of the qubit on which the barrier acts.
The final example below shows how the circuit depth ultimately increases, even though the single-qubit gates where merged using the single-qubit gates merging pass.