Recursive Variational Quantum Compiling
Variational quantum compiling (VQC) algorithms aim to approximate deep
quantum circuits with shallow parameterized ansatzes, making them more suitable
for NISQ hardware. In this article a variant of VQC named the recursive
variational quantum compiling (RVQC) algorithm is proposed. Existing VQC
algorithms typically require coherently executing the full circuit during
compilation. Under the influence of noise, sufficiently deep target circuits
make compiling unfeasible using ordinary VQC. Since the compiling is often
accomplished using a gradient-based quantum-classical approach, the quantum
noise manifest as a noisy gradient during optimization, making convergence hard
to obtain. On the other hand, RVQC can compile a circuit by first dividing it
into $N$ shorter sub-circuits, then evaluate one sub-circuit at a time. As a
result, the circuit depth required to implement RVQC is not dependent on the
depth of the target circuit, but on the depth of the sub-circuits. Choosing a
high enough $N$ thus ensures sufficiently shallow sub-circuit which can be
successfully compiled individually. RVQC was compared with VQC on a noise model
of the IBM Santiago device with the goal of compiling several randomly
generated five-qubit circuits of approximately depth 1000. It was shown that
VQC was not able to converge within 500 iterations of optimization. On the
other hand, RVQC was able to converge to a fidelity of $0.90 \pm 0.05$ within a
total of 500 iterations when splitting the target circuits into $N = 5$ parts.
Stian Bilek Kristian Wold