Noise resilient compilation policies for quantum approximate optimization algorithm

Abstract

Quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid algorithm to solve hard combinatorial optimization problems using noisy quantum devices. The multiqubit CPHASE gates used in the quantum circuit for QAOA are commutative i.e., the order of the gates can be altered without changing the output state. This re-ordering leads to the execution of more gates in parallel and a smaller number of additional SWAP gates to compile the QAOA circuit resulting in lower circuit-depth and gate-count. A less number of gates generally indicates a lower accumulation of gate-errors, and a reduced circuit-depth means less decoherence time for the qubits. However, near-term quantum devices exhibit significant variations in the gate success probabilities. Variation-aware compilation policies (i.e. putting most gate operations on qubits with higher gate success probabilities) can enhance the probability of successful program execution on the hardware. The greater flexibility of QAOA-circuits offer better scope of optimization with QAOA-tailored compilation policies. This paper presents an argument for compilation policies to exploit the unique characteristics of QAOA-circuits alongside the variation-awareness of the noisy devices. We present two procedures - variation-aware qubit placement (VQP) and variation-aware iterative mapping (VIM) that can improve the circuit success probability quite significantly (≈8.408X on average) for a set of QAOA-MaxCut problems on ibmq_16_melbourne.