Dynamic-ADAPT-QAOA: An algorithm with shallow and noise-resilient circuits

TL;DR

Dynamic-ADAPT-QAOA is a new algorithm that reduces circuit depth and noise sensitivity for quantum optimization on NISQ devices by dynamically selecting operations, outperforming standard ADAPT-QAOA in noise resilience.

Contribution

It introduces a dynamic approach to ADAPT-QAOA that significantly lowers circuit depth and enhances noise resilience for near-term quantum hardware.

Findings

Dynamic-ADAPT-QAOA reduces CNOT count compared to standard ADAPT-QAOA.

It achieves an order-of-magnitude improvement in noise resilience.

The algorithm remains effective for systems with 6-10 qubits at gate-error probabilities above 10^{-3}.

Abstract

The quantum approximate optimization algorithm (QAOA) is an appealing proposal to solve NP problems on noisy intermediate-scale quantum (NISQ) hardware. Making NISQ implementations of the QAOA resilient to noise requires short ansatz circuits with as few CNOT gates as possible. Here, we present Dynamic-ADAPT-QAOA. Our algorithm significantly reduces the circuit depth and the CNOT count of standard ADAPT-QAOA, a leading proposal for near-term implementations of the QAOA. Throughout our algorithm, the decision to apply CNOT-intensive operations is made dynamically, based on algorithmic benefits. Using density-matrix simulations, we benchmark the noise resilience of ADAPT-QAOA and Dynamic-ADAPT-QAOA. We compute the gate-error probability $p_\text{gate}^\star$ below which these algorithms provide, on average, more accurate solutions than the classical, polynomial-time approximation algorithm by Goemans and Williamson. For small systems with $6-10$ qubits, we show that $p_{\text{gate}}^\star>10^{-3}$ for Dynamic-ADAPT-QAOA. Compared to standard ADAPT-QAOA, this constitutes an order-of-magnitude improvement in noise resilience. This improvement should make Dynamic-ADAPT-QAOA viable for implementations on superconducting NISQ hardware, even in the absence of error mitigation.