Abstract
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently understood about QAOA's performance beyond its lowest-depth variant. An essential but missing ingredient for understanding and deploying QAOA is a constructive approach to carry out the outer-loop classical optimization. We provide an in-depth study of the performance of QAOA on MaxCut problems by developing an efficient parameter-optimization procedure and revealing its ability to exploit non-adiabatic operations. Building on observed patterns in optimal parameters, we propose heuristic strategies for initializing optimizations to find quasi-optimal $p$-level QAOA parameters in $O(\text{poly}(p))$ time, whereas the standard strategy of random initialization requires $2^{O(p)}$ optimization runs to achieve similar performance. We then benchmark QAOA and compare it with quantum annealing, especially on difficult instances where adiabatic quantum annealing fails due to small spectral gaps. The comparison reveals that QAOA can learn via optimization to utilize non-adiabatic mechanisms to circumvent the challenges associated with vanishing spectral gaps. Finally, we provide a realistic resource analysis on the experimental implementation of QAOA. When quantum fluctuations in measurements are accounted for, we illustrate that optimization will be important only for problem sizes beyond numerical simulations, but accessible on near-term devices. We propose a feasible implementation of large MaxCut problems with a few hundred vertices in a system of 2D neutral atoms, reaching the regime to challenge the best classical algorithms.
Highlights
As quantum computing technology develops, there is a growing interest in finding useful applications of near-term quantum machines [1]
Comparing the quantum approximate optimization algorithm (QAOA) with quantum annealing, we find that the former can learn via optimization to utilize diabatic mechanisms [15,16,17,18] and overcome the challenges faced by adiabatic quantum annealing due to very small spectral gaps
III, we describe some patterns found for QAOA optimal parameters and introduce heuristic optimization strategies based on the observed patterns
Summary
As quantum computing technology develops, there is a growing interest in finding useful applications of near-term quantum machines [1]. Even at the lowest circuit depth (p 1⁄4 1), the QAOA has nontrivial provable performance guarantees [2,10] and is not efficiently simulatable by classical computers [11] It is, an appealing algorithm to explore quantum speedups on near-term quantum machines. Based on the observed patterns, we develop strategies for selecting initial parameters in optimization, which allow us to efficiently optimize the QAOA at a cost scaling polynomially in p This scaling is in stark contrast to the 2OðpÞ optimization runs required by random initialization approaches. Considering realistic experimental implementations, we study the effects of quantum “projection noise” in measurement: We find that, for numerically accessible problem sizes, the QAOA can often obtain the solution among measurement outputs before the best variational parameters are found.
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