Abstract
The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical algorithm that seeks to achieve approximate solutions to optimization problems by iteratively alternating between intervals of controlled quantum evolution. Here, we examine the effect of analog precision errors on QAOA performance from the perspective of both algorithmic training and performance guarantees. Leveraging cumulant expansions, we recast the faulty QAOA as a control problem in which precision errors are expressed as multiplicative control noise and derive bounds on the performance of QAOA. We show using both analytical techniques and numerical simulations that fixed precision implementations of QAOA circuits are subject to an exponential degradation in performance dependent upon the number of optimal QAOA layers and magnitude of the precision error. Despite this significant reduction, we show that it is possible to mitigate precision errors in QAOA via digitization of the variational parameters at the cost of increasing circuit depth.
| Original language | English |
|---|---|
| Article number | 023240 |
| Journal | Physical Review Research |
| Volume | 7 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 2025 |
Funding
G.Q., P.T., P. Lougovski, K.S., E.D., and I.H. acknowledge funding from the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research (ASCR) Quantum Computing Application Teams program, under fieldwork Proposal No. ERKJ347 and the Accelerated Research in Quantum Computing program under Awards No. DE-SC0020316 and No. DE-SC0025509. P. Lotshaw was supported at ORNL by the Defense Advanced Research Project Agency, Defense Science Office under Contract No. HR001120C0046 with Georgia Tech Research Institute. This work has been partially supported by U.S. DOE Grant No. DE-FG02-13ER41967. ORNL is managed by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 for the U.S. Department of Energy. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. Government purposes.