Approximate Boltzmann distributions in quantum approximate optimization

Journal Article · 11 October 2023 · Physical Review A

DOI: https://doi.org/10.1103/physreva.108.042411 · OSTI ID:2203825

Lotshaw, Phillip C.  ^[1]; Siopsis, George  ^[2]; Ostrowski, James ^[2]; Herrman, Rebekah ^[2]; Alam, Rizwanul ^[2]; Powers, Sarah  ^[1]; Humble, Travis S. ^[1]

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1. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
2. University of Tennessee, Knoxville, TN (United States)

Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from QAOA circuits solving 7200 random MaxCut instances, with $$n$$ = 14–23 qubits and depth parameter $$p$$ ≤ 12 and find that the average basis state probabilities follow approximate Boltzmann distributions: The average probabilities scale exponentially with their energy (cut value), with a peak at the optimal solution. Furthermore, we describe the rate of exponential scaling or effective temperature in terms of a series with a leading-order term $$T$$ ~ $$C$$_min/$$n$$ $$\sqrt{p}$$, with $$C$$_min the optimal solution energy. Using this scaling, we generate approximate output distributions with up to 38 qubits and find these give accurate accounts of important performance metrics in cases we can simulate exactly.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); National Science Foundation (NSF)
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 2203825
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 4 Vol. 108; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English