Unconventional quantum annealing methods for difficult trial problems
Open accessAbstract
We consider a range of unconventional modifications to quantum annealing (QA), applied to an artificial trial problem with continuously tunable difficulty. In this problem, inspired by ``transverse field chaos'' in larger systems, classical and quantum methods are steered toward a false local minimum. To go from this local minimum to the global minimum, all $N$ spins must flip, making this problem exponentially difficult to solve. We numerically study this problem by using a variety of new methods from the literature: inhomogeneous driving, adding transverse couplers, and other types of coherent oscillations in the transverse field terms (collectively known as RFQA, which stands for Random Field Quantum Annealing or Radio Frequency Quantum Annealing). We show that all of these methods improve the scaling of the time to solution (relative to the standard uniform sweep evolution) in at least some regimes. Comparison of these methods could help identify promising paths towards a demonstrable quantum speedup over classical algorithms in solving some realistic problems with near-term quantum annealing hardware.
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Adaptations to standard QA comprise the utilization of time-dependent Hamiltonians, non-stoquastic Hamiltonians, transverse couplers, and counter-diabatic driving terms.
“Adaptations to the standard QA mentioned in Section 2 comprise the utilization of timedependent Hamiltonians [136], non-stoquastic Hamiltonians [62], transverse couplers [136], and counter-diabatic driving terms [111].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [136]
Adapted annealing schedules, reverse annealing, and spatially inhomogeneous driving represent possible adaptations to the annealing procedure in QA.
“In this regard, adapted annealing schedules [27, 88], reverse annealing [62], as well as spatially inhomogeneous driving [136] represent according possible adaptations.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [136]
Proposals to overcome the problem of a shrinking spectral gap include inhomogeneous driving, RFQA-M, and RFQA-D.
“Proposals to overcome the problem of a shrinking spectral gap: inhomogeneous driving, RFQA-M, RFQA-D [136].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [136]
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Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study
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“Tang and Kapit [136] provide an empirical benchmark study on mitigation techniques concerning the shrinking energy gap.”
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- Authors
- Tang, Z., & Kapit, E.
- Affiliations
- Colorado School of Mines (US)
- ORCID
- Kapit, Eliot
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2021-03-22
- Volume
- 103
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W3101542424
- Cited by
- 8
- References
- 68
- Citations by year
- 2026: 1 · 2025: 3 · 2023: 1 · 2022: 2 · 2021: 1
- FWCI
- 0.35
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (PHY-1653820)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- quantum annealing, coherent oscillations, solution time, spin systems, quantum advantage, near-term quantum devices
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