Optimization using quantum mechanics: quantum annealing through adiabatic evolution
Open accessAbstract
We review here some recent work in the field of quantum annealing, alias adiabatic quantum computation. The idea of quantum annealing is to perform optimization by a quantum adiabatic evolution which tracks the ground state of a suitable time-dependent Hamiltonian, where 'ℏ' is slowly switched off. We illustrate several applications of quantum annealing strategies, starting from textbook toy-models—double-well potentials and other one-dimensional examples, with and without disorder. These examples display in a clear way the crucial differences between classical and quantum annealing. We then discuss applications of quantum annealing to challenging hard optimization problems, such as the random Ising model, the travelling salesman problem and Boolean satisfiability problems. The techniques used to implement quantum annealing are either deterministic Schrödinger's evolutions, for the toy models, or path-integral Monte Carlo and Green's function Monte Carlo approaches, for the hard optimization problems. The crucial role played by disorder and the associated non-trivial Landau–Zener tunnelling phenomena is discussed and emphasized.
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During the adiabatic process, entangled qubits naturally evolve into the ground state of a given Hamiltonian to find the optimal vector of binary decisions for the corresponding QUBO problem.
“During this process, entangled qubits naturally evolve into the ground state of a given Hamiltonian to fi nd the optimal vector of binary decisions for the corresponding quadratic unconstrained binary optimization (QUBO) problem 8 -10 .”
From Quantum annealing for combinatorial optimization: a benchmarking study (2025) · cites this paper as [8]
Section 1.1 explains that annealing aims to reach the ground state of a Hamiltonian encoding an optimization problem, and §1.3 says the system follows that ground state if the annealing is sufficiently slow. The paper does not specifically describe a QUBO problem or an optimal vector of binary decisions. It also describes the initial spin state as a product state, not as entangled qubits that naturally reach the optimum without an adiabaticity condition. Page numbers are unavailable in our copy. (LLM, conf=0.86)
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References 89 · Cited by 354
Research works printed but not linked: 8
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- [82]82. Das A and Chakrabarti B K 2005 Quantum Annealing and Related Optimization Methods ed A Das and B K Chakrabarti (Berlin: Springer) p 217
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- Authors
- Santoro, G. E., & Tosatti, E.
- Affiliations
- The Abdus Salam International Centre for Theoretical Physics (ICTP) (IT)
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2006-08-18
- Volume
- 39
- Issue
- 36
- Pages
- R393-R431
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2040797887
- Cited by
- 354
- References
- 89
- Citations by year
- 2026: 9 · 2025: 30 · 2024: 21 · 2023: 24 · 2022: 20 · 2021: 23 · 2020: 25 · 2019: 24 · 2018: 24 · 2017: 20 · 2016: 18 · 2015: 23 · 2014: 14 · 2013: 5 · 2012: 10
- FWCI
- 14.83
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- SDL (submittedVersion)
- Funders
- Ministero dell’Istruzione, dell’Università e della Ricerca (COFIN-2003)
- 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 › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- quantum annealing, adiabatic quantum computation, optimization, double-well potential, disorder, random Ising model, traveling salesman problem, Boolean satisfiability, path integral Monte Carlo, Green's function Monte Carlo
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