Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian Using Nuclear Magnetic Resonance
Open accessAbstract
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm proposed by Wu, Byrd, and Lidar [Phys. Rev. Lett. 89, 057904 (2002).10.1103/PhysRevLett.89.057904] to find the low-lying spectrum of a pairing Hamiltonian. While the number of elementary quantum gates required scales polynomially with the size of the system, it increases inversely to the desired error bound E. Making such simulations robust to decoherence using fault tolerance requires an additional factor of approximately 1/E gates. These constraints, along with the effects of control errors, are illustrated using a three qubit NMR system.
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When digital quantum simulation operates with fault-tolerant quantum error correction, its output can be trusted to a known finite precision.
“When such a digital quantum simulation operates with fault-tolerant quantum error correction [63], we can trust its output to a known finite precision.”
From Can one trust quantum simulators? (2012) · cites this paper as [63]
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“[15] establish limits of quantum simulation.”
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Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
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“Moreover, locality from global observables, consisting of a sum of local observables, also leads to short-time advantages.”
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Quantum Computing Resource Estimate of Molecular Energy SimulationPreprint
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Error scaling in fault tolerant quantum computation
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Quantum Algorithms and Complexity for Continuous Problems
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- Authors
- Brown, K. R., Clark, R. J., & Chuang, I. L.
- Affiliations
- Massachusetts Institute of Technology (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-08-04
- Volume
- 97
- Issue
- 5
- Pages
- 050504-050504
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2025107850
- Cited by
- 98
- References
- 34
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 4 · 2022: 3 · 2021: 2 · 2019: 4 · 2018: 5 · 2017: 2 · 2016: 1 · 2015: 6 · 2014: 9 · 2013: 6 · 2012: 9
- FWCI
- 6.47
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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 simulation, pairing Hamiltonian, NMR quantum computing, low-lying spectrum, fault tolerance, decoherence, control error, three-qubit systems
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