Quantum Simulation of Time-Dependent Hamiltonians and the Convenient Illusion of Hilbert Space
Open accessAbstract
We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a well-known counting argument. This also demonstrates that a computational model based on arbitrarily rapidly changing Hamiltonians is no more powerful than the standard quantum circuit model.
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For many physical systems, both k and m are limited: 2 or 3-body interactions are the norm for fundamental processes, and higher interaction orders are generally hard to engineer.
“For many physical systems, both k and m are limited: 2 or 3-body interactions are the norm for fundamental processes, and higher interaction orders are generally hard to engineer here [37-39].”
From Enhancing the Charging Power of Quantum Batteries (2017) · cites this paper as [38]
Antisymmetrization can be enforced by reversing a suitable sorting algorithm and uncomputing ancillas to make the procedure reversible.
“Antisymmetrization can be enforced by reversing a suitable sorting algorithm and uncomputing ancillas to make the procedure reversible 286 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [286]
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- Authors
- Poulin, D., Qarry, A., Somma, R., & Verstraete, F.
- Affiliations
- Université de Sherbrooke (CA)
- Centre for Quantum Technologies (SG)
- Los Alamos National Laboratory (US)
- University of Vienna (AT)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2011-04-29
- Volume
- 106
- Issue
- 17
- Pages
- 170501-170501
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2053987271
- Cited by
- 265
- References
- 23
- Citations by year
- 2026: 9 · 2025: 29 · 2024: 18 · 2023: 19 · 2022: 37 · 2021: 41 · 2020: 17 · 2019: 14 · 2018: 8 · 2017: 14 · 2016: 6 · 2015: 12 · 2014: 13 · 2013: 9 · 2012: 15
- FWCI
- 12.07
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- National University of Singapore (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- National Science Foundation
- 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, time-dependent Hamiltonian, quantum many-body states, quantum circuit model, computational power
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