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Solving strongly correlated electron models on a quantum computer
Open accessAbstract
One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine the ground state phase diagram of a quantum model and the properties of its phases is more involved. Using the Hubbard model as a prototypical example, we here show all the steps necessary to determine its phase diagram and ground state properties on a quantum computer. In particular, we discuss strategies for efficiently determining and preparing the ground state of the Hubbard model starting from various mean-field states with broken symmetry. We present an efficient procedure to prepare arbitrary Slater determinants as initial states and present the complete set of quantum circuits needed to evolve from these to the ground state of the Hubbard model. We show that, using efficient nesting of the various terms each time step in the evolution can be performed with just $\mathcal{O}(N)$ gates and $\mathcal{O}(\log N)$ circuit depth. We give explicit circuits to measure arbitrary local observables and static and dynamic correlation functions, both in the time and frequency domain. We further present efficient non-destructive approaches to measurement that avoid the need to re-prepare the ground state after each measurement and that quadratically reduce the measurement error.
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“In the long term, quantum simulation using quantum computers has great potential to wield a broad influence on the world [48, 49, 50].”
From Quantum Computing in the NISQ era and beyond (2018) · cites this paper as [49]
Experimental — accuracy not yet measuredIn the citing paper
“The cost of estimating the correct ground state energy depends directly on the overlap of the initial state with the ground state, and it becomes progressively more expensive as the overlap with the correct ground state decreases [20, 48–50].”
From Drug design on quantum computers (2024) · cites this paper as [48]
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“Even though the run-time has improved over time [48, 49], the dependence on the overlap of the initial and target states cannot be circumvented [50].”
From Drug design on quantum computers (2024) · cites this paper as [48]
In the citing paper
“Correspondingly, most of the experimental implementations so far have employed methods that better tolerate these fluctuations, such as Nelder-Mead and Particle-Swarm Optimization (PSO) 353 , which are gradient free. More recently the Simultaneous Perturbation Stochastic Approximation (SPSA) has been applied 354,355 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [354]
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- M. B. Hastings, 2015, Quantum Inf. Comput., 15, 1
- D. Poulin, 2015, Quantum Inf. Comput., 15, 361
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Quantum Computing in the NISQ era and beyond
Preskill, J. (2018) · Quantum · doi:10.22331/q-2018-08-06-79 · Cited by 8,830
“ena where quantum computers seem to have a clear advantage over classical ones. In the long term, quantum simulation using quantum computers has great potential to wield a broad influence on the world [42, 43, 44]. Advances in quantum chemistry, facilitated by quantum computing, might precipitate the design of new phar…”
BackgroundQuantum computational chemistry
McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C., & Yuan, X. (2020) · Reviews of Modern Physics · doi:10.1103/revmodphys.92.015003 · Cited by 1,621
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Metadata
- Authors
- Wecker, D., Hastings, M. B., Wiebe, N., Clark, B. K., Nayak, C., & Troyer, M.
- Affiliations
- Microsoft (United States) (US)
- ETH Zurich (CH)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2015-12-10
- Volume
- 92
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2167110831
- Cited by
- 285
- References
- 52
- Citations by year
- 2026: 12 · 2025: 41 · 2024: 31 · 2023: 40 · 2022: 39 · 2021: 36 · 2020: 34 · 2019: 16 · 2018: 20 · 2017: 9 · 2016: 7
- FWCI
- 11.74
- 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 (1066293)
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- European Research Council (SIMCOFE)
- Aspen Center for Physics
- 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 › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Keywords
- Hubbard model, strongly correlated electrons, quantum simulation, ground state preparation, phase diagram, Slater determinants, quantum circuits, circuit depth, correlation functions, non-destructive measurement, measurement error reduction, quantum computing
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