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Cited by 285Quantum Computing Algorithms and ArchitectureQuantum many-body systemsCold Atom Physics and Bose-Einstein Condensates

Solving strongly correlated electron models on a quantum computer

Open access
Wecker, Dave, Hastings, Matthew B., Wiebe, Nathan, Clark, Bryan K., Nayak, Chetan, Troyer, Matthias·2015·Physical Review A
DOI 10.1103/physreva.92.062318
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Abstract

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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Crossref · 10.1103/physreva.92.062318

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58 of 58 references verified0 citation errors · 0 not checkable

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  • In the long term, quantum simulation using quantum computers has great potential to wield a broad influence on the world.

    “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]

    The abstract (p. 1) calls simulation of quantum models a main application of future quantum computers, and the Conclusions (p. 24) say they could be a powerful tool for problems in strongly correlated electron models. These passages support substantial scientific potential, but not the broader claim of influence on the world. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • 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 decreases.

    “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]

  • The dependence of QPE run-time on the overlap of the initial and target states cannot be circumvented.

    “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]

  • Most experimental implementations so far have employed gradient-free methods that better tolerate fluctuations, such as Nelder-Mead and Particle-Swarm Optimization, and more recently SPSA has been applied.

    “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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Research works printed but not linked: 16

  1. 5 G. Ortiz, J. Gubernatis, E. Knill, and R. Laflamme, Physical Review A 64 , 022319 (2001).
  2. 8 H. F. Trotter, Proc. Amer. Math. Soc. 10 , 545 (1959).
  3. 13 D. Abrams and S. Lloyd, Physical Review Letters 79 , 2586 (1997).
  4. 14 D. Abrams and S. Lloyd, Physical Review Letters 83 , 5162 (1999).
  5. 35 P. W. Anderson, Materials Research Bulletin 8 , 153 (1973).
  6. 38 R. M. Fye, D. J. Scalapino, and R. T. Scalettar, Physical Review B 46 , 8667 (1992).
  7. 39 E. Altman and A. Auerbach, Physical Review B 65 , 104508 (2002).
  8. 40 H. Tsunetsugu, M. Troyer, and T. M. Rice, Physical Review B 49 , 16078 (1994).
  9. 41 M. Troyer, H. Tsunetsugu, and T. M. Rice, Physical Review B 53 , 251 (1996).
  10. 42 P. W. Anderson, P. A. Lee, M. Randeria, T. M. Rice, N. Trivedi, and F. C. Zhang, Journal of Physics: Condensed Matter 16 , R755 (2004).
  11. 44 J. Roland and N. J. Cerf, Physical Review A 65 , 042308 (2002).
  12. 45 D. A. Lidar, A. T. Rezakhani, and A. Hamma, Journal of Mathematical Physics 50 , 102106 (2009).
  13. 46 N. Wiebe and N. S. Babcock, New Journal of Physics 14 , 013024 (2012).
  14. 47 N. Wiebe, D. Berry, P. Høyer, and B. C. Sanders, Journal of Physics A: Mathematical and Theoretical 43 , 065203 (2010).
  15. 51 J. Huyghebaert and H. De Raedt, Journal of Physics A: Mathematical and General 23 , 5777 (1990).
  16. 52 R. Babbush, J. McClean, D. Wecker, A. Aspuru-Guzik, and N. Wiebe, Physical Review A 91 , 022311 (2015).

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Authors
Wecker, D., Hastings, M. B., Wiebe, N., Clark, B. K., Nayak, C., & Troyer, M.
Affiliations
  • Microsoft (United States) (US)
  • ETH Zurich (CH)
ORCID
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
DOI
10.1103/physreva.92.062318
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
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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