Quantum circuits for strongly correlated quantum systems
Open accessAbstract
We present an approach to gain detailed control on the quantum simulation of strongly correlated quantum many-body systems by constructing the explicit finite quantum circuits that diagonalize their dynamics. As a particularly simple instance, the full dynamics of a one-dimensional Quantum Ising model in a transverse field with four spins is shown to be reproduced using a quantum circuit of only six local gates. This opens up the possibility of experimentally producing strongly correlated states, their time evolution at zero time, and even thermal superpositions at zero temperature. Our method also allows one to uncover the exact circuits corresponding to models that exhibit topological order and to stabilizer states.
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Quantum circuits that diagonalize spin Hamiltonians have been proposed in recent years.
“As a specific example of an application benchmark, quantum circuits that diagonalize spin Hamiltonians have been proposed in recent years (Cervera-Lierta, 2018; Schmoll and Orús, 2017; Verstraete et al. , 2009).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Verstraete et al., 2009
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Fermionic wave packet scattering: a quantum computing approach
Chai, Y., Crippa, A., Jansen, K., Kühn, S., Pascuzzi, V. R., Tacchino, F., & Tavernelli, I. (2025) · Quantum · doi:10.22331/q-2025-02-19-1638 · Cited by 15 · see citing works
Conformal Field Theory from Lattice Fermions
Osborne, T. J., & Stottmeister, A. (2022) · Communications in Mathematical Physics · doi:10.1007/s00220-022-04521-8 · Cited by 13 · see citing works
Large-scale simulations of Floquet physics on near-term quantum computers
Eckstein, T., Mansuroglu, R., Czarnik, P., Zhu, J., Hartmann, M. J., Cincio, Ł., Sornborger, A. T., & Holmes, Z. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00866-1 · Cited by 11 · see citing works
On the geometry of stabilizer states
García, H. J., Markov, I. L., & Cross, A. W. (2014) · Quantum Information and Computation · doi:10.5555/2638682.2638691 · Cited by 11 · see citing works
Robbins, K., & Love, P. J. (2021) · Physical Review A · doi:10.1103/physreva.104.022412 · Cited by 11 · see citing works
Rizzi, M., Montangero, S., Silvi, P., Giovannetti, V., & Fazio, R. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/7/075018 · Cited by 10 · see citing works
Protecting subspaces by acting on the outside
Busch, J., & Beige, A. (2010) · Journal of Physics Conference Series · doi:10.1088/1742-6596/254/1/012009 · Cited by 10 · see citing works
Compressed quantum metrology for the Ising Hamiltonian
Boyajian, W. L., Skotiniotis, M., Dür, W., & Kraus, B. (2016) · Physical Review A · doi:10.1103/physreva.94.062326 · Cited by 10 · see citing works
Preparing ground states with a broken symmetry with variational quantum algorithms
Vogt, N., Zanker, S., Reiner, J.-M., Marthaler, M., Eckl, T., & Marusczyk, A. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/abe568 · Cited by 15 · see citing works
A hybrid quantum-classical method for electron-phonon systems
Denner, M. M., Miessen, A., Yan, H., Tavernelli, I., Neupert, T., Demler, E., & Wang, Y. (2023) · Communications Physics · doi:10.1038/s42005-023-01353-3 · Cited by 9 · see citing works
Variational Quantum Computing for Quantum Simulation: Principles, Implementations, and Challenges
Galvão, L. Q., de Souza, A. B. M., Moret, M. A., & Cruz, C. (2025) · Brazilian Journal of Physics · doi:10.1007/s13538-025-01946-z · Cited by 8 · see citing works
Efficient Ancilla-Free Reversible and Quantum Circuits for the Hidden Weighted Bit Function
Bravyi, S. B., Yoder, T. J., & Maslov, D. (2021) · IEEE Transactions on Computers · doi:10.1109/tc.2021.3076435 · Cited by 8 · see citing works
Simulation of gauge transformations on systems of ultracold atoms
Boada, O., Celi, A., Latorre, J. I., & Picó, V. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/11/113055 · Cited by 8 · see citing works
Self-citationCompressed simulation of thermal and excited states of the one-dimensional XY model
Boyajian, W. L., & Kraus, B. (2015) · Physical Review A · doi:10.1103/physreva.92.032323 · Cited by 8 · see citing works
From entanglement renormalisation to the disentanglement of quantum double models
Aguado, M. (2011) · Annals of Physics · doi:10.1016/j.aop.2011.07.007 · Cited by 7 · see citing works
Entanglement in many-body quantum systems
Cirac, J. I. (2012) · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · doi:10.48550/arxiv.1205.3742 · Cited by 9 · see citing works
- Authors
- Verstraete, F., Cirac, J. I., & Latorre, J. I.
- Affiliations
- University of Vienna (AT)
- Max Planck Society (DE)
- Universitat de Barcelona (ES)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2009-03-16
- Volume
- 79
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2008394317
- Cited by
- 158
- References
- 16
- Citations by year
- 2026: 10 · 2025: 17 · 2024: 14 · 2023: 18 · 2022: 15 · 2021: 15 · 2020: 13 · 2019: 10 · 2018: 7 · 2017: 6 · 2016: 1 · 2015: 3 · 2014: 6 · 2012: 1
- FWCI
- 7.22
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (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 circuits, strongly correlated systems, quantum simulation, quantum many-body systems, quantum Ising model, transverse field, local gates, topological order, stabilizer states
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