{"id":315124,"date":"2026-02-24T18:17:14","date_gmt":"2026-02-24T18:17:14","guid":{"rendered":"https:\/\/www.newsbeep.com\/ie\/315124\/"},"modified":"2026-02-24T18:17:14","modified_gmt":"2026-02-24T18:17:14","slug":"simulating-fermions-with-a-digital-quantum-computer","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/ie\/315124\/","title":{"rendered":"Simulating fermions with a digital quantum computer"},"content":{"rendered":"

Manin, Y. Computable and Uncomputable (Sovetskoye Radio, 1980).<\/p>\n

Feynman, R. P. in Feynman and Computation, 133\u2013153 (CRC Press, 2018).<\/p>\n

Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Arute, F. et al. Observation of separated dynamics of charge and spin in the Fermi\u2013Hubbard model. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2010.07965<\/a> (2020).<\/p>\n

Farrell, R. C., Illa, M., Ciavarella, A. N. & Savage, M. J. Scalable circuits for preparing ground states on digital quantum computers: the Schwinger model vacuum on 100 qubits. PRX Quantum 5, 020315 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Acharya, R. et al. Suppressing quantum errors by scaling a surface code logical qubit. Nature 614, 676\u2013681 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 626, 58\u201365 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Paetznick, A. et al. Demonstration of logical qubits and repeated error correction with better-than-physical error rates. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2404.02280<\/a> (2024).<\/p>\n

Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153\u2013185 (2014).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Abrams, D. S. & Lloyd, S. Simulation of many-body Fermi systems on a universal quantum computer. Phys. Rev. Lett. 79, 2586\u20132589 (1997).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Ortiz, G., Gubernatis, J., Knill, E. & Laflamme, R. Quantum algorithms for fermionic simulations. Phys. Rev. A 64, 022319 (2001).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Lanyon, B. P. et al. Towards quantum chemistry on a quantum computer. Nat. Chem. 2, 106\u2013111 (2010).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Wecker, D., Bauer, B., Clark, B. K., Hastings, M. B. & Troyer, M. Gate-count estimates for performing quantum chemistry on small quantum computers. Phys. Rev. A 90, 022305 (2014).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Reiher, M., Wiebe, N., Svore, K. M., Wecker, D. & Troyer, M. Elucidating reaction mechanisms on quantum computers. Proc. Natl Acad. Sci. USA 114, 7555\u20137560 (2017).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulated quantum computation of molecular energies. Science 309, 1704\u20131707 (2005).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Whitfield, J. D., Biamonte, J. & Aspuru-Guzik, A. Simulation of electronic structure Hamiltonians using quantum computers. Mol. Phys. 109, 735\u2013750 (2011).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Cao, Y. et al. Quantum chemistry in the age of quantum computing. Chem. Rev. 119, 10856\u201310915 (2019).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bauer, B., Bravyi, S., Motta, M. & Chan, G. K.-L. Quantum algorithms for quantum chemistry and quantum materials science. Chem. Rev. 120, 12685\u201312717 (2020).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C. & Yuan, X. Quantum computational chemistry. Rev. Mod. Phys. 92, 015003 (2020).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Motta, M. & Rice, J. E. Emerging quantum computing algorithms for quantum chemistry. Wiley Interdiscip. Rev. Comput. Mol. Sci. 12, e1580 (2022).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Kassal, I., Jordan, S. P., Love, P. J., Mohseni, M. & Aspuru-Guzik, A. Polynomial-time quantum algorithm for the simulation of chemical dynamics. Proc. Natl Acad. Sci. USA 105, 18681\u201318686 (2008).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Sawaya, N. P. D. & Huh, J. Quantum algorithm for calculating molecular vibronic spectra. J. Phys. Chem. Lett. 10, 3586\u20133591 (2019).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Ollitrault, P. J., Mazzola, G. & Tavernelli, I. Nonadiabatic molecular quantum dynamics with quantum computers. Phys. Rev. Lett. 125, 260511 (2020).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Miessen, A., Ollitrault, P. J., Tacchino, F. & Tavernelli, I. Quantum algorithms for quantum dynamics. Nat. Comp. Sci. 3, 25\u201337 (2023).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

O\u2019Malley, P. J. J. et al. Scalable quantum simulation of molecular energies. Phys. Rev. X 6, 031007 (2016).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Kandala, A. et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242 (2017).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Colless, J. I. et al. Computation of molecular spectra on a quantum processor with an error-resilient algorithm. Phys. Rev. X 8, 011021 (2018).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Hempel, C. et al. Quantum chemistry calculations on a trapped-ion quantum simulator. Phys. Rev. X 8, 031022 (2018).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Google AI Quantum and Collaborators et al. Hartree-Fock on a superconducting qubit quantum computer. Science 369, 1084\u20131089 (2020).<\/p>\n

Article<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Navickas, T. et al. Experimental quantum simulation of chemical dynamics. J. Am. Chem. Soc. 147, 23566\u201323573 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Hubbard, J. Electron correlations in narrow energy bands. Proc. Roy. Soc. Lond. A 276, 238\u2013257 (1963).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Oftelie, L. B. et al. Simulating quantum materials with digital quantum computers. Quantum Sci. Technol. 6, 043002 (2021).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Wecker, D. et al. Solving strongly correlated electron models on a quantum computer. Phys. Rev. A 92, 062318 (2015).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Cade, C., Mineh, L., Montanaro, A. & Stanisic, S. Strategies for solving the Fermi-Hubbard model on near-term quantum computers. Phys. Rev. B 102, 235122 (2020).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Garc\u00eda-Ripoll, J. J., Solano, E. & Martin-Delgado, M. A. Quantum simulation of Anderson and Kondo lattices with superconducting qubits. Phys. Rev. B 77, 024522 (2008).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bravyi, S. & Gosset, D. Complexity of quantum impurity problems. Commun. Math. Phys. 356, 451\u2013500 (2017).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jamet, F. et al. Anderson impurity solver integrating tensor network methods with quantum computing. APL Quantum 2, 016121 (2025).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Rubin, N. C. et al. Fault-tolerant quantum simulation of materials using Bloch orbitals. PRX Quantum 4, 040303 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Clinton, L. et al. Towards near-term quantum simulation of materials. Nat. Commun. 15, 211 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Berry, D. W. et al. Quantum simulation of realistic materials in first quantization using non-local pseudopotentials. npj Quantum Inf. 10, 130 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bauer, B., Wecker, D., Millis, A. J., Hastings, M. B. & Troyer, M. Hybrid quantum-classical approach to correlated materials. Phys. Rev. X 6, 031045 (2016).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Haah, J., Hastings, M. B., Kothari, R. & Low, G. H. Quantum algorithm for simulating real time evolution of lattice Hamiltonians. SIAM J. Comput. 52, FOCS18\u2013250 (2021).<\/p>\n

MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Babbush, R. et al. Low-depth quantum simulation of materials. Phys. Rev. X 8, 011044 (2018).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Kogut, J. & Susskind, L. Hamiltonian formulation of Wilson\u2019s lattice gauge theories. Phys. Rev. D 11, 395 (1975).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Nielsen, H. B. & Ninomiya, M. Absence of neutrinos on a lattice: (I). Proof by homotopy theory. Nucl. Phys. B 185, 20\u201340 (1981).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jordan, S. P., Lee, K. S. & Preskill, J. Quantum computation of scattering in scalar quantum field theories. Quant. Inf. Comput. 14, 1014\u20131080 (2011).<\/p>\n

MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jordan, S. P., Lee, K. S. & Preskill, J. Quantum algorithms for quantum field theories. Science 336, 1130\u20131133 (2012).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jordan, S. P., Krovi, H., Lee, K. S. & Preskill, J. BQP-completeness of scattering in scalar quantum field theory. Quantum 2, 44 (2018).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jordan, S. P., Lee, K. S. & Preskill, J. Quantum algorithms for fermionic quantum field theories. Preprint at https:\/\/doi.org\/10.48550\/arXiv.1404.7115<\/a> (2014).<\/p>\n

Garc\u00eda-\u00c1lvarez, L. et al. Fermion-fermion scattering in quantum field theory with superconducting circuits. Phys. Rev. Lett. 114, 070502 (2015).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Zohar, E. & Cirac, J. I. Removing staggered fermionic matter in U(N) and SU(N) lattice gauge theories. Phys. Rev. D 99, 114511 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Lamm, H., Lawrence, S., Yamauchi, Y. & Collaboration, N. General methods for digital quantum simulation of gauge theories. Phys. Rev. D 100, 034518 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Banuls, M. C. et al. Simulating lattice gauge theories within quantum technologies. Eur. Phys. J. D 74, 1\u201342 (2020).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Kan, A. & Nam, Y. Lattice quantum chromodynamics and electrodynamics on a universal quantum computer. Quant. Sci. Technol. https:\/\/doi.org\/10.1088\/2058-9565\/aca0b8<\/a> (2021).<\/p>\n

Tong, Y., Albert, V. V., McClean, J. R., Preskill, J. & Su, Y. Provably accurate simulation of gauge theories and bosonic systems. Quantum 6, 816 (2022).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bauer, C. W. et al. Quantum simulation for high-energy physics. PRX Quantum 4, 027001 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bauer, C. W., Davoudi, Z., Klco, N. & Savage, M. J. Quantum simulation of fundamental particles and forces. Nat. Rev. Phys. 5, 420\u2013432 (2023).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Irmejs, R., Ba\u00f1uls, M.-C. & Cirac, J. I. Quantum simulation of \\({{\\rm{{\\mathbb{Z}}}}}_{2}\\) lattice gauge theory with minimal resources. Phys. Rev. D 108, 074503 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Lamm, H., Li, Y.-Y., Shu, J., Wang, Y.-L. & Xu, B. Block encodings of discrete subgroups on a quantum computer. Phys. Rev. D 110, 054505 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Rhodes, M. L., Kreshchuk, M. & Pathak, S. Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques. PRX Quantum 5, 040347 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Watson, J. D. et al. Quantum algorithms for simulating nuclear effective field theories. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2312.05344<\/a> (2023).<\/p>\n

Schwinger, J. Gauge invariance and mass. II. Phys. Rev. 128, 2425 (1962).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

K\u00fchn, S., Cirac, J. I. & Ba\u00f1uls, M.-C. Quantum simulation of the Schwinger model: a study of feasibility. Phys. Rev. A 90, 042305 (2014).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Alexandru, A. et al. Gluon field digitization for quantum computers. Phys. Rev. D 100, 114501 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Davoudi, Z., Raychowdhury, I. & Shaw, A. Search for efficient formulations for Hamiltonian simulation of non-Abelian lattice gauge theories. Phys. Rev. D 104, 074505 (2021).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Farhi, E., Goldstone, J., Gutmann, S. & Sipser, M. Quantum computation by adiabatic evolution. Preprint at https:\/\/doi.org\/10.48550\/arXiv.quant-ph\/0001106<\/a> (2000).<\/p>\n

Albash, T. & Lidar, D. A. Adiabatic quantum computation. Rev. Mod. Phys. 90, 015002 (2018).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Kato, T. On the adiabatic theorem of quantum mechanics. J. Phys. Soc. Jpn 5, 435\u2013439 (1950).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Lee, S. et al. Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry. Nat. Commun. 14, 1952 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Kitaev, A. Y. Quantum measurements and the Abelian stabilizer problem. Preprint at https:\/\/doi.org\/10.48550\/arXiv.quant-ph\/9511026<\/a> (1995).<\/p>\n

Temme, K., Osborne, T. J., Vollbrecht, K. G., Poulin, D. & Verstraete, F. Quantum metropolis sampling. Nature 471, 87\u201390 (2011).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chen, C.-F., Kastoryano, M. J., Brand\u00e3o, F. G. & Gily\u00e9n, A. Quantum thermal state preparation. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2303.18224<\/a> (2023).<\/p>\n

Chen, C.-F., Kastoryano, M. J. & Gily\u00e9n, A. An efficient and exact noncommutative quantum Gibbs sampler. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2311.09207<\/a> (2023).<\/p>\n

Cubitt, T. S. Dissipative ground state preparation and the dissipative quantum eigensolver. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2303.11962<\/a> (2023).<\/p>\n

Zhang, D., Bosse, J. L. & Cubitt, T. Dissipative quantum Gibbs sampling. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2304.04526<\/a> (2023).<\/p>\n

Endo, S., Kurata, I. & Nakagawa, Y. O. Calculation of the Green\u2019s function on near-term quantum computers. Phys. Rev. Res. 2, 033281 (2020).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Keen, T., Dumitrescu, E. & Wang, Y. Quantum algorithms for ground-state preparation and Green\u2019s function calculation. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2112.05731<\/a> (2021).<\/p>\n

Irmejs, R. & Santos, R. A. Approximating dynamical correlation functions with constant depth quantum circuits. Quantum 9, 1639 (2025).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Piccinelli, S., Tacchino, F., Tavernelli, I. & Carleo, G. Efficient calculation of Green\u2019s functions on quantum computers via simultaneous circuit perturbation. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2505.05563<\/a> (2025).<\/p>\n

Huang, H.-Y., Kueng, R. & Preskill, J. Predicting many properties of a quantum system from very few measurements. Nat. Phys. 16, 1050\u20131057 (2020).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Elben, A. et al. The randomized measurement toolbox. Nat. Rev. Phys. 5, 9\u201324 (2023).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Busch, P. Informationally complete sets of physical quantities. Int. J. Theor. Phys. 30, 1217\u20131227 (1991).<\/p>\n

Article<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Zhao, A., Rubin, N. C. & Miyake, A. Fermionic partial tomography via classical shadows. Phys. Rev. Lett. 127, 110504 (2021).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Wan, K., Huggins, W. J., Lee, J. & Babbush, R. Matchgate shadows for fermionic quantum simulation. Commun. Math. Phys. 404, 629\u2013700 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Low, G. H. Classical shadows of fermions with particle number symmetry. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2208.08964<\/a> (2022).<\/p>\n

King, R., Gosset, D., Kothari, R. & Babbush, R. Triply efficient shadow tomography. PRX Quantum 6, 010336 (2025).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Lloyd, S. Universal quantum simulators. Science 273, 1073\u20131078 (1996).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Suzuki, M. General theory of fractal path integrals with applications to many-body theories and statistical physics. J. Math. Phys. 32, 400\u2013407 (1991).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Campbell, E. Random compiler for fast Hamiltonian simulation. Phys. Rev. Lett. 123, 070503 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Childs, A. M., Ostrander, A. & Su, Y. Faster quantum simulation by randomization. Quantum 3, 182 (2019).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chen, C.-F., Huang, H.-Y., Kueng, R. & Tropp, J. A. Concentration for random product formulas. PRX Quantum 2, 040305 (2021).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Faehrmann, P. K., Steudtner, M., Kueng, R., Kieferova, M. & Eisert, J. Randomizing multi-product formulas for Hamiltonian simulation. Quantum 6, 806 (2022).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Cho, C.-H., Berry, D. W. & Hsieh, M.-H. Doubling the order of approximation via the randomized product formula. Phys. Rev. A 109, 062431 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Kivlichan, I. D. et al. Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via Trotterization. Quantum 4, 296 (2020).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bosse, J. L. et al. Efficient and practical Hamiltonian simulation from time-dependent product formulas. Nat. Commun. 16, 2673 (2025).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Childs, A. M. & Su, Y. Nearly optimal lattice simulation by product formulas. Phys. Rev. Lett. 123, 050503 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Childs, A. M., Su, Y., Tran, M. C., Wiebe, N. & Zhu, S. Theory of Trotter error with commutator scaling. Phys. Rev. X 11, 011020 (2021).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Low, G. H. & Chuang, I. L. Optimal Hamiltonian simulation by quantum signal processing. Phys. Rev. Lett. 118, 010501 (2017).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Low, G. H. & Chuang, I. L. Hamiltonian simulation by qubitization. Quantum 3, 163 (2019).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Gily\u00e9n, A., Su, Y., Low, G. H. & Wiebe, N. Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In Proc. 51st Annual ACM SIGACT Symposium on Theory of Computing 193\u2013204 (ACM, 2019).<\/p>\n

Motlagh, D. & Wiebe, N. Generalized quantum signal processing. PRX Quantum 5, 020368 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Childs, A. M. & Wiebe, N. Hamiltonian simulation using linear combinations of unitary operations. Quant. Inf. Comput. 12, 901\u2013 924 (2012).<\/p>\n

MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Babbush, R. et al. Encoding electronic spectra in quantum circuits with linear T complexity. Phys. Rev. X 8, 041015 (2018).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Berry, D. W. & Childs, A. M. Black-box Hamiltonian simulation and unitary implementation. Quant. Inf. Comput. 12, 29\u201362 (2009).<\/p>\n

MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Berry, D. W. et al. Improved techniques for preparing eigenstates of fermionic Hamiltonians. npj Quantum Inf. 4, 1\u20137 (2018).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Babbush, R., Berry, D. W., McClean, J. R. & Neven, H. Quantum simulation of chemistry with sublinear scaling in basis size. npj Quantum Inf. 5, 92 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Su, Y., Berry, D. W., Wiebe, N., Rubin, N. & Babbush, R. Fault-tolerant quantum simulations of chemistry in first quantization. PRX Quantum 2, 040332 (2021).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Babbush, R. et al. Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods. Nat. Commun. 14, 4058 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Georges, T. N. et al. Quantum simulations of chemistry in first quantization with any basis set. npj Quantum Inf. 11, 55 (2025).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Wick, G. C., Wightman, A. S. & Wigner, E. P. The Intrinsic Parity of Elementary Particles 102\u2013106 (Springer, 1997).<\/p>\n

Bravyi, S. B. & Kitaev, A. Y. Fermionic quantum computation. Ann. Phys. 298, 210\u2013226 (2002).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chien, R. W. & Klassen, J. Optimizing fermionic encodings for both Hamiltonian and hardware. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2210.05652<\/a> (2022).<\/p>\n

Cobanera, E., Ortiz, G. & Nussinov, Z. The bond-algebraic approach to dualities. Adv. Phys. 60, 679\u2013798 (2011).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jordan, P. & Wigner, E. About the Pauli exclusion principle. Z. Phys. 47, 631\u2013651 (1928).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Lieb, E., Schultz, T. & Mattis, D. Two soluble models of an antiferromagnetic chain. Ann. Phys. 16, 407\u2013466 (1961).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chiew, M. & Strelchuk, S. Discovering optimal fermion\u2013qubit mappings through algorithmic enumeration. Quantum 7, 1145 (2023).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Parella-Dilm\u00e9, T. et al. Reducing entanglement with physically inspired fermion-to-qubit mappings. PRX Quantum 5, 030333 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jones, N. C. et al. Faster quantum chemistry simulation on fault-tolerant quantum computers. New J. Phys. 14, 115023 (2012).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Wan, K. Exponentially faster implementations of Select(H) for fermionic Hamiltonians. Quantum 5, 380 (2021).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Seeley, J. T., Richard, M. J., Love, P. J. & Love, P. J. The Bravyi-Kitaev transformation for quantum computation of electronic structure. J. Chem. Phys. 137, 224109 (2012).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Steudtner, M. & Wehner, S. Fermion-to-qubit mappings with varying resource requirements for quantum simulation. New J. Phys. 20, 063010 (2018).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bravyi, S., Gambetta, J. M., Mezzacapo, A. & Temme, K. Tapering off qubits to simulate fermionic Hamiltonians. Preprint at https:\/\/doi.org\/10.48550\/arXiv.1701.08213<\/a> (2017).<\/p>\n

Wang, Q., Li, M., Monroe, C. & Nam, Y. Resource-optimized fermionic local-Hamiltonian simulation on a quantum computer for quantum chemistry. Quantum 5, 509 (2021).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Wang, Q., Cian, Z.-P., Li, M., Markov, I. L. & Nam, Y. Ever more optimized simulations of fermionic systems on a quantum computer. In 2023 60th ACM\/IEEE Design Automation Conference (DAC) 1\u20136 (IEEE, 2023).<\/p>\n

Miller, A., Zimbor\u00e1s, Z., Knecht, S., Maniscalco, S. & Garc\u00eda-P\u00e9rez, G. Bonsai algorithm: grow your own fermion-to-qubit mappings. PRX Quantum 4, 030314 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Miller, A., Glos, A. & Zimbor\u00e1s, Z. Treespilation: architecture- and state-optimised fermion-to-qubit mappings. npj Quant. Inf. https:\/\/doi.org\/10.1038\/s41534-025-01170-2<\/a> (2024).<\/p>\n

Jiang, Z., Kalev, A., Mruczkiewicz, W. & Neven, H. Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning. Quantum 4, 276 (2020).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Vlasov, A. Y. Clifford algebras, spin groups and qubit trees. Quanta 11, 97\u2013114 (2022).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chiew, M., Harrison, B. & Strelchuk, S. Ternary tree transformations are equivalent to linear encodings of the Fock basis. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2412.07578<\/a> (2024).<\/p>\n

McDowall-Rose, H., Shaikh, R. A. & Yeh, L. From fermions to qubits: a ZX-calculus perspective. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2505.06212<\/a> (2025).<\/p>\n

Havl\u00ed\u010dek, V., Troyer, M. & Whitfield, J. D. Operator locality in the quantum simulation of fermionic models. Phys. Rev. A 95, 032332 (2017).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Harrison, B. et al. A Sierpinski triangle fermion-to-qubit transform. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2409.04348<\/a> (2024).<\/p>\n

Yu, J., Liu, Y., Sugiura, S., Voorhis, T. V. & Zeytino\u011flu, S. Clifford circuit based heuristic optimization of fermion-to-qubit mappings. J. Chem. Theory Comput. 21, 9430\u20139443 (2025).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Arcos, M., Apel, H. & Cubitt, T. Encodings of observable subalgebras. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2502.20591<\/a> (2025).<\/p>\n

Setia, K. et al. Reducing qubit requirements for quantum simulations using molecular point group symmetries. J. Chem. Theory Comput. 16, 6091\u20136097 (2020).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Shee, Y., Tsai, P.-K., Hong, C.-L., Cheng, H.-C. & Goan, H.-S. Qubit-efficient encoding scheme for quantum simulations of electronic structure. Phys. Rev. Res. 4, 023154 (2022).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Harrison, B., Nelson, D., Adamiak, D. & Whitfield, J. Reducing the qubit requirement of Jordan-Wigner encodings of N-mode, K-fermion systems from N to \\(\\lceil {\\log }_{2}(\\begin{array}{c}N\\\\ K\\end{array})\\rceil \\). Preprint at https:\/\/doi.org\/10.48550\/arXiv.2211.04501<\/a> (2023).<\/p>\n

Kirby, W., Fuller, B., Hadfield, C. & Mezzacapo, A. Second-quantized fermionic operators with polylogarithmic qubit and gate complexity. PRX Quantum 3, 020351 (2022).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Carolan, J. & Schaeffer, L. Succinct fermion data structures. In 16th Innovations in Theoretical Computer Science Conference (ed. Meka, R.) Vol. 325 (ITCS, 2025).<\/p>\n

Lieb, E. H. & Robinson, D. W. The finite group velocity of quantum spin systems. Commun. Math. Phys. 28, 251\u2013257 (1972).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Hastings, M. B. in Quantum Theory from Small to Large Scales: Lecture Notes of the Les Houches Summer School Vol. 95, 171\u2013212 (Oxford Univ. Press, 2010).<\/p>\n

Tran, M. C. et al. Locality and digital quantum simulation of power-law interactions. Phys. Rev. X 9, 031006 (2019).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bringewatt, J. & Davoudi, Z. Parallelization techniques for quantum simulation of fermionic systems. Quantum 7, 975 (2023).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Ball, R. Fermions without fermion fields. Phys. Rev. Lett. 95, 176407 (2005).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Levin, M. & Wen, X.-G. Quantum ether: photons and electrons from a rotor model. Phys. Rev. B 73, 035122 (2006).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Verstaete, F. & Cirac, J. I. Mapping local Hamiltonians of fermions to local Hamiltonians of spins. J. Stat. Mech. Theory Exp. 2005, P09012 (2005).<\/p>\n

Article<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Steudtner, M. & Wehner, S. Quantum codes for quantum simulation of fermions on a square lattice of qubits. Phys. Rev. A 99, 022308 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Setia, K., Bravyi, S., Mezzacapo, A. & Whitfield, J. D. Superfast encodings for fermionic quantum simulation. Phys. Rev. Res. 1, 033033 (2019).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Jiang, Z., McClean, J., Babbush, R. & Neven, H. Majorana loop stabilizer codes for error mitigation in fermionic quantum simulations. Phys. Rev. Appl. 12, 064041 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chen, Y.-A. & Kapustin, A. Bosonization in three spatial dimensions and a 2-form gauge theory. Phys. Rev. B 100, 245127 (2019).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chen, Y.-A. Exact bosonization in arbitrary dimensions. Phys. Rev. Res. 2, 033527 (2020).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chien, R. W. & Whitfield, J. D. Custom fermionic codes for quantum simulation. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2009.11860<\/a> (2020).<\/p>\n

Derby, C., Klassen, J., Bausch, J. & Cubitt, T. Compact fermion to qubit mappings. Phys. Rev. B 104, 035118 (2021).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Derby, C. & Klassen, J. A compact fermion to qubit mapping part 2: Alternative lattice geometries. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2101.10735<\/a> (2021).<\/p>\n

Li, K. & Po, H. C. Higher-dimensional Jordan-Wigner transformation and auxiliary Majorana fermions. Phys. Rev. B 106, 115109 (2022).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chen, Y.-A., Gorshkov, A. V. & Xu, Y. Error-correcting codes for fermionic quantum simulation. SciPost Phys. 16, 033 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Nys, J. & Carleo, G. Quantum circuits for solving local fermion-to-qubit mappings. Quantum 7, 930 (2023).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Algaba, M. G., Sriluckshmy, P., Leib, M. & \u0160imkovic IV, F. Low-depth simulations of fermionic systems on square-grid quantum hardware. Quantum 8, 1327 (2024).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Gottesman, D. Stabilizer Codes and Quantum Error Correction. PhD thesis, California Institute of Technology (1997).<\/p>\n

Chien, R. W., Setia, K., Bonet-Monroig, X., Steudtner, M. & Whitfield, J. D. Simulating quantum error mitigation in fermionic encodings. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2303.02270<\/a> (2023).<\/p>\n

Zhang, D. & Cubitt, T. Quantum error transmutation. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2310.10278<\/a> (2023).<\/p>\n

\u0160imkovic, F. IV, Leib, M. & Pereira, F. R. F. Low-weight high-distance error correcting fermionic encodings. Am. Phys. Soc. 6, 043123 (2024).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Papi\u010d, M. et al. Near-term fermionic simulation with subspace noise tailored quantum error mitigation. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2503.11785<\/a> (2025).<\/p>\n

Algaba, M. G., Papi\u010d, M., de Vega, I., Calzona, A. & \u0160imkovic IV, F. Fermion-to-qubit encodings with arbitrary code distance. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2505.02916<\/a> (2025).<\/p>\n

Landahl, A. J. & Morrison, B. C. Logical fermions for fault-tolerant quantum simulation. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2110.10280<\/a> (2021).<\/p>\n

Levin, M. & Wen, X.-G. Fermions, strings, and gauge fields in lattice spin models. Phys. Rev. B 67, 245316 (2003).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chen, Y.-A., Kapustin, A. & Radi\u010devi\u0107, D. Exact bosonization in two spatial dimensions and a new class of lattice gauge theories. Ann. Phys. 393, 234\u2013253 (2018).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2\u201330 (2003).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Walker, K. & Wang, Z. (3+1)-TQFTs and topological insulators. Front. Phys. 7, 150\u2013159 (2012).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Tsui, L. & Wen, X.-G. Lattice models that realize \\({{\\rm{{\\mathbb{Z}}}}}_{n}-1\\) symmetry-protected topological states for even n. Phys. Rev. B 101, 035101 (2020).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chen, Y.-A. & Tata, S. Higher cup products on hypercubic lattices: application to lattice models of topological phases. J. Math. Phys. 64, 091902 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Haah, J. Algebraic methods for quantum codes on lattices. Revista Colombiana de Matem\u00e1ticas 50, 299\u2013349 (2016).<\/p>\n

Article<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Chen, Y.-A. et al. Equivalence between fermion-to-qubit mappings in two spatial dimensions. PRX Quantum 4, 010326 (2023).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Guaita, T. On the locality of qubit encodings of local fermionic modes. Quantum 9, 1644 (2024).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Bravyi, S., Hastings, M. B. & Verstraete, F. Lieb-Robinson bounds and the generation of correlations and topological quantum order. Phys. Rev. Lett. 97, 050401 (2006).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Higgott, O. et al. Optimal local unitary encoding circuits for the surface code. Quantum 5, 517 (2021).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

O\u2019Brien, O. & Strelchuk, S. Ultrafast hybrid fermion-to-qubit mapping. Phys. Rev. B 109, 115149 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Babbush, R. et al. Exponentially more precise quantum simulation of fermions in the configuration interaction representation. Quantum Sci. Technol. 3, 015006 (2018).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Low, G. H. et al. Fast quantum simulation of electronic structure by spectrum amplification. Phys. Rev. X 15, 041016 (2025).<\/p>\n


\n Google Scholar<\/a>\u00a0\n <\/p>\n

Campbell, E. T. Early fault-tolerant simulations of the Hubbard model. Quantum Sci. Technol. 7, 015007 (2021).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Luthra, S., Moylett, A. E., Browne, D. E. & Campbell, E. T. Unlocking early fault-tolerant quantum computing with mitigated magic dilution. Quantum Sci. Technol. 10, 045066 (2025).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Nigmatullin, R. et al. Experimental demonstration of break-even for the compact fermionic encoding. Nat. Phys. 21, 1319\u20131325 (2025).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Evered, S. J. et al. Probing the Kitaev honeycomb model on a neutral-atom quantum computer. Nature 645, 341\u2013347 (2025).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Tan, T. R. et al. Analog quantum simulation of chemical dynamics with a trapped-ion system. In APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts Vol. 2022, C08-005 (APS, 2022).<\/p>\n

Flannigan, S. et al. Propagation of errors and quantitative quantum simulation with quantum advantage. Quantum Sci. Technol. 7, 045025 (2022).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Trivedi, R., Franco Rubio, A. & Cirac, J. I. Quantum advantage and stability to errors in analogue quantum simulators. Nat. Commun. 15, 6507 (2024).<\/p>\n

Article<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Liu, Y. et al. Toward mixed analog-digital quantum signal processing: quantum AD\/DA conversion and the Fourier transform. IEEE Trans. Sig. Process. 73, 3641 (2024).<\/p>\n

Article<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Crane, E. et al. Hybrid oscillator-qubit quantum processors: simulating fermions, bosons, and gauge fields. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2409.03747<\/a> (2024).<\/p>\n

Mudassar, M., Chien, R. W. & Gottesman, D. Encoding Majorana codes. Phys. Rev. A 110, 032430 (2024).<\/p>\n

Article<\/a>\u00a0
\n ADS<\/a>\u00a0
\n MathSciNet<\/a>\u00a0
\n
\n Google Scholar<\/a>\u00a0\n <\/p>\n

Schuckert, A., Crane, E., Gorshkov, A. V., Hafezi, M. & Gullans, M. J. Fermion-qubit fault-tolerant quantum computing. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2411.08955<\/a> (2024).<\/p>\n","protected":false},"excerpt":{"rendered":"Manin, Y. Computable and Uncomputable (Sovetskoye Radio, 1980). Feynman, R. P. in Feynman and Computation, 133\u2013153 (CRC Press,…\n","protected":false},"author":2,"featured_media":315125,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[4967,1437,61,21530,60,248,28213,13141,82],"class_list":{"0":"post-315124","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-computational-science","9":"tag-general","10":"tag-ie","11":"tag-information-theory-and-computation","12":"tag-ireland","13":"tag-physics","14":"tag-quantum-chemistry","15":"tag-quantum-simulation","16":"tag-science"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/posts\/315124","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/comments?post=315124"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/posts\/315124\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/media\/315125"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/media?parent=315124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/categories?post=315124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/tags?post=315124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}