Abstract
Contemporary quantum technologies face major difficulties in fault tolerant quantum computing with error correction, and focus instead on various shades of quantum simulation (Noisy Intermediate Scale Quantum, NISQ) devices, analogue and digital quantum simulators and quantum annealers. There is a clear need and quest for such systems that, without necessarily simulating quantum dynamics of some physical systems, can generate massive, controllable, robust, entangled, and superposition states. This will, in particular, allow the control of decoherence, enabling the use of these states for quantum communications (e.g. to achieve efficient transfer of information in a safer and quicker way), quantum metrology, sensing and diagnostics (e.g. to precisely measure phase shifts of light fields, or to diagnose quantum materials). In this Chapter we present a vision of the golden future of quantum simulators in the decades to come.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Icfo qot website, https://www.icfo.eu/research-group/11/qot/news/437/
Quside website, https://www.linkedin.com/company/quside/?originalSubdomain=es
S. Aaronson, A. Arkhipov, The computational complexity of linear optics, in Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, STOC ’11, New York, NY, USA, 2011 (Association for Computing Machinery), pp. 333–342
M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. Gonzá lez-Cuadra, P.R. Grzybowski, S. Hands, F. Jendrzejewski, J. Jünemann, G. Juzeliūnas, V. Kasper, A. Piga, S.-J. Ran, M. Rizzi, G. Sierra, L. Tagliacozzo, E. Tirrito, T.V. Zache, J. Zakrzewski, E. Zohar, M. Lewenstein, Cold atoms meet lattice gauge theory. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 380(2216) (2021)
A. Aloy, J. Tura, F. Baccari, A. Acín, M. Lewenstein, R. Augusiak, Device-independent witnesses of entanglement depth from two-body correlators. Phys. Rev. Lett. 123, 100507 (2019)
E. Altman, K.R. Brown, G. Carleo, L.D. Carr, E. Demler, C. Chin, B. DeMarco, S.E. Economou, M.A. Eriksson, K.-M.C. Fu, M. Greiner, K.R. Hazzard, R.G. Hulet, A.J. Kollár, B.L. Lev, M.D. Lukin, R. Ma, X. Mi, S. Misra, C. Monroe, K. Murch, Z. Nazario, K.-K. Ni, A.C. Potter, P. Roushan, M. Saffman, M. Schleier-Smith, I. Siddiqi, R. Simmonds, M. Singh, I. Spielman, K. Temme, D.S. Weiss, J. Vučković, V. Vuletić, J. Ye, M. Zwierlein, Quantum simulators: architectures and opportunities. PRX Quantum 2, 017003 (2021)
K. Amini, J. Biegert, F. Calegari, A. Chacón, M.F. Ciappina, A. Dauphin, D.K. Efimov, C.F. de Morisson Faria, K. Giergiel, P. Gniewek, A.S. Landsman, M. Lesiuk, M. Mandrysz, A.S. Maxwell, R. Moszyński, L. Ortmann, J.A. Pérez-Hernández, A. Picón, E. Pisanty, J. Prauzner-Bechcicki, K. Sacha, N. Suárez, A. Zair, J. Zakrzewski, M. Lewenstein, Symphony on strong field approximation. Rep. Progress Phys. 82(11), 116001 (2019)
J. Argüello-Luengo, A. González-Tudela, T. Shi, P. Zoller, J.I. Cirac. Analogue quantum chemistry simulation. Nature 574(7777), 215–218 (2019)
S. Arora, B. Barak, Computational Complexity: A Modern Approach, 1st edn. (Cambridge University Press, Cambridge, 2009)
F. Arute, K. Arya, R. Babbush, D. Bacon, J.C. Bardin, R. Barends, R. Biswas, S. Boixo, F.G.S.L. Brandao, D.A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, K. Guerin, S. Habegger, M.P. Harrigan, M.J. Hartmann, A. Ho, M. Hoffmann, T. Huang, T.S. Humble, S.V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, J. Kelly, P.V. Klimov, S. Knysh, A. Korotkov, F. Kostritsa, D. Landhuis, M. Lindmark, E. Lucero, D. Lyakh, S. Mandrà, J.R. McClean, M. McEwen, A. Megrant, X. Mi, K. Michielsen, M. Mohseni, J. Mutus, O. Naaman, M. Neeley, C. Neill, M.Y. Niu, E. Ostby, A. Petukhov, J.C. Platt, C. Quintana, E.G. Rieffel, P. Roushan, N.C. Rubin, D. Sank, K.J. Satzinger, V. Smelyanskiy, K.J. Sung, M.D. Trevithick, A. Vainsencher, B. Villalonga, T. White, Z.J. Yao, P. Yeh, A. Zalcman, H. Neven, J. M. Martinis, Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)
S. Asban, S. Mukamel, Scattering-based geometric shaping of photon-photon interactions. Phys. Rev. Lett. 123, 260502 (2019)
F. Baccari, C. Gogolin, P. Wittek, A. Ací n, Verifying the output of quantum optimizers with ground-state energy lower bounds. Phys. Rev. Res. 2(4) (2020)
W. Bakr, J. Gillen, A. Peng, S. Fölling, M. Greiner, A quantum gas microscope for detecting single atoms in a hubbard-regime optical lattice. Nature 462(7269), 74–77 (2009)
M.C. Bañuls, R. Blatt, J. Catani, A. Celi, J.I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C.A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski, P. Zoller, Simulating lattice gauge theories within quantum technologies. Eur. Phys. J. D 74(8), 165 (2020)
T. Barthel, R. Hübener, Solving condensed-matter ground-state problems by semidefinite relaxations. Phys. Rev. Lett. 108, 200404 (2012)
D.N. Basov, A. Asenjo-Garcia, P.J. Schuck, X. Zhu, A. Rubio, Polariton panorama. Nanophotonics 10(1), 549–577 (2021)
T. Baumgratz, M.B. Plenio, Lower bounds for ground states of condensed matter systems. New J. Phys. 14(2), 023027 (2012)
H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A.S. Zibrov, M. Endres, M. Greiner, V. Vuletic, M.D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579 (2017)
K. Bharti, A. Cervera-Lierta, T.H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J.S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.-C. Kwek, A. Aspuru-Guzik, Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys. 94, 015004 (2022)
A. Blais, A.L. Grimsmo, S.M. Girvin, A. Wallraff, Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021)
D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Semeghini, S. Ebadi, T.T. Wang, A.A. Michailidis, N. Maskara, W.W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuletic, M.D. Lukin, Controlling quantum many-body dynamics in driven rydberg atom arrays. Science 371(6536), 1355–1359 (2021)
O. Boada, A. Celi, J.I. Latorre, M. Lewenstein, Quantum simulation of an extra dimension. Phys. Rev. Lett. 108, 133001 (2012)
A. Bohrdt, C.S. Chiu, G. Ji, M. Xu, D. Greif, M. Greiner, E. Demler, F. Grusdt, M. Knap, Classifying snapshots of the doped hubbard model with machine learning. Nat. Phys. 15(9), 921–924 (2019)
F. Böttcher, J.-N. Schmidt, J. Hertkorn, K.S.H. Ng, S.D. Graham, M. Guo, T. Langen, T. Pfau, New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids. Rep. Progress Phys. 84(1), 012403 (2020)
T. Boulier, M.J. Jacquet, A. Maître, G. Lerario, F. Claude, S. Pigeon, Q. Glorieux, A. Amo, J. Bloch, A. Bramati, E. Giacobino, Microcavity polaritons for quantum simulation. Adv. Quantum Technol. 3(11), 2000052 (2020)
T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B.P. Lanyon, P. Zoller, R. Blatt, C.F. Roos, Probing renyi entanglement entropy via randomized measurements. Science 364(6437), 260–263 (2019)
C.R. Cabrera, L. Tanzi, J. Sanz, B. Naylor, P. Thomas, P. Cheiney, L. Tarruell, Quantum liquid droplets in a mixture of bose-einstein condensates. Science 359(6373), 301–304 (2018)
Y. Cao, D. Rodan-Legrain, O. Rubies-Bigorda, J.M. Park, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583(7815), 215–220 (2020)
Y. Cao, J. Romero, J.P. Olson, M. Degroote, P.D. Johnson, M. Kieferová, I.D. Kivlichan, T. Menke, B. Peropadre, N.P.D. Sawaya, S. Sim, L. Veis, A. Aspuru-Guzik, Quantum chemistry in the age of quantum computing. Chem. Rev. 119(19), 10856–10915 (2019)
G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, L. Zdeborová, Machine learning and the physical sciences. Rev. Mod. Phys. 91, 045002 (2019)
I. Carusotto, A. Houck, A. Kollár, P. Roushan, D. Schuster, J. Simon, Photonic materials in circuit quantum electrodynamics. Nat. Phys. 16, 03 (2020)
A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I.B. Spielman, G. Juzeliūnas, M. Lewenstein, Synthetic gauge fields in synthetic dimensions. Phys. Rev. Lett. 112, 043001 (2014)
A. Cervera-Lierta, Icfo theory lecture: noisy intermediate-scale quantum algorithms 1 (2022). https://youtu.be/pyB9d8fVTt0
A. Cervera-Lierta, Icfo theory lecture: Noisy intermediate-scale quantum algorithms 2 (2022). https://youtu.be/ooNEw64zfbg
T. Chanda, M. Lewenstein, J. Zakrzewski, L. Tagliacozzo, Phase diagram of \(1+1\mathrm {D}\) abelian-higgs model and its critical point. Phys. Rev. Lett. 128, 090601 (2022)
T. Chanda, J. Zakrzewski, M. Lewenstein, L. Tagliacozzo, Confinement and lack of thermalization after quenches in the bosonic schwinger model. Phys. Rev. Lett. 124, 180602 (2020)
L.W. Cheuk, M.A. Nichols, M. Okan, T. Gersdorf, V.V. Ramasesh, W.S. Bakr, T. Lompe, M.W. Zwierlein, Quantum-gas microscope for fermionic atoms. Phys. Rev. Lett. 114, 193001 (2015)
C.S. Chiu, G. Ji, A. Bohrdt, M. Xu, M. Knap, E. Demler, F. Grusdt, M. Greiner, D. Greif, String patterns in the doped hubbard model. Science 365(6450), 251–256 (2019)
L.W. Clark, N. Schine, C. Baum, N. Jia, J. Simon, Observation of laughlin states made of light. Nature 582(7810), 41–45 (2020)
T.M. Cover, J.A. Thomas, Elements of Information Theory. Wiley Series in Telecommunications and Signal Processing, 2nd edn. (Wiley-Interscience, New York, 2006)
M. Dalmonte, B. Vermersch, P. Zoller, Quantum simulation and spectroscopy of entanglement Hamiltonians. Nat. Phys. 14(8), 827–831 (2018)
A. Dawid, J. Arnold, B. Requena, A. Gresch, M. Płodzień, K. Donatella, K.A. Nicoli, P. Stornati, R. Koch, M. Büttner, R. Okuła, G. Muñoz Gil, R.A. Vargas-Hernández, A. Cervera-Lierta, J. Carrasquilla, V. Dunjko, M. Gabrié, P. Huembeli, E. van Nieuwenburg, F. Vicentini, L. Wang, S.J. Wetzel, G. Carleo, E. Greplova, R. Krems, F. Marquardt, M. Tomza, M. Lewenstein, A. Dauphin, Modern applications of machine learning in quantum sciences (2022), arXiv:2204.04198(quant-ph)
A. D’Errico, F. Cardano, M. Maffei, A. Dauphin, R. Barboza, C. Esposito, B. Piccirillo, M. Lewenstein, P. Massignan, L. Marrucci, Two-dimensional topological quantum walks in the momentum space of structured light. Optica 7(2), 108–114 (2020)
D.P. DiVincenzo, The physical implementation of quantum computation. Fortschritte der Physik 48(9–11), 771–783 (2000)
A. Doherty, Y.-C. Liang, B. Toner, S. Wehner, The quantum moment problem and bounds on entangled multi-prover games. Proceedings of the Annual IEEE Conference on Computational Complexity (2008), pp. 199–210
S. Ebadi, A. Keesling, M. Cain, T.T. Wang, H. Levine, D. Bluvstein, G. Semeghini, A. Omran, J. Liu, R. Samajdar, X.-Z. Luo, B. Nash, X. Gao, B. Barak, E. Farhi, S. Sachdev, N. Gemelke, L. Zhou, S. Choi, H. Pichler, S. Wang, M. Greiner, V. Vuletic, M.D. Lukin, Quantum optimization of maximum independent set using rydberg atom arrays. Science 376(6598), 1209–1215 (2022). https://doi:10.1126/science.abo6587
S. Ebadi, T.T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W.W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuletić, M.D. Lukin, Quantum phases of matter on a 256-atom programmable quantum simulator. Nature 595(7866), 227–232 (2021)
A. Elben, S.T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, P. Zoller, The randomized measurement toolbox. Nat Rev Phys 5, 9–24 (2023). https://doi.org/10.1038/s42254-022-00535-2
A. Elben, B. Vermersch, M. Dalmonte, J.I. Cirac, P. Zoller, Rényi entropies from random quenches in atomic hubbard and spin models. Phys. Rev. Lett. 120, 050406 (2018)
A. Elben, J. Yu, G. Zhu, M. Hafezi, F. Pollmann, P. Zoller, B. Vermersch, Many-body topological invariants from randomized measurements in synthetic quantum matter. Sci. Adv. 6(15), eaaz3666 (2020)
E. Farhi, J. Goldstone, S. Gutmann, M. Sipser, Quantum computation by adiabatic evolution. Quantum Phys. (2000). arXiv
R.P. Feynman, Simulating physics with computers. Int. J. Theor. Phys. 21(6), 467–488 (1982)
J. Fraxanet, D. Gonzá lez-Cuadra, T. Pfau, M. Lewenstein, T. Langen, L. Barbiero, Topological quantum critical points in the extended bose-hubbard model. Phys. Rev. Lett. 128(4) (2022)
A. Glos, A. Krawiec, Z. Zimborás, Space-efficient binary optimization for variational quantum computing. npj Quantum Inf. 8(1), 39 (2022)
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms. Nature 415(6867), 39–44 (2002)
C. Gross, W.S. Bakr, Quantum gas microscopy for single atom and spin detection. Nat. Phys. 17(12), 1316–1323 (2021)
C. Huang, F. Ye, X. Chen, Y.V. Kartashov, V.V. Konotop, L. Torner, Localization-delocalization wavepacket transition in pythagorean aperiodic potentials. Sci. Rep. 6(1), 32546 (2016)
H. Hübener, U. De Giovannini, C. Schäfer, J. Andberger, M. Ruggenthaler, J. Faist, A. Rubio, Engineering quantum materials with chiral optical cavities. Nat. Mater. 20(4), 438–442 (2021)
W.J. Huggins, J.R. McClean, N.C. Rubin, Z. Jiang, N. Wiebe, K.B. Whaley, R. Babbush, Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers. npj Quantum Inf. 7(1), 23 (2021)
D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, and P. Zoller. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998)
S. Julià-Farré, M. Müller, M. Lewenstein, A. Dauphin, Self-trapped polarons and topological defects in a topological mott insulator. Phys. Rev. Lett. 125, 240601 (2020)
D. Kennes, M. Claassen, L. Xian, A. Georges, A. Millis, J. Hone, C. Dean, D. Basov, A. Pasupathy, A. Rubio, Moiré heterostructures as a condensed-matter quantum simulator. Nat. Phys. 17, 1–9 (2021)
J. King, S. Yarkoni, J. Raymond, I. Ozfidan, A.D. King, M.M. Nevisi, J.P. Hilton, C.C. McGeoch, Quantum annealing amid local ruggedness and global frustration. J. Phys. Soc. Jpn. 88(6), 061007 (2019)
E. Knill, R. Laflamme, G. Milburn, A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)
M.S. Könz, W. Lechner, H.G. Katzgraber, M. Troyer, Scaling overhead of embedding optimization problems in quantum annealing. Phys. Rev. X Quantum 2, 040322 (2021)
C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M.K. Joshi, P. Jurcevic, C.A. Muschik, P. Silvi, R. Blatt, C.F. Roos, P. Zoller, Self-verifying variational quantum simulation of lattice models. Nature 569(7756), 355–360 (2019)
K. Kottmann, A. Haller, A. Acín, G.E. Astrakharchik, M. Lewenstein, Supersolid-superfluid phase separation in the extended bose-hubbard model. Phys. Rev. B 104, 174514 (2021)
K. Kottmann, P. Huembeli, M. Lewenstein, A. Acín, Unsupervised phase discovery with deep anomaly detection. Phys. Rev. Lett. 125, 170603 (2020)
S. Kuhr, Quantum-gas microscopes: a new tool for cold-atom quantum simulators. Natl. Sci. Rev. 3(2), 170–172 (2016)
C. Lagoin, U. Bhattacharya, T. Grass, R. Chhajlany, T. Salamon, K. Baldwin, L. Pfeiffer, M. Lewenstein, M. Holzmann, F. Dubin, Extended Bose-Hubbard model with dipolar excitons. Nature 609, 485–489 (2022). https://doi.org/10.1038/s41586-022-05123-z
R. Landauer, Irreversibility and heat generation in the computing process. IBM J. Res. Develop. 5(3), 183–191 (1961)
J.B. Lasserre, Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11(3), 796–817 (2001)
P.A. Lee, From high temperature superconductivity to quantum spin liquid: progress in strong correlation physics. Rep. Progress Phys. 71(1), 012501 (2007)
S. Lee, J. Lee, H. Zhai, Y. Tong, A.M. Dalzell, A. Kumar, P. Helms, J. Gray, Z.-H. Cui, W. Liu, M. Kastoryano, R.B. Babbush, J. Preskill, D.R. Reichman, E.T. Campbell, E.F. Valeev, L. Lin, G.K.-L.C. Chan, Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry. Nat Commun 14, 1952 (2023). https://doi.org/10.1038/s41467-023-37587-6
M. Lewenstein, P. Balcou, M.Y. Ivanov, A. L’Huillier, P.B. Corkum, Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994)
M. Lewenstein, M. Ciappina, E. Pisanty, J. Rivera-Dean, P. Stammer, T. Lamprou, P. Tzallas, Generation of optical schrödinger cat states in intense laser - matter interactions. Nat. Phys. 17 (2021)
M. Lewenstein, A. Sanpera, V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems (Oxford University Press, Oxford, 2012)
X. Lu, P. Stepanov, W. Yang, M. Xie, M.A. Aamir, I. Das, C. Urgell, K. Watanabe, T. Taniguchi, G. Zhang, A. Bachtold, A.H. MacDonald, D.K. Efetov, Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574(7780), 653–657 (2019)
R. Ma, B. Saxberg, C. Owens, N. Leung, Y. Lu, J. Simon, D.I. Schuster, A dissipatively stabilized mott insulator of photons. Nature 566(7742), 51–57 (2019)
D.J.C. MacKay, Information Theory, Inference, and Learning Algorithms (Cambridge University Press, Cambridge, 2003)
I.I. Manin, Vychislimoe i nevychislimoe (Sov. radio, Moskva, 1980)
E.A. Martinez, C.A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, R. Blatt, Real-time dynamics of lattice gauge theories with a few-qubit quantum computer. Nature 534(7608), 516–519 (2016)
D.A. Mazziotti, Variational minimization of atomic and molecular ground-state energies via the two-particle reduced density matrix. Phys. Rev. A 65, 062511 (2002)
A.J. McCaskey, Z.P. Parks, J. Jakowski, S.V. Moore, T.D. Morris, T.S. Humble, R.C. Pooser, Quantum chemistry as a benchmark for near-term quantum computers. npj Quantum Inf. 5(1), 99 (2019)
N. Moll, P. Barkoutsos, L.S. Bishop, J.M. Chow, A. Cross, D.J. Egger, S. Filipp, A. Fuhrer, J.M. Gambetta, M. Ganzhorn, A. Kandala, A. Mezzacapo, P. Müller, W. Riess, G. Salis, J. Smolin, I. Tavernelli, K. Temme, Quantum optimization using variational algorithms on near-term quantum devices. Quantum Sci. Technol. 3(3), 030503 (2018)
C. Monroe, W.C. Campbell, L.-M. Duan, Z.-X. Gong, A.V. Gorshkov, P.W. Hess, R. Islam, K. Kim, N.M. Linke, G. Pagano, P. Richerme, C. Senko, N.Y. Yao, Programmable quantum simulations of spin systems with trapped ions. Rev. Mod. Phys. 93, 025001 (2021)
S. Mugel, A. Dauphin, P. Massignan, L. Tarruell, M. Lewenstein, C. Lobo, A. Celi, Measuring Chern numbers in Hofstadter strips. SciPost Phys. 3, 012 (2017)
G. Müller-Rigat, A. Aloy, M. Lewenstein, I. Frérot, Inferring nonlinear many-body bell inequalities from average two-body correlations: Systematic approach for arbitrary spin-j ensembles. PRX Quantum 2(3), (2021)
G. Müller-Rigat, M. Lewenstein, I. Frérot, Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities, Quantum 6, 887 (2022). https://doi.org/10.22331/q-2022-12-29-887
M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, K. Fujisawa, Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm. J. Chem. Phys. 114(19), 8282–8292 (2001)
M. Navascués, S. Pironio, A. Acín, A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations. New J. Phys. 10(7), 073013 (2008)
F. Pan, K. Chen, P. Zhang, Solving the sampling problem of the sycamore quantum. Phys. Rev. Lett. 129, 090502 (2022)
F. Pan, P. Zhang, Simulation of quantum circuits using the big-batch tensor network method. Phys. Rev. Lett. 128, 030501 (2022)
G.S. Paraoanu, Recent progress in quantum simulation using superconducting circuits. J. Low Temp. Phys. 175(5–6), 633–654 (2014)
P.A. Parrilo, Semidefinite programming relaxations for semialgebraic problems. Math. Program. 96(2), 293–320 (2003)
A. Perdomo-Ortiz, A. Feldman, A. Ozaeta, S.V. Isakov, Z. Zhu, B. O’Gorman, H.G. Katzgraber, A. Diedrich, H. Neven, J. de Kleer, B. Lackey, R. Biswas, Readiness of quantum optimization machines for industrial applications. Phys. Rev. Appl. 12, 014004 (2019)
S. Pironio, M. Navascué s, A. Acín, Convergent relaxations of polynomial optimization problems with noncommuting variables. SIAM J. Optim. 20(5), 2157–2180 (2010)
J. Preskill, Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018)
S.-J. Ran, E. Tirrito, C. Peng, X. Chen, L. Tagliacozzo, G. Su, M. Lewenstein, Tensor Network Contractions (Springer International Publishing, New York, 2020)
M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, T. Monz, A universal qudit quantum processor with trapped ions. Nat. Phys. 18, 1053–1057 (2022). https://doi.org/10.1038/s41567-022-01658-0
T. Salamon, A. Celi, R.W. Chhajlany, I. Frérot, M. Lewenstein, L. Tarruell, D. Rakshit, Simulating twistronics without a twist. Phys. Rev. Lett. 125, 030504 (2020)
S.D. Sarma, Quantum computing has a hype problem. MIT Technology Review (2022). https://www.technologyreview.com/2022/03/28/1048355/quantum-computing-has-a-hype-problem/
N. Schine, A. Ryou, A. Gromov, A. Sommer, J. Simon, Synthetic landau levels for photons. Nature 534(7609), 671–675 (2016)
F. Schlawin, D.M. Kennes, M.A. Sentef, Cavity quantum materials. Appl. Phys. Rev. 9(1), 011312 (2022)
P. Scholl, M. Schuler, H.J. Williams, A.A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T.C. Lang, T. Lahaye, A.M. Läuchli, A. Browaeys, Quantum simulation of 2d antiferromagnets with hundreds of rydberg atoms. Nature 595(7866), 233–238 (2021)
M. Schuld, N. Killoran, Is quantum advantage the right goal for quantum machine learning? PRX Quantum 3, 030101 (2022)
G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T.T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletic, M.D. Lukin, Probing topological spin liquids on a programmable quantum simulator. Science 374(6572), 1242–1247 (2021)
J.F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, S. Kuhr, Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467(7311), 68–72 (2010)
P. Sierant, M. Lewenstein, J. Zakrzewski, Polynomially filtered exact diagonalization approach to many-body localization. Phys. Rev. Lett. 125, 156601 (2020)
P. St-Jean, A. Dauphin, P. Massignan, B. Real, O. Jamadi, M. Milicevic, A. Lemaître, A. Harouri, L. Le Gratiet, I. Sagnes, S. Ravets, J. Bloch, A. Amo, Measuring topological invariants in a polaritonic analog of graphene. Phys. Rev. Lett. 126, 127403 (2021)
P. Stepanov, I. Das, X. Lu, A. Fahimniya, K. Watanabe, T. Taniguchi, F.H.L. Koppens, J. Lischner, L. Levitov, D.K. Efetov, Untying the insulating and superconducting orders in magic-angle graphene. Nature 583(7816), 375–378 (2020)
D. Stilck França, R. García-Patrón, Limitations of optimization algorithms on noisy quantum devices. Nat. Phys. 17(11), 1221–1227 (2021)
R.N. Tazhigulov, S.-N. Sun, R. Haghshenas, H. Zhai, A.T.K. Tan, N.C. Rubin, R. Babbush, A.J. Minnich, G.K.-L. Chan, Simulating challenging correlated molecules and materials on the sycamore quantum processor, PRXQuantum 3, 040318 (2022). https://link.aps.org/doi/10.1103/PRXQuantum.3.040318
J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G.H. Booth, J. Tennyson, The Variational Quantum Eigensolver: A review of methods and best practices, Physics Reports 986, (2022). https://doi.org/10.1016/j.physrep.2022.08.003
N. Tishby, Statistical physics and machine learning: a 30 year perspective. https://www.youtube.com/watch?v=BUfnIT92ukM
A. Trabesinger, Quantum simulation. Nat. Phys. 8(4), 263–263 (2012)
J. Tura, R. Augusiak, A.B. Sainz, T. Vé rtesi, M. Lewenstein, A. Acín, Detecting nonlocality in many-body quantum states. Science 344(6189), 1256–1258 (2014)
L. Vandenberghe, S. Boyd, Semidefinite programming. SIAM Rev. 38(1), 49–95 (1996)
P. Wang, Y. Zheng, X. Chen, C. Huang, Y.V. Kartashov, L. Torner, V.V. Konotop, F. Ye, Localization and delocalization of light in photonic moiré lattices. Nature 577(7788), 42–46 (2019)
S.R. White, Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863–2866 (1992)
R. Yamada, M. Lewenstein, Interpreting quantum randomness. AI & Music S+T+ARTS (2021). https://www.youtube.com/watch?v=Z-GLxgg0Z18
J. Zhang, G. Pagano, P.W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A.V. Gorshkov, Z.-X. Gong, C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551(7682), 601–604 (2017)
H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, P. Hu, X.-Y. Yang, W.-J. Zhang, H. Li, Y. Li, X. Jiang, L. Gan, G. Yang, L. You, Z. Wang, L. Li, N.-L. Liu, C.-Y. Lu, J.-W. Pan, Quantum computational advantage using photons. Science 370(6523), 1460–1463 (2020)
Acknowledgements
We acknowledge Antonio Acín and Leticia Taruell for their contributions to the manuscript. Over several years, we have been publishing mini-reviews of our “achievements” on the ICFO Web Page in the News section [1]. These text were edited with the help of Alina Hirschmann, whose irreplaceable help is highly appreciated. We have adopted here some of these mini-reviews, mostly of the papers from our groups, but we also acknowledge courtesy of Adrian Bachtold, Alexandre Dauphin, Dima Efetov and Lluis Torner for being able to use their texts. JF, TS and ML acknowledge support from: ERC AdG NOQIA; Agencia Estatal de Investigación (R&D project CEX2019-000910-S, funded by MCIN / AEI / 10.13039 / 501100011033, Plan National FIDEUA PID2019-106901GB-I00, FPI, QUANTERA MAQS PCI2019-111828-2, Proyectos de I+D+I “Retos Colaboración” QUSPIN RTC2019-007196-7); Fundació Cellex; Fundació Mir-Puig; Generalitat de Catalunya through the European Social Fund FEDER and CERCA program (AGAUR Grant No. 2017 SGR 134, QuantumCAT U16-011424, co-funded by ERDF Operational Program of Catalonia 2014–2020); EU Horizon 2020 FET-OPEN OPTOlogic (Grant No 899794); National Science Centre, Poland (Symfonia Grant No. 2016/20/W/ST4/00314); European Union’s Horizon 2020 research and innovation programme under the Marie-Skołdowska-Curie grant agreement No 101029393 (STREDCH) and No 847648 (“La Caixa” Junior Leaders fellowships ID100010434: LCF/BQ/PI19/11690013, LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012, LCF/BQ/PR21/11840013).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Fraxanet, J., Salamon, T., Lewenstein, M. (2023). The Coming Decades of Quantum Simulation. In: Citro, R., Lewenstein, M., Rubio, A., Schleich, W.P., Wells, J.D., Zank, G.P. (eds) Sketches of Physics. Lecture Notes in Physics, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-031-32469-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-031-32469-7_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-32468-0
Online ISBN: 978-3-031-32469-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)