Designing calibration and expressivity-efficient instruction sets for quantum computing

Rigetti, "Rigetti Aspen-8," https://medium.com/rigetti/rigetti-aspen-8-on-aws-236d9dc11613, 2020.

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, and J. M. Martinis, "Quantum supremacy using a programmable superconducting processor," Nature, vol. 574, no. 7779, pp. 505--510, 2019.

D. M. Abrams, N. Didier, B. R. Johnson, M. P. da Silva, and C. A. Ryan, "Implementation of the XY interaction family with calibration of a single pulse," arXiv:1912.04424, 2019.

B. Foxen, C. Neill, A. Dunsworth, P. Roushan, B. Chiaro, A. Megrant, J. Kelly, Z. Chen, K. Satzinger, R. Barends, F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, S. Boixo, D. Buell, B. Burkett, Y. Chen, R. Collins, E. Farhi, A. Fowler, C. Gidney, M. Giustina, R. Graff, M. Harrigan, T. Huang, S. V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, P. Klimov, A. Korotkov, F. Kostritsa, D. Landhuis, E. Lucero, J. McClean, M. McEwen, X. Mi, M. Mohseni, J. Y. Mutus, O. Naaman, M. Neeley, M. Niu, A. Petukhov, C. Quintana, N. Rubin, D. Sank, V. Smelyanskiy, A. Vainsencher, T. C. White, Z. Yao, P. Yeh, A. Zalcman, H. Neven, and J. M. Martinis, "Demonstrating a Continuous Set of Two-Qubit Gates for Near-Term Quantum Algorithms," Phys. Rev. Lett., vol. 125, p. 120504, Sep 2020.

J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, "Quantum machine learning," Nature, vol. 549, Sep 2017.

A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O'Brien, "A variational eigenvalue solver on a photonic quantum processor," Nature Communications, vol. 5, Jul 2014.

B. Bauer, S. Bravyi, M. Motta, and G. K.-L. Chan, "Quantum algorithms for quantum chemistry and quantum materials science," arXiv:2001.03685, 2020.

J. Preskill, "Quantum Computing in the NISQ era and beyond," Quantum, vol. 2, p. 79, Aug. 2018.

Y. Nam, J.-S. Chen, N. C. Pisenti, K. Wright, C. Delaney, D. Maslov, K. R. Brown, S. Allen, J. M. Amini, J. Apisdorf, K. M. Beck, A. Blinov, V. Chaplin, M. Chmielewski, C. Collins, S. Debnath, K. M. Hudek, A. M. Ducore, M. Keesan, S. M. Kreikemeier, J. Mizrahi, P. Solomon, M. Williams, J. D. Wong-Campos, D. Moehring, C. Monroe, and J. Kim, "Ground-state energy estimation of the water molecule on a trapped-ion quantum computer," npj Quantum Information, vol. 6, no. 1, p. 33, Apr 2020.

J. S. Otterbach, R. Manenti, N. Alidoust, A. Bestwick, M. Block, B. Bloom, S. Caldwell, N. Didier, E. S. Fried, S. Hong, P. Karalekas, C. B. Osborn, A. Papageorge, E. C. Peterson, G. Prawiroatmodjo, N. Rubin, C. A. Ryan, D. Scarabelli, M. Scheer, E. A. Sete, P. Sivarajah, R. S. Smith, A. Staley, N. Tezak, W. J. Zeng, A. Hudson, B. R. Johnson, M. Reagor, M. P. da Silva, and C. Rigetti, "Unsupervised machine learning on a hybrid quantum computer," arXiv:1712.05771, 2017.

J. Kelly, R. Barends, A. G. Fowler, A. Megrant, E. Jeffrey, T. C. White, D. Sank, J. Y. Mutus, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O'Malley, C. Quintana, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, and J. M. Martinis, "State preservation by repetitive error detection in a superconducting quantum circuit," Nature, vol. 519, no. 7541, pp. 66--69, Mar 2015.

S. Boixo, S. V. Isakov, V. N. Smelyanskiy, R. Babbush, N. Ding, Z. Jiang, M. J. Bremner, J. M. Martinis, and H. Neven, "Characterizing quantum supremacy in near-term devices," Nature Physics, vol. 14, no. 6, pp. 595--600, Jun 2018.

N. Lacroix, C. Hellings, C. K. Andersen, A. Di Paolo, A. Remm, S. Lazar, S. Krinner, G. J. Norris, M. Gabureac, J. Heinsoo, A. Blais, C. Eichler, and A. Wallraff, "Improving the performance of deep quantum optimization algorithms with continuous gate sets," PRX Quantum, vol. 1, no. 2, p. 110304, 2020.

IBM, "IBM Quantum Experience Devices," https://quantum-computing.ibm.com/, 2020.

P. Murali, J. M. Baker, A. Javadi-Abhari, F. T. Chong, and M. Martonosi, "Noise-Adaptive Compiler Mappings for Noisy Intermediate-Scale Quantum Computers," in Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, 2019, pp. 1015--1029.

P. Murali, N. M. Linke, M. Martonosi, A. J. Abhari, N. H. Nguyen, and C. H. Alderete, "Full-Stack, Real-System Quantum Computer Studies: Architectural Comparisons and Design Insights," in Proceedings of the 46th International Symposium on Computer Architecture, ser. ISCA '19. New York, NY, USA: Association for Computing Machinery, 2019, p. 527--540. [Online].

S. S. Tannu and M. K. Qureshi, "Not All Qubits Are Created Equal: A Case for Variability-Aware Policies for NISQ-Era Quantum Computers," in Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems. ACM, 2019, pp. 987--999.

S. Nishio, Y. Pan, T. Satoh, H. Amano, and R. V. Meter, "Extracting Success from IBM's 20-Qubit Machines Using Error-Aware Compilation," ACM Journal on Emerging Technologies in Computing Systems (JETC), vol. 16, no. 3, pp. 1--25, 2020.

R. S. Smith, M. J. Curtis, and W. J. Zeng, "A practical quantum instruction set architecture," arXiv:1608.03355, 2016.

A. W. Cross, L. S. Bishop, J. A. Smolin, and J. M. Gambetta, "Open quantum assembly language," arXiv:1707.03429, 2017.

X. Fu, L. Riesebos, M. A. Rol, J. van Straten, J. van Someren, N. Khammassi, I. Ashraf, R. F. L. Vermeulen, V. Newsum, K. K. L. Loh, J. C. de Sterke, W. J. Vlothuizen, R. N. Schouten, C. G. Almudever, L. DiCarlo, and K. Bertels, "eQASM: An Executable Quantum Instruction Set Architecture," in 2019 IEEE International Symposium on High Performance Computer Architecture (HPCA), 2019, pp. 224--237.

K. Bertels, A. Sarkar, T. Hubregtsen, M. Serrao, A. A. Mouedenne, A. Yadav, A. Krol, I. Ashraf, and C. G. Almudever, "Quantum computer architecture toward full-stack quantum accelerators," IEEE Transactions on Quantum Engineering, vol. 1, pp. 1--17, 2020.

M. Kjaergaard, M. E. Schwartz, A. Greene, G. O. Samach, A. Bengtsson, M. O'Keeffe, C. M. McNally, J. Braumüller, D. K. Kim, P. Krantz, M. Marvian, A. Melville, B. M. Niedzielski, Y. Sung, R. Winik, J. Yoder, D. Rosenberg, K. Obenland, S. Lloyd, T. P. Orlando, I. Marvian, S. Gustavsson, and W. D. Oliver, "A quantum instruction set implemented on a superconducting quantum processor," 2020, arXiv:2001.08838.

X. Zou, S. P. Premaratne, M. A. Rol, S. Johri, V. Ostroukh, D. J. Michalak, R. Caudillo, J. S. Clarke, L. DiCarlo, and A. Y. Matsuura, "Enhancing a near-term quantum accelerator's instruction set architecture for materials science applications," IEEE Transactions on Quantum Engineering, vol. 1, pp. 1--7, 2020.

D. Maslov, S. M. Falconer, and M. Mosca, "Quantum circuit placement," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 27, no. 4, pp. 752--763, 2008.

M. Y. Siraichi, V. F. d. Santos, S. Collange, and F. M. Q. Pereira, "Qubit allocation," in Proceedings ofthe 2018 International Symposium on Code Generation and Optimization. ACM, 2018, pp. 113--125.

D. Venturelli, M. Do, E. Rieffel, and J. Frank, "Compiling quantum circuits to realistic hardware architectures using temporal planners," Quantum Science and Technology, vol. 3, no. 2, p. 025004, 2018.

A. Zulehner and R. Wille, "Compiling SU (4) quantum circuits to IBM QX architectures," in Proceedings of the 24th Asia and South Pacific Design Automation Conference. ACM, 2019, pp. 185--190.

G. Li, Y. Ding, and Y. Xie, "Tackling the qubit mapping problem for NISQ-era quantum devices," in Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems. ACM, 2019, pp. 1001--1014.

P. Murali, D. C. McKay, M. Martonosi, and A. Javadi-Abhari, "Software Mitigation of Crosstalk on Noisy Intermediate-Scale Quantum Computers," in Proceedings of the Twenty-Fifth International Conference on Architectural Support for Programming Languages and Operating Systems, 2020, pp. 1001--1016.

H. Abraham, AduOffei, R. Agarwal, I. Y. Akhalwaya, G. Aleksandrowicz, T. Alexander, E. Arbel, A. Asfaw, C. Azaustre, AzizNgoueya, A. Bansal, P. Barkoutsos, G. Barron, L. Bello, Y. Ben-Haim, D. Bevenius, L. S. Bishop, S. Bolos, S. Bosch, S. Bravyi, D. Bucher, A. Burov, F. Cabrera, P. Calpin, L. Capelluto, J. Carballo, G. Carrascal, A. Chen, C.-F. Chen, E. Chen, J. C. Chen, R. Chen, J. M. Chow, S. Churchill, C. Claus, C. Clauss, R. Cocking, A. J. Cross, A. W. Cross, S. Cross, J. Cruz-Benito, C. Culver, A. D. Córcoles-Gonzales, S. Dague, T. E. Dandachi, M. Daniels, M. Dartiailh, DavideFrr, A. R. Davila, A. Dekusar, D. Ding, J. Doi, E. Drechsler, Drew, E. Dumitrescu, K. Dumon, I. Duran, K. EL-Safty, E. Eastman, P. Eendebak, D. Egger, M. Everitt, P. M. Fernández, A. H. Ferrera, R. Fouilland, FranckChevallier, A. Frisch, A. Fuhrer, M. GEORGE, J. Gacon, B. G. Gago, C. Gambella, J. M. Gambetta, A. Gammanpila, L. Garcia, S. Garion, A. Gilliam, A. Giridharan, J. Gomez-Mosquera, S. de la Puente González, J. Gorzinski, I. Gould, D. Greenberg, D. Grinko, W. Guan, J. A. Gunnels, M. Haglund, I. Haide, I. Hamamura, O. C. Hamido, V. Havlicek, J. Hellmers, Ł. Herok, S. Hillmich, H. Horii, C. Howington, S. Hu, W. Hu, R. Huisman, H. Imai, T. Imamichi, K. Ishizaki, R. Iten, T. Itoko, JamesSeaward, A. Javadi, A. Javadi-Abhari, Jessica, M. Jivrajani, K. Johns, Jonathan-Shoemaker, T. Kachmann, N. Kanazawa, Kang-Bae, A. Karazeev, P. Kassebaum, S. King, Knabberjoe, Y. Kobayashi, A. Kovyrshin, R. Krishnakumar, V. Krishnan, K. Krsulich, G. Kus, R. LaRose, E. Lacal, R. Lambert, J. Lapeyre, J. Latone, S. Lawrence, C. Lee, G. Li, D. Liu, P. Liu, Y. Maeng, A. Malyshev, J. Manela, J. Marecek, M. Marques, D. Maslov, D. Mathews, A. Matsuo, D. T. McClure, C. McGarry, D. McKay, D. McPherson, S. Meesala, T. Metcalfe, M. Mevissen, A. Mezzacapo, R. Midha, Z. Minev, A. Mitchell, N. Moll, M. D. Mooring, R. Morales, N. Moran, MrF, P. Murali, J. Müggenburg, D. Nadlinger, K. Nakanishi, G. Nannicini, P. Nation, E. Navarro, Y. Naveh, S. W. Neagle, P. Neuweiler, P. Niroula, H. Norlen, L. J. O'Riordan, O. Ogunbayo, P. Ollitrault, S. Oud, D. Padilha, H. Paik, Y. Pang, S. Perriello, A. Phan, F. Piro, M. Pistoia, C. Piveteau, A. Pozas-iKerstjens, V. Prutyanov, D. Puzzuoli, J. Pérez, Quintiii, R. I. Rahman, A. Raja, N. Ramagiri, A. Rao, R. Raymond, R. M.-C. Redondo, M. Reuter, J. Rice, D. M. Rodríguez, RohithKarur, M. Rossmannek, M. Ryu, T. SAPV, SamFerracin, M. Sandberg, R. Sapra, H. Sargsyan, A. Sarkar, N. Sathaye, B. Schmitt, C. Schnabel, Z. Schoenfeld, T. L. Scholten, E. Schoute, J. Schwarm, I. F. Sertage, K. Setia, N. Shammah, Y. Shi, A. Silva, A. Simonetto, N. Singstock, Y. Siraichi, I. Sitdikov, S. Sivarajah, M. B. Sletfjerding, J. A. Smolin, M. Soeken, I. O. Sokolov, SooluThomas, Starfish, D. Steenken, M. Stypulkoski, S. Sun, K. J. Sung, H. Takahashi, I. Tavernelli, C. Taylor, P. Taylour, S. Thomas, M. Tillet, M. Tod, M. Tomasik, E. de la Torre, K. Trabing, M. Treinish, TrishaPe, W. Turner, Y. Vaknin, C. R. Valcarce, F. Varchon, A. C. Vazquez, V. Villar, D. Vogt-Lee, C. Vuillot, J. Weaver, R. Wieczorek, J. A. Wildstrom, E. Winston, J. J. Woehr, S. Woerner, R. Woo, C. J. Wood, R. Wood, S. Wood, S. Wood, J. Wootton, D. Yeralin, D. Yonge-Mallo, R. Young, J. Yu, C. Zachow, L. Zdanski, H. Zhang, C. Zoufal, and Zoufalc, "Qiskit: An open-source framework for quantum computing," 2019.

A. W. Cross, L. S. Bishop, S. Sheldon, P. D. Nation, and J. M. Gambetta, "Validating quantum computers using randomized model circuits," Phys. Rev. A, vol. 100, no. 3, p. 032328, 2019.

Rigetti, "Rigetti quantum computing service," https://www.qcs.rigetti.com/, 2020.

F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, S. Boixo, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, S. Demura, A. Dunsworth, D. Eppens, E. Farhi, A. Fowler, B. Foxen, C. Gidney, M. Giustina, R. Graff, S. Habegger, M. P. Harrigan, A. Ho, S. Hong, T. Huang, L. B. Ioffe, S. V. Isakov, E. Jeffrey, Z. Jiang, C. Jones, D. Kafri, K. Kechedzhi, J. Kelly, S. Kim, P. V. Klimov, A. N. Korotkov, F. Kostritsa, D. Landhuis, P. Laptev, M. Lindmark, M. Leib, E. Lucero, O. Martin, J. M. Martinis, J. R. McClean, M. McEwen, A. Megrant, X. Mi, M. Mohseni, W. Mruczkiewicz, J. Mutus, O. Naaman, M. Neeley, C. Neill, F. Neukart, H. Neven, M. Y. Niu, T. E. O'Brien, B. O'Gorman, E. Ostby, A. Petukhov, H. Putterman, C. Quintana, P. Roushan, N. C. Rubin, D. Sank, K. J. Satzinger, A. Skolik, V. Smelyanskiy, D. Strain, M. Streif, K. J. Sung, M. Szalay, A. Vainsencher, T. White, Z. J. Yao, P. Yeh, A. Zalcman, and L. Zhou, "Quantum approximate optimization of non-planar graph problems on a planar superconducting processor," arXiv:2004.04197, 2020.

D. C. McKay, C. J. Wood, S. Sheldon, J. M. Chow, and J. M. Gambetta, "Efficient Z gates for quantum computing," Phys. Rev. A, vol. 96, p. 022330, Aug 2017.

A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, "Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets," Nature, vol. 549, Sep 2017.

E. Farhi, J. Goldstone, and S. Gutmann, "A quantum approximate optimization algorithm," arXiv:1411.4028, 2014.

E. C. Peterson, G. E. Crooks, and R. S. Smith, "Two-qubit circuit depth and the monodromy polytope," Quantum, vol. 4, p. 247, 2020.

P. V. Klimov, J. Kelly, J. M. Martinis, and H. Neven, "The snake optimizer for learning quantum processor control parameters," arXiv:2006.04594, 2020.

R. R. Tucci, "A rudimentary quantum compiler (2cnd ed.)," arXiv:9902062, 1999.

N. Khaneja, R. Brockett, and S. J. Glaser, "Time optimal control in spin systems," Phys. Rev. A, vol. 63, no. 3, p. 032308, 2001.

B. Kraus and J. Cirac, "Optimal creation of entanglement using a two-qubit gate," Phys. Rev. A, vol. 63, no. 6, p. 062309, 2001.

F. Vatan and C. Williams, "Optimal quantum circuits for general two-qubit gates," Phys. Rev. A, vol. 69, no. 3, p. 032315, 2004.

M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, "Quantum circuits for general multiqubit gates," Phys. Rev. Lett., vol. 93, no. 13, p. 130502, 2004.

R. Iten, R. Colbeck, and M. Christandl, "Quantum circuits for quantum channels," Phys. Rev. A, vol. 95, no. 5, p. 052316, 2017.

D. Maslov, C. Young, D. M. Miller, and G. W. Dueck, "Quantum circuit simplification using templates," in Design, Automation and Test in Europe, 2005, pp. 1208--1213 Vol. 2.

R. S. Smith, E. C. Peterson, M. Skilbeck, and E. Davis, "An open-source, industrial-strength optimizing compiler for quantum programs," Quantum Science and Technology, 2020.

T. Jones and S. C. Benjamin, "Quantum compilation and circuit optimisation via energy dissipation," arXiv:1811.03147, 2018.

S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborger, and P. J. Coles, "Quantum-assisted quantum compiling," Quantum, vol. 3, p. 140, 2019.

M. G. Davis, E. Smith, A. Tudor, K. Sen, I. Siddiqi, and C. Iancu, "Heuristics for quantum compiling with a continuous gate set," arXiv:1912.02727, 2019.

H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, "An adaptive variational algorithm for exact molecular simulations on a quantum computer," Nature communications, vol. 10, no. 1, pp. 1--9, 2019.

R. Fletcher, Practical Methods of Optimization, 2nd ed. New York, NY, USA: John Wiley & Sons, 1987.

J. Liu and H. Zhou, "Reliability Modeling of NISQ-Era Quantum Computers," in 2020 IEEE International Symposium on Workload Characterization, ser. IISWC, 2020.

N. M. Linke, D. Maslov, M. Roetteler, S. Debnath, C. Figgatt, K. A. Landsman, K. Wright, and C. Monroe, "Experimental comparison of two quantum computing architectures," Proceedings of the National Academy of Sciences, vol. 114, no. 13, pp. 3305--3310, 2017. [Online]. Available: https://www.pnas.org/content/114/13/3305

K. Wright, K. M. Beck, S. Debnath, J. M. Amini, Y. Nam, N. Grzesiak, J.-S. Chen, N. C. Pisenti, M. Chmielewski, C. Collins, K. M. Hudek, J. Mizrahi, J. D. Wong-Campos, S. Allen, J. Apisdorf, P. Solomon, M. Williams, A. M. Ducore, A. Blinov, S. M. Kreikemeier, V. Chaplin, M. Keesan, C. Monroe, and J. Kim, "Benchmarking an 11-qubit quantum computer," Nature Communications, vol. 10, no. 1, p. 5464, Nov 2019.

Z. Wang, S. Hadfield, Z. Jiang, and E. G. Rieffel, "Quantum approximate optimization algorithm for MaxCut: A fermionic view," Phys. Rev. A, vol. 97, no. 2, p. 022304, 2018.

F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, A. Bengtsson, S. Boixo, M. Broughton, B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, Y. Chen, Z. Chen, B. Chiaro, R. Collins, S. Cotton, W. Courtney, S. Demura, A. Derk, A. Dunsworth, D. Eppens, T. Eckl, C. Erickson, E. Farhi, A. Fowler, B. Foxen, C. Gidney, M. Giustina, R. Graff, J. A. Gross, S. Habegger, M. P. Harrigan, A. Ho, S. Hong, T. Huang, W. Huggins, L. Ioffe, S. V. Isakov, E. Jeffrey, Z. Jiang, C. Jones, D. Kafri, K. Kechedzhi, J. Kelly, S. Kim, P. Klimov, A. Korotkov, F. Kostritsa, D. Landhuis, P. Laptev, M. Lindmark, E. Lucero, M. Marthaler, O. Martin, J. M. Martinis, A. Marusczyk, S. McArdle, J. McClean, T. McCourt, M. McEwen, A. Megrant, C. Mejuto-Zaera, X. Mi, M. Mohseni, W. Mruczkiewicz, J. Mutus, O. Naaman, M. Neeley, C. Neill, H. Neven, M. Newman, M. Y. Niu, T. E. O'brien, E. Ostby, B. Pat'o, A. Petukhov, H. Putterman, C. Quintana, J. Reiner, P. Roushan, N. Rubin, D. Sank, K. Satzinger, V. Smelyanskiy, D. Strain, K. J. Sung, P. Schmitteckert, M. Szalay, N. M. Tubman, A. Vainsencher, T. White, N. Vogt, Z. Yao, P. Yeh, A. Zalcman, and S. Zanker, "Observation of separated dynamics of charge and spin in the fermi-hubbard model," arXiv:2010.07965, 2020.

P. W. Shor, "Algorithms for quantum computation: Discrete logarithms and factoring," in Proceedings 35th annual symposium on foundations of computer science. Ieee, 1994, pp. 124--134.

M. A. Nielsen and I. Chuang, "Quantum computation and quantum information," 2002.

Google, "Recirq," https://github.com/quantumlib/ReCirq, 2020.

S. Aaronson and L. Chen, "Complexity-theoretic foundations of quantum supremacy experiments," arXiv:1612.05903, 2016.

C. Neill, P. Roushan, K. Kechedzhi, S. Boixo, S. V. Isakov, V. Smelyanskiy, A. Megrant, B. Chiaro, A. Dunsworth, K. Arya, R. Barends, B. Burkett, Y. Chen, Z. Chen, A. Fowler, B. Foxen, M. Giustina, R. Graff, E. Jeffrey, T. Huang, J. Kelly, P. Klimov, E. Lucero, J. Mutus, M. Neeley, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, H. Neven, and J. M. Martinis, "A blueprint for demonstrating quantum supremacy with superconducting qubits," Science, vol. 360, no. 6385, pp. 195--199, 2018. [Online]. Available: https://science.sciencemag.org/content/360/6385/195

C. Rigetti, J. M. Gambetta, S. Poletto, B. L. T. Plourde, J. M. Chow, A. D. Córcoles, J. A. Smolin, S. T. Merkel, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, "Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1 ms," Phys. Rev. B, vol. 86, p. 100506, Sep 2012. [Online].