Quantum Computing in the NISQ era and beyond Quantum
Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away - we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.
[1] P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Rev. 41, 303-332 (1999), 10.1137/S0036144598347011. https://doi.org/10.1137/S0036144598347011
[2] A. P. Lund, M. J. Bremner, and T. C. Ralph, Quantum sampling problems, BosonSampling, and quantum supremacy, npj Quantum Information 3: 15 (2017), arXiv:1702.03061, 10.1038/s41534-017-0018-2. https://doi.org/10.1038/s41534-017-0018-2 arXiv:1702.03061
[3] A. W. Harrow and A. Montanaro, Quantum computational supremacy, Nature 549, 203-209 (2017), 10.1038/nature23458. https://doi.org/10.1038/nature23458
[4] S. P. Jordan, Quantum algorithm zoo, http://math.nist.gov/quantum/zoo/. http://math.nist.gov/quantum/zoo/
[5] A. Montanaro, Quantum algorithms: an overview, npj Quantum Information, 15023 (2016), arXiv:1511.04206, 10.1038/npjqi.2015.23. https://doi.org/10.1038/npjqi.2015.23 arXiv:1511.04206
[6] L. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett. 79, 325 (1997), arXiv:quant-ph/9706033, 10.1103/PhysRevLett.79.325. https://doi.org/10.1103/PhysRevLett.79.325 arXiv:quant-ph/9706033
[7] C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, Strengths and weaknesses of quantum computing, SIAM J. Comput. 26, 1510-1523 (1997), arXiv:quant-ph/9701001, 10.1137/S0097539796300933. https://doi.org/10.1137/S0097539796300933 arXiv:quant-ph/9701001
[8] R. B. Laughlin and D. Pines, The theory of everything, PNAS 97, 28-31 (2000), 10.1073/pnas.97.1.28. https://doi.org/10.1073/pnas.97.1.28
[9] R. P. Feynman, Simulating physics with computers, Int. J. Theor. Physics 21, 467-488 (1982).
[10] D. Gottesman, An introduction to quantum error correction and fault-tolerant quantum computation, Proceedings of Symposia in Applied Matthematics 68 (2010), arXiv:0904.2557. arXiv:0904.2557
[11] S. Boixo, S. V. Isakov, V. N. Smelyansky, R. Babbush, N. Ding, Z. Jiang, M. J. Bremner, J. M. Martinis, and H. Neven, Characterizing quantum supremacy in near-term devices, Nature Physics 14, 595-600 (2018), arXiv:1608.00263 (2016), 10.1038/s41567-018-0124-x. https://doi.org/10.1038/s41567-018-0124-x arXiv:1608.00263
[12] S. Aaronson and L. Chen, Complexity-theoretic foundations of quantum supremacy experiments, arXiv:1612.05903 (2017). arXiv:1612.05903
[13] E. Pednault, J. A. Gunnels, G. Nannicini, L. Horesh, T. Magerlein, E. Solomonik, and R. Wisnieff, Breaking the 49-qubit barrier in the simulation of quantum circuits, arXiv:1710.05867 (2017). arXiv:1710.05867
[14] C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, and D. M. Lucas, High-fidelity quantum logic gates using trapped-ion hyperfine qubits, Phys. Rev. Lett. 117, 060504 (2016), arXiv:1512.04600, 10.1103/PhysRevLett.117.060504. https://doi.org/10.1103/PhysRevLett.117.060504 arXiv:1512.04600
[15] R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O'Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, Superconducting quantum circuits at the surface code threshold for fault tolerance, Nature 508, 500-503 (2014), arXiv:1402.4848, 10.1038/nature13171. https://doi.org/10.1038/nature13171 arXiv:1402.4848
[16] D. J. Bernstein, J. Buchmann, E. Dahmen, editors, Post-Quantum Cryptography, Springer (2009), 10.1007/978-3-540-88702-7. https://doi.org/10.1007/978-3-540-88702-7
[17] R. Allaume, C. Branciard, J. Bouda, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Lnger, N. Ltkenhaus, C. Monyk, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, Using quantum key distribution for cryptographic purposes: a survey, Theoretical Computer Science 560, 62-81 (2014), arXiv:quant-ph/0701168, 10.1016/j.tcs.2014.09.018. https://doi.org/10.1016/j.tcs.2014.09.018 arXiv:quant-ph/0701168
[18] S. Muralidharan, L. Li, J. Kim, N Ltkenhaus, M. D. Lukin, and L. Jiang, Efficient long distance quantum communication, Scientific Reports 6, 20463 (2016), arXiv:1509.08435, 10.1038/srep20463. https://doi.org/10.1038/srep20463 arXiv:1509.08435
[19] P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, Experimentally generated randomness certified by the impossibility of superluminal signals, Nature 556, 223-226 (2018), arXiv:1803.06219, 10.1038/s41586-018-0019-0. https://doi.org/10.1038/s41586-018-0019-0 arXiv:1803.06219
[20] Z. Brakerski, P. Christiano, U. Mahadev, U. Vazirani, and T. Vidick, Certifiable randomness from a single quantum device, arXiv:1804.00640 (2018). arXiv:1804.00640
[21] C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017), arXiv:1611.04691, 10.1103/RevModPhys.89.035002. https://doi.org/10.1103/RevModPhys.89.035002 arXiv:1611.04691
[22] J. Preskill, Quantum computing and the entanglement frontier, 25th Solvay Conference on Physics (2011), arXiv:1203.5813. arXiv:1203.5813
[23] S. Khot, Hardness of approximation, Proceedings of the International Congress of Mathematicians (2014).
[24] E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv:1411.4028 (2014). arXiv:1411.4028
[25] J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, The theory of variational hybrid quantum-classical algorithms, New J. Phys. 18, 023023 (2016), arXiv:1509.04279, 10.1038/ncomms5213. https://doi.org/10.1038/ncomms5213 arXiv:1509.04279
[26] D. A. Spielman and S.-H. Teng, Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time, Journal of the ACM 51, 385-463 (2004), arXiv:cs/0111050, 10.1145/990308.990310. https://doi.org/10.1145/990308.990310 arXiv:cs/0111050
[27] Y. LeCun, Y. Bengio, and G. Hinton, Deep learning, Nature 521, 436-444 (2015), 10.1038/nature14539. https://doi.org/10.1038/nature14539
[28] T. F. Rnnow, Z. Wang, J. Job, S. Boixo, S. V. Isakov, D. Wecker, J. M. Martinis, D. A. Lidar, and M. Troyer, Defining and detecting quantum speedup, Science 345, 420-424 (2014), 10.1126/science.1252319. https://doi.org/10.1126/science.1252319
[29] S. Mandr, H. G. Katzgraber, and C. Thomas, The pitfalls of planar spin-glass benchmarks: raising the bar for quantum annealers (again), Quantum Sci. Technol. 2, 038501 (2017), arXiv:1703.00622, 10.1088/2058-9565/aa7877. https://doi.org/10.1088/2058-9565/aa7877 arXiv:1703.00622
[30] T. Albash and D. A. Lidar, Adiabatic quantum computing, Rev. Mod. Phys. 90, 015002 (2018), arXiv:1611.04471, 10.1103/RevModPhys.90.015002. https://doi.org/10.1103/RevModPhys.90.015002 arXiv:1611.04471
[31] D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, Adiabatic quantum computation is equivalent to standard quantum computation, SIAM Rev. 50, 755-787 (2008), arXiv:quant-ph/0405098. arXiv:quant-ph/0405098
[32] S. Bravyi, D. DiVincenzo, R. I. Oliveira, and B. M. Terhal, The complexity of stoquastic local Hamiltonian problems, Quant. Inf. Comp. 8, 0361-0385 (2008), arXiv:quant-ph/0606140. arXiv:quant-ph/0606140
[33] M. Jarret, S. P. Jordan, and B. Lackey, Adiabatic optimization versus diffusion Monte Carlo, Phys. Rev. A 94, 042318 (2016), arXiv:1607.03389, 10.1103/PhysRevA.94.042318. https://doi.org/10.1103/PhysRevA.94.042318 arXiv:1607.03389
[34] A. D. King, J. Carrasquilla, I. Ozfidan, J. Raymond, E. Andriyash, A. Berkley, M. Reis, T. M. Lanting, R. Harris, G. Poulin-Lamarre, A. Yu. Smirnov, C. Rich, F. Altomare, P. Bunyk, J. Whittaker, L. Swenson, E. Hoskinson, Y. Sato, M. Volkmann, E. Ladizinsky, M. Johnson, J. Hilton, and M. H. Amin, Observation of topological phenomena in a programmable lattice of 1,800 qubits, arXiv:1803.02047 (2018). arXiv:1803.02047
[35] I. H. Kim, Noise-resilient preparation of quantum many-body ground states, arXiv:1703.00032 (2017). arXiv:1703.00032
[36] I. H. Kim and B. Swingle, Robust entanglement renormalization on a noisy quantum computer, arXiv:1711.07500 (2017). arXiv:1711.07500
[37] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Nature 549, 195-202 (2017), arXiv:1611.09347, 10.1038/nature23474. https://doi.org/10.1038/nature23474 arXiv:1611.09347
[38] S. Aaronson, Read the fine print, Nature Physics 11, 291-293 (2015), 10.1038/nphys3272. https://doi.org/10.1038/nphys3272
[39] X. Gao, Z. Zhang, and L. Duan, An efficient quantum algorithm for generative machine learning, arXiv:1711.02038 (2017). arXiv:1711.02038
[40] A. W. Harrow, A. Hassidim, and S. Lloyd, Quantum algorithm for linear systems of equations, Phys. Rev. Lett. 103, 150502 (2009), arXiv:0811.3171, 10.1103/PhysRevLett.103.150502. https://doi.org/10.1103/PhysRevLett.103.150502 arXiv:0811.3171
[41] B. D. Clader, B. C. Jacobs, and C. R. Sprouse, Preconditioned quantum linear system algorithm, Phys. Rev. Lett. 110, 250504 (2013), arXiv:1301.2340, 10.1103/PhysRevLett.110.250504. https://doi.org/10.1103/PhysRevLett.110.250504 arXiv:1301.2340
[42] A. Montanaro and S. Pallister, Quantum algorithms and the finite element method, Phys. Rev. A 93, 032324 (2016), arXiv:1512.05903, 10.1103/PhysRevA.93.032324. https://doi.org/10.1103/PhysRevA.93.032324 arXiv:1512.05903
[43] P. C. S. Costa, S. Jordan, and A. Ostrander, Quantum algorithm for simulating the wave equation, arXiv:1711.05394 (2017). arXiv:1711.05394
[44] I. Kerenidis and A. Prakash, Quantum recommendation systems, arXiv:1603.08675 (2016). arXiv:1603.08675
[45] E. Tang, A quantum-inspired classical algorithm for recommendation systems, Electronic Colloquium on Computational Complexity, TR18-12 (2018).
[46] F. G. S. L. Brando and K. Svore, Quantum speed-ups for semidefinite programming, Proceedings of FOCS 2017, arXiv:1609.05537 (2017). arXiv:1609.05537
[47] F. G. S. L. Brando, A. Kalev, T. Li, C. Y.-Y. Lin, K. M. Svore, and X. Wu, Exponential quantum speed-ups for semidefinite programming with applications to quantum learning, arXiv:1710.02581 (2017). arXiv:1710.02581
[48] M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, Elucidating reaction mechanisms on quantum computers, PNAS 117, 7555-7560 (2017), arXiv:1605.03590, 10.1073/pnas.1619152114. https://doi.org/10.1073/pnas.1619152114 arXiv:1605.03590
[49] D. Wecker, M. B. Hastings, N. Wiebe, B. K. Clark, C. Nayak, and M. Troyer, Solving strongly correlated electron models on a quantum computer, Phys. Rev. A 92, 062310 (2015), arXiv:1506.05135, 10.1103/PhysRevA.92.062318. https://doi.org/10.1103/PhysRevA.92.062318 arXiv:1506.05135
[50] J. Olson, Y. Cao, J. Romero, P. Johnson, P.-L. Dallaire-Demers, N. Sawaya, P. Narang, I. Kivlichan, M. Wasielewski, A. Aspuru-Guzik, Quantum information and computation for chemistry, NSF Workshop Report, arXiv:1706.05413 (2017). arXiv:1706.05413
[51] H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V Vuleti, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature 551, 579-584 (2017), arXiv:1707.04344, 10.1038/nature24622. https://doi.org/10.1038/nature24622 arXiv:1707.04344
[52] J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, arXiv:1708.01044 (2017), 10.1038/nature24654. https://doi.org/10.1038/nature24654 arXiv:1708.01044
[53] E. T. Campbell, B. M. Terhal, and C. Vuillot, The steep road towards robust and universal quantum computation, arXiv:1612.07330 (2016). arXiv:1612.07330
[54] J. J. Wallman and J. Emerson, Noise tailoring for scalable quantum computation via randomized compiling, Phys. Rev. A 94, 052325 (2016), arXiv:1512:01098, 10.1103/PhysRevA.94.052325. https://doi.org/10.1103/PhysRevA.94.052325 arXiv:1512
[55] J. Combes, C. Granade, C. Ferrie, and S. T. Flammia, Logical randomized benchmarking, arXiv:1702.03688 (2017). arXiv:1702.03688
[56] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012), arXiv:1208.0928, 10.1103/PhysRevA.86.032324. https://doi.org/10.1103/PhysRevA.86.032324 arXiv:1208.0928
[57] S. Das Sarma, M. Freedman, and C. Nayak, Majorana zero modes and topological quantum computation, npj Quantum Information 1, 15001 (2015), arXiv:1501.02813, 10.1038/npjqi.2015.1. https://doi.org/10.1038/npjqi.2015.1 arXiv:1501.02813
[1] Vojtch Havlek, Antonio D. Crcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta, "Supervised learning with quantum-enhanced feature spaces", Nature 567 7747, 209 (2019).
[2] Abhinav Kandala, Kristan Temme, Antonio D. Crcoles, Antonio Mezzacapo, Jerry M. Chow, and Jay M. Gambetta, "Error mitigation extends the computational reach of a noisy quantum processor", Nature 567 7749, 491 (2019).
[3] Andrew D. King, Juan Carrasquilla, Jack Raymond, Isil Ozfidan, Evgeny Andriyash, Andrew Berkley, Mauricio Reis, Trevor Lanting, Richard Harris, Fabio Altomare, Kelly Boothby, Paul I. Bunyk, Colin Enderud, Alexandre Frchette, Emile Hoskinson, Nicolas Ladizinsky, Travis Oh, Gabriel Poulin-Lamarre, Christopher Rich, Yuki Sato, Anatoly Yu. Smirnov, Loren J. Swenson, Mark H. Volkmann, Jed Whittaker, Jason Yao, Eric Ladizinsky, Mark W. Johnson, Jeremy Hilton, and Mohammad H. Amin, "Observation of topological phenomena in a programmable lattice of 1,800 qubits", Nature 560 7719, 456 (2018).
[4] Seth Lloyd and Christian Weedbrook, "Quantum Generative Adversarial Learning", Physical Review Letters 121 4, 040502 (2018).
[5] Victor V. Albert, Kyungjoo Noh, Kasper Duivenvoorden, Dylan J. Young, R. T. Brierley, Philip Reinhold, Christophe Vuillot, Linshu Li, Chao Shen, S. M. Girvin, Barbara M. Terhal, and Liang Jiang, "Performance and structure of single-mode bosonic codes", Physical Review A 97 3, 032346 (2018).
[6] Panagiotis Kl. Barkoutsos, Jerome F. Gonthier, Igor Sokolov, Nikolaj Moll, Gian Salis, Andreas Fuhrer, Marc Ganzhorn, Daniel J. Egger, Matthias Troyer, Antonio Mezzacapo, Stefan Filipp, and Ivano Tavernelli, "Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions", Physical Review A 98 2, 022322 (2018).
[7] Guillaume Verdon, Michael Broughton, Jarrod R. McClean, Kevin J. Sung, Ryan Babbush, Zhang Jiang, Hartmut Neven, and Masoud Mohseni, "Learning to learn with quantum neural networks via classical neural networks", arXiv:1907.05415.
[8] Pierre-Luc Dallaire-Demers and Nathan Killoran, "Quantum generative adversarial networks", Physical Review A 98 1, 012324 (2018).
[9] Gavin E. Crooks, "Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition", arXiv:1905.13311.
[10] Edward Grant, Marcello Benedetti, Shuxiang Cao, Andrew Hallam, Joshua Lockhart, Vid Stojevic, Andrew G. Green, and Simone Severini, "Hierarchical quantum classifiers", npj Quantum Information 4, 65 (2018).
[11] J. Preskill, "Simulating quantum field theory with a quantum computer", The 36th Annual International Symposium on Lattice Field Theory. 22-28 July 24 (2018).
[12] Zhang Jiang, Kevin J. Sung, Kostyantyn Kechedzhi, Vadim N. Smelyanskiy, and Sergio Boixo, "Quantum Algorithms to Simulate Many-Body Physics of Correlated Fermions", Physical Review Applied 9 4, 044036 (2018).
[13] Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon Benjamin, and Xiao Yuan, "Quantum computational chemistry", arXiv:1808.10402.
[14] Jianxin Chen, Fang Zhang, Cupjin Huang, Michael Newman, and Yaoyun Shi, "Classical Simulation of Intermediate-Size Quantum Circuits", arXiv:1805.01450.
[15] Yuxuan Du, Min-Hsiu Hsieh, Tongliang Liu, and Dacheng Tao, "The Expressive Power of Parameterized Quantum Circuits", arXiv:1810.11922.
[16] Tameem Albash and Daniel A. Lidar, "Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing", Physical Review X 8 3, 031016 (2018).
[17] Ling Hu, Shu-Hao Wu, Weizhou Cai, Yuwei Ma, Xianghao Mu, Yuan Xu, Haiyan Wang, Yipu Song, Dong-Ling Deng, Chang-Ling Zou, and Luyan Sun, "Quantum generative adversarial learning in a superconducting quantum circuit", Science Advances 5 1, eaav2761 (2019).
[18] Aram Harrow and John Napp, "Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms", arXiv:1901.05374.
[19] Guillaume Verdon, Jason Pye, and Michael Broughton, "A Universal Training Algorithm for Quantum Deep Learning", arXiv:1806.09729.
[20] Kentaro Heya, Yasunari Suzuki, Yasunobu Nakamura, and Keisuke Fujii, "Variational Quantum Gate Optimization", arXiv:1810.12745.
[21] Ramis Movassagh, "Quantum supremacy and random circuits", arXiv:1909.06210.
[22] Bryan O'Gorman, William J. Huggins, Eleanor G. Rieffel, and K. Birgitta Whaley, "Generalized swap networks for near-term quantum computing", arXiv:1905.05118.
[23] Yudong Cao, Jonathan Romero, Jonathan P. Olson, Matthias Degroote, Peter D. Johnson, Mria Kieferov, Ian D. Kivlichan, Tim Menke, Borja Peropadre, Nicolas P. D. Sawaya, Sukin Sim, Libor Veis, and Aln Aspuru-Guzik, "Quantum Chemistry in the Age of Quantum Computing", arXiv:1812.09976.
[24] Sebastien Piat, Nairi Usher, Simone Severini, Mark Herbster, Tommaso Mansi, and Peter Mountney, "Image classification with quantum pre-training and auto-encoders", International Journal of Quantum Information 16 8, 1840009-332 (2018).
[25] Eric R. Anschuetz, Jonathan P. Olson, Aln Aspuru-Guzik, and Yudong Cao, "Variational Quantum Factoring", arXiv:1808.08927.
[26] Brian Swingle and Nicole Yunger Halpern, "Resilience of scrambling measurements", Physical Review A 97 6, 062113 (2018).
[27] Xun Gao and Luming Duan, "Efficient classical simulation of noisy quantum computation", arXiv:1810.03176.
[28] Jonathan Romero and Alan Aspuru-Guzik, "Variational quantum generators: Generative adversarial quantum machine learning for continuous distributions", arXiv:1901.00848.
[29] Maria Schuld and Nathan Killoran, "Quantum machine learning in feature Hilbert spaces", arXiv:1803.07128.
[30] Swamit S. Tannu and Moinuddin K. Qureshi, "A Case for Variability-Aware Policies for NISQ-Era Quantum Computers", arXiv:1805.10224.
[31] Mark Fingerhuth, Tom Babej, and Christopher Ing, "A quantum alternating operator ansatz with hard and soft constraints for lattice protein folding", arXiv:1810.13411.
[32] Sumsam Ullah Khan, Ahsan Javed Awan, and Gemma Vall-Llosera, "K-Means Clustering on Noisy Intermediate Scale Quantum Computers", arXiv:1909.12183.
[33] Gushu Li, Yufei Ding, and Yuan Xie, "Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices", arXiv:1809.02573.
[34] A. Garcia-Saez and J. I. Latorre, "Addressing hard classical problems with Adiabatically Assisted Variational Quantum Eigensolvers", arXiv:1806.02287.
[35] Javier Gil Vidal and Dirk Oliver Theis, "Calculus on parameterized quantum circuits", arXiv:1812.06323.
[36] Kazuki Ikeda, Yuma Nakamura, and Travis S. Humble, "Application of Quantum Annealing to Nurse Scheduling Problem", Scientific Reports 9, 12837 (2019).
[37] Alwin Zulehner and Robert Wille, "Compiling SU(4) Quantum Circuits to IBM QX Architectures", arXiv:1808.05661.
[38] Juan Miguel Arrazola, Thomas R. Bromley, and Patrick Rebentrost, "Quantum approximate optimization with Gaussian boson sampling", Physical Review A 98 1, 012322 (2018).
[39] Zhang Jiang, Jarrod McClean, Ryan Babbush, and Hartmut Neven, "Majorana Loop Stabilizer Codes for Error Mitigation in Fermionic Quantum Simulations", Physical Review Applied 12 6, 064041 (2019).
[40] Salonik Resch and Ulya R. Karpuzcu, "Quantum Computing: An Overview Across the System Stack", arXiv:1905.07240.
[41] Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, and Mark Howard, "Simulation of quantum circuits by low-rank stabilizer decompositions", arXiv:1808.00128.
[42] Zhong-Xiao Man, Yun-Jie Xia, and Rosario Lo Franco, "Temperature effects on quantum non-Markovianity via collision models", Physical Review A 97 6, 062104 (2018).
View post:
Quantum Computing in the NISQ era and beyond Quantum
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- Quantum Computing Is Closer Than Insurers Think - Insurance Innovation Reporter - August 29th, 2026 [August 29th, 2026]
- Quantum Progress: From The Lab To The Real World - Forbes - August 29th, 2026 [August 29th, 2026]
- Ready before the hardware is: How agencies can get ahead of the quantum curve - Federal News Network - August 29th, 2026 [August 29th, 2026]
- Practical, self-correcting quantum computers could soon be developed in US with new funding - Interesting Engineering - August 29th, 2026 [August 29th, 2026]
- Stop Waiting for Q-Day: The Quantum Clock Is Ticking - Clearance Jobs - August 29th, 2026 [August 29th, 2026]
- Illinois-led regional quantum hub NSF HQAN renewed to pursue industry-ready computing and workforce development - The Grainger College of Engineering - August 29th, 2026 [August 29th, 2026]
- Scientists Are Building Quantum Computers That Fix Their Own Mistakes - Gadget Review - August 29th, 2026 [August 29th, 2026]
- Scientists Are Building Quantum Computers That Fix Their Own Mistakes - Yahoo Tech - August 29th, 2026 [August 29th, 2026]
- The Quantum Computer Revolution Is Tantalizingly Close - Advisor Perspectives - August 29th, 2026 [August 29th, 2026]
- 1 Quantum Computing Stock That Looks Like a Screaming Buy Right Now - Yahoo Finance - August 23rd, 2026 [August 23rd, 2026]
- Want to muck around with a real quantum computer? Now you can - The Conversation - August 23rd, 2026 [August 23rd, 2026]
- How Fujitsu is bridging quantum readiness and enterprise needs - cio.com - August 23rd, 2026 [August 23rd, 2026]
- New EPB CEO talks about the broadband companys work with quantum - Fierce Network - August 23rd, 2026 [August 23rd, 2026]
- D-Wave Quantum expands footprint for planned HQ - The Business Journals - August 23rd, 2026 [August 23rd, 2026]
- The Quantum Computing Race Is Heating Up: The Top 3 Stocks to Buy Right Now - The Motley Fool - August 23rd, 2026 [August 23rd, 2026]
- Quantum Computings Revolutionary Promise Is Bringing Real-World Solutions - Newsweek - August 23rd, 2026 [August 23rd, 2026]
- Quantum Computing vs. Red Cat: Which High-Growth Innovation Stock Is a Better Buy in 2026? - Yahoo Finance - August 23rd, 2026 [August 23rd, 2026]
- London Cluster Backs Early-stage Quantum Health Innovation - Quantum Zeitgeist - August 23rd, 2026 [August 23rd, 2026]
- D-Wave Quantum Stock Rallies 8% Following Outperform Initiation From BMO Capital Citing Commercial Revenue Growth - TIKR.com - August 23rd, 2026 [August 23rd, 2026]
- Leeds Researchers Balance Quantum Repeater Speed And Reach - Quantum Zeitgeist - August 23rd, 2026 [August 23rd, 2026]
- As IBM achieves modular quantum cold chain milestone, is it time to think about cold swapping? - diginomica - August 23rd, 2026 [August 23rd, 2026]
- The global race to make a practical quantum computer just took a big leap forward - The Conversation - August 18th, 2026 [August 18th, 2026]
- Two Quantum Computing Stocks Are Starting to Pull Ahead of the Pack - fool.com - August 18th, 2026 [August 18th, 2026]
- 1 Quantum Stock Near 52-Week Lows With Nvidia Partnership Backing Is Poised to Rebound - Yahoo Finance - August 18th, 2026 [August 18th, 2026]
- From Beaches to Bits to Qubits Silicons Journey in Quantum Computing - The Quantum Insider - August 18th, 2026 [August 18th, 2026]
- The Quantum Computing Race Is On: Meet The ETF Capturing Sector-Wide Momentum - Barchart.com - August 18th, 2026 [August 18th, 2026]
- 1 Quantum Stock Near 52-Week Lows With Nvidia Partnership Backing Is Poised to Rebound - fool.com - August 18th, 2026 [August 18th, 2026]
- This researcher is helping fend off quantum computing security risks - Northeastern Global News - August 18th, 2026 [August 18th, 2026]
- Quantum computing is coming fast. Are utilities ready? - Utility Dive - August 18th, 2026 [August 18th, 2026]
- Quantum Computer Markets: Who Leads? Report: Evaluating 12 Strategic Vendor Profiles, Cloud Services, and Competitive Rankings of IBM, Quantinuum,... - August 18th, 2026 [August 18th, 2026]
- Quantinuum: Pioneering The Future Of Quantum Computing (NASDAQ:QNT) - Seeking Alpha - August 18th, 2026 [August 18th, 2026]
- Eclypses And Sterling Team Up to Deliver Quantum-Resistant Cryptography to Federal Government Systems - The Quantum Insider - August 18th, 2026 [August 18th, 2026]
- CEE Is Building Quantum Hardware. Q2B Copenhagen Is Where It Gets a Seat at the Table - The Recursive - August 18th, 2026 [August 18th, 2026]
- The Hardest Part of Quantum-Proofing a Company Isn't the Encryption. It's Deciding Where to Start - Investing News Network - August 18th, 2026 [August 18th, 2026]
- IonQ partners with CMC to expand quantum access to Canadian researchers - Seeking Alpha - August 18th, 2026 [August 18th, 2026]
- This Quantum Computing Stock Just Scored a Major Breakthrough Deal. How to Play QNT Here. - Barchart.com - August 18th, 2026 [August 18th, 2026]
- Quantum Computing Earnings Offered a Reality Check. What Comes Next. - Barron's - August 18th, 2026 [August 18th, 2026]
- A pizza box, a 1991 flashback, and the ghosts of Route 128 - The Boston Globe - August 18th, 2026 [August 18th, 2026]
- Two Quantum Computing Stocks Are Starting to Pull Ahead of the Pack - The Globe and Mail - August 18th, 2026 [August 18th, 2026]
- Quantum AI: Expanding the Boundaries of Financial Decision-Making - Mexico Business News - August 18th, 2026 [August 18th, 2026]
- Infleqtion To Show Quantum Tech At SC26 In Chicago - Quantum Zeitgeist - August 18th, 2026 [August 18th, 2026]
- Inside the Trump administrations $2 billion push to build the worlds first useful quantum computer - Fast Company - August 9th, 2026 [August 9th, 2026]
- This Trillion-Dollar AI Stock Offers Better Quantum Computing Exposure Than IonQ, Rigetti, or D-Wave at a Multi-Year Valuation Low - fool.com - August 9th, 2026 [August 9th, 2026]
- This Trillion-Dollar AI Stock Offers Better Quantum Computing Exposure Than IonQ, Rigetti, or D-Wave at a Multi-Year Valuation Low - Currently.com - August 9th, 2026 [August 9th, 2026]
- These researchers seek to quiet the noise in quantum computing - Northeastern Global News - August 9th, 2026 [August 9th, 2026]
- This tiny gold crystal could bring quantum technology out of the deep freeze - sciencedaily.com - August 9th, 2026 [August 9th, 2026]
- Post-Quantum Cryptography Timelines: When Will Organizations Migrate? - thequantuminsider.com - August 9th, 2026 [August 9th, 2026]
- Silicon Superconducting Modality Stakes a Claim in Quantum Landscape - Communications of the ACM - August 9th, 2026 [August 9th, 2026]
- D-Wave Reports Bookings Surge as Quarterly Revenue Holds Steady - thequantuminsider.com - August 9th, 2026 [August 9th, 2026]
- Congress Eyes Boosting Quantum Funds as Global Race Heats Up - Yahoo Finance - August 9th, 2026 [August 9th, 2026]
- QuSecure Exec Says Quantum Threat Timeline Moved to 2029 - ExecutiveBiz - August 9th, 2026 [August 9th, 2026]
- Xanadu Reports Higher Revenue in 2Q 2026, Expands U.S. Operations - thequantuminsider.com - August 9th, 2026 [August 9th, 2026]
- Jeremy O'Brien, The Complete Story Of The PsiQuantum Founder - Quantum Zeitgeist - August 9th, 2026 [August 9th, 2026]
- Pasqal Receives SEC Clearance for Proposed SPAC Combination With Bleichroeder - thequantuminsider.com - August 9th, 2026 [August 9th, 2026]
- Engineers build world's first portable diamond-powered quantum computer it works at room temperature and can be plugged into an outlet -... - August 7th, 2026 [August 7th, 2026]
- Israel rolls out tender for national quantum computer, and plans for advanced AI push - The Times of Israel - August 5th, 2026 [August 5th, 2026]
- Quantum computing is helping AT&T solve network problems in seconds: D-Wave CEO - Yahoo Finance - July 28th, 2026 [July 28th, 2026]
- Quantum Computing Stocks: Here's How WisdomTree Sizes Up The Industry - Investor's Business Daily - July 28th, 2026 [July 28th, 2026]