Quantum-assisted quantum compiling

Sumeet Khatri; Ryan LaRose; Alexander Poremba; Lukasz Cincio; Andrew T. Sornborger; Patrick J. Coles

doi:10.22331/q-2019-05-13-140

Quantum-assisted quantum compiling

Sumeet Khatri^1,2, Ryan LaRose^1,3, Alexander Poremba^1,4, Lukasz Cincio¹, Andrew T. Sornborger⁵, and Patrick J. Coles¹

¹Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM USA.
²Hearne Institute for Theoretical Physics and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA USA.
³Department of Computational Mathematics, Science, and Engineering and Department of Physics and Astronomy, Michigan State University, East Lansing, MI USA.
⁴Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA USA.
⁵Information Sciences, Los Alamos National Laboratory, Los Alamos, NM USA.

Published:	2019-05-13, volume 3, page 140
Eprint:	arXiv:1807.00800v5
Doi:	https://doi.org/10.22331/q-2019-05-13-140
Citation:	Quantum 3, 140 (2019).

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Abstract

Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. To this end, we propose a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitary $U$ and a trainable unitary $V$ as the cost function to be evaluated on the quantum computer. More precisely, to ensure that QAQC scales well with problem size, our cost involves not only the global overlap ${\rm Tr}(V^†U)$ but also the local overlaps with respect to individual qubits. We introduce novel short-depth quantum circuits to quantify the terms in our cost function, and we prove that our cost cannot be efficiently approximated with a classical algorithm under reasonable complexity assumptions. We present both gradient-free and gradient-based approaches to minimizing this cost. As a demonstration of QAQC, we compile various one-qubit gates on IBM's and Rigetti's quantum computers into their respective native gate alphabets. Furthermore, we successfully simulate QAQC up to a problem size of 9 qubits, and these simulations highlight both the scalability of our cost function as well as the noise resilience of QAQC. Future applications of QAQC include algorithm depth compression, black-box compiling, noise mitigation, and benchmarking.

Popular summary

Ordinary computers require a compiler that converts one's code into a machine-level language. Quantum computers require a compiler as well. However, a new challenge for such "quantum compilers" is that they should be optimal, i.e., they should return a machine-level program that has as few operations as possible. This optimality is crucial for current noisy quantum devices, where longer programs accumulate more errors while shorter programs avoid errors. In this work, we introduce an algorithm for optimal quantum compiling. The key feature that allows for optimality is that we propose to use quantum computers themselves to assist in the compiling process. Hence, our algorithm is called quantum-assisted quantum compiling (QAQC, pronounced "Quack").

The idea is that one needs to quantify the distance between the original program and the compiled program, with the goal of trying to minimize this distance. We prove that this distance calculation cannot be done efficiently on a classical computer. On the other hand, we provide an efficient quantum circuit for computing it.

In addition to shortening the length of one's quantum program, QAQC can be used to learn algorithms that compensate for a given quantum computer's noise and also to benchmark the noise processes occurring on a quantum computer. We successfully implement QAQC for small programs using currently available quantum computers from IBM and Rigetti, and we use simulators to explore the compilation of larger programs. Overall, QAQC appears to be a promising tool for mitigating errors in the era of noisy intermediate-scale quantum computers.

► BibTeX data

@article{Khatri2019quantumassisted,
  doi = {10.22331/q-2019-05-13-140},
  url = {https://doi.org/10.22331/q-2019-05-13-140},
  title = {Quantum-assisted quantum compiling},
  author = {Khatri, Sumeet and LaRose, Ryan and Poremba, Alexander and Cincio, Lukasz and Sornborger, Andrew T. and Coles, Patrick J.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {140},
  month = may,
  year = {2019}
}

► References

[1] P. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Journal on Computing 26, 1484 (1997).
https://doi.org/10.1137/S0097539795293172

[2] E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv:1411.4028 (2014).
arXiv:1411.4028

[3] R. P. Feynman, Simulating physics with computers, International Journal of Theoretical Physics 21, 467 (1982).
https://doi.org/10.1007/BF02650179

[4] J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
https://doi.org/10.22331/q-2018-08-06-79

[5] J. Preskill, Quantum computing and the entanglement frontier, arXiv:1203.5813 (2012).
arXiv:1203.5813

[6] C. Neill, P. Roushan, K. Kechedzhi, S. Boixo, S. V. Isakov, V. Smelyanskiy, et al., A blueprint for demonstrating quantum supremacy with superconducting qubits, Science 360, 195 (2018).
https://doi.org/10.1126/science.aao4309

[7] D. Venturelli, M. Do, E. Rieffel, and J. Frank, Compiling quantum circuits to realistic hardware architectures using temporal planners, Quantum Science and Technology 3, 025004 (2018).
https://doi.org/10.1088/2058-9565/aaa331

[8] K. E. C. Booth, M. Do, J. C. Beck, E. Rieffel, D. Venturelli, and J. Frank, Comparing and integrating constraint programming and temporal planning for quantum circuit compilation, arXiv:1803.06775 (2018).
arXiv:1803.06775

[9] L. Cincio, Y. Subaşi, A. T. Sornborger, and P. J. Coles, Learning the quantum algorithm for state overlap, New Journal of Physics 20, 113022 (2018).
https://doi.org/10.1088/1367-2630/aae94a

[10] D. Maslov, G. W. Dueck, D. M. Miller, and C. Negrevergne, Quantum circuit simplification and level compaction, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 27, 436 (2008).
https://doi.org/10.1109/TCAD.2007.911334

[11] A. G. Fowler, Constructing arbitrary Steane code single logical qubit fault-tolerant gates, Quantum Information and Computation 11, 867 (2011).
http://dl.acm.org/citation.cfm?id=2230936.2230946

[12] J. Booth Jr, Quantum compiler optimizations, arXiv:1206.3348 (2012).
arXiv:1206.3348

[13] Y. Nam, N. J. Ross, Y. Su, A. M. Childs, and D. Maslov, Automated optimization of large quantum circuits with continuous parameters, npj Quantum Information 4, 23 (2018).
https://doi.org/10.1038/s41534-018-0072-4

[14] F. T. Chong, D. Franklin, and M. Martonosi, Programming languages and compiler design for realistic quantum hardware, Nature 549, 180 (2017).
https://doi.org/10.1038/nature23459

[15] L. E. Heyfron and E. T. Campbell, An efficient quantum compiler that reduces T count, Quantum Science and Technology 4, 015004 (2018).
https://doi.org/10.1088/2058-9565/aad604

[16] T. Häner, D. S. Steiger, K. Svore, and M. Troyer, A software methodology for compiling quantum programs, Quantum Science and Technology 3, 020501 (2018).
https://doi.org/10.1088/2058-9565/aaa5cc

[17] A. Oddi and R. Rasconi, in International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (Springer, 2018) pp. 446–461.
https://link.springer.com/chapter/10.1007/978-3-319-93031-2_32

[18] 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 5, 4213 (2014).
https://doi.org/10.1038/ncomms5213

[19] P. D. Johnson, J. Romero, J. Olson, Y. Cao, and A. Aspuru-Guzik, QVECTOR: an algorithm for device-tailored quantum error correction, arXiv:1711.02249 (2017).
arXiv:1711.02249

[20] M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, A generative modeling approach for benchmarking and training shallow quantum circuits, arXiv:1801.07686 (2018a).
arXiv:1801.07686

[21] K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Quantum circuit learning, Physical Review A 98, 032309 (2018).
https://doi.org/10.1103/PhysRevA.98.032309

[22] G. Verdon, J. Pye, and M. Broughton, A Universal Training Algorithm for Quantum Deep Learning, arXiv:1806.09729 (2018).
arXiv:1806.09729

[23] J. Romero, J. P. Olson, and A. Aspuru-Guzik, Quantum autoencoders for efficient compression of quantum data, Quantum Science and Technology 2, 045001 (2017).
https://doi.org/10.1088/2058-9565/aa8072

[24] J. Romero, J. P. Olson, and A. Aspuru-Guzik, Quantum autoencoders for short depth quantum circuit synthesis, GitHub article (2018).
https://github.com/zapatacomputing/cusp_cirq_demo/blob/master/cusp_protocol.pdf

[25] B. Dive, A. Pitchford, F. Mintert, and D. Burgarth, In situ upgrade of quantum simulators to universal computers, Quantum 2, 80 (2018).
https://doi.org/10.22331/q-2018-08-08-80

[26] E. Knill and R. Laflamme, Power of one bit of quantum information, Physical Review Letters 81, 5672 (1998).
https://doi.org/10.1103/PhysRevLett.81.5672

[27] K. Fujii, H. Kobayashi, T. Morimae, H. Nishimura, S. Tamate, and S. Tani, Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error, Physical Review Letters 120, 200502 (2018).
https://doi.org/10.1103/PhysRevLett.120.200502

[28] B. Rosgen and J. Watrous, in 20th Annual IEEE Conference on Computational Complexity (CCC'05) (2005) pp. 344–354.
https://doi.org/10.1109/CCC.2005.21

[29] R. S. Smith, M. J. Curtis, and W. J. Zeng, A practical quantum instruction set architecture, arXiv:1608.03355 (2016).
arXiv:1608.03355

[30] A. W. Cross, L. S. Bishop, J. A. Smolin, and J. M. Gambetta, Open Quantum Assembly Language, arXiv:1707.03429 (2017).
arXiv:1707.03429

[31] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
https://doi.org/10.1017/CBO9780511976667

[32] A. Kitaev, Quantum computations: algorithms and error correction, Russian Mathematical Surveys 52, 1191 (1997).
https://doi.org/10.1070/RM1997v052n06ABEH002155

[33] C. M. Dawson and M. A. Nielsen, The Solovay-Kitaev algorithm, Quantum Information and Compututation 6, 81 (2006).
http://dl.acm.org/citation.cfm?id=2011679.2011685

[34] T. T. Pham, R. Van Meter, and C. Horsman, Optimization of the Solovay-Kitaev algorithm, Physical Review A 87, 052332 (2013).
https://doi.org/10.1103/PhysRevA.87.052332

[35] V. Kliuchnikov, D. Maslov, and M. Mosca, Asymptotically optimal approximation of single qubit unitaries by Clifford and T circuits using a constant number of ancillary qubits, Physical Review Letters 110, 190502 (2013).
https://doi.org/10.1103/PhysRevLett.110.190502

[36] V. Kliuchnikov, A. Bocharov, and K. M. Svore, Asymptotically optimal topological quantum compiling, Physical Review Letters 112, 140504 (2014).
https://doi.org/10.1103/PhysRevLett.112.140504

[37] Y. Zhiyenbayev, V. M. Akulin, and A. Mandilara, Quantum compiling with diffusive sets of gates, Physical Review A 98, 012325 (2018).
https://doi.org/10.1103/PhysRevA.98.012325

[38] M. Horodecki, P. Horodecki, and R. Horodecki, General teleportation channel, singlet fraction, and quasidistillation, Physical Review A 60, 1888 (1999).
https://doi.org/10.1103/PhysRevA.60.1888

[39] M. A. Nielsen, A simple formula for the average gate fidelity of a quantum dynamical operation, Physics Letters A 303, 249 (2002).
https://doi.org/10.1016/S0375-9601(02)01272-0

[40] A. Gepp and P. Stocks, A review of procedures to evolve quantum algorithms, Genetic Programming and Evolvable Machines 10, 181 (2009).
https://doi.org/10.1007/s10710-009-9080-7

[41] M. Suzuki, Fractal decomposition of exponential operators with applications to many-body theories and monte carlo simulations, Physics Letters A 146, 319 (1990).
https://doi.org/10.1016/0375-9601(90)90962-N

[42] T. Jones and S. C. Benjamin, Quantum compilation and circuit optimisation via energy dissipation, arXiv:1811.03147 (2018).
arXiv:1811.03147

[43] J. C. Garcia-Escartin and P. Chamorro-Posada, Swap test and Hong-Ou-Mandel effect are equivalent, Physical Review A 87, 052330 (2013).
https://doi.org/10.1103/PhysRevA.87.052330

[44] P. W. Shor and S. P. Jordan, Estimating jones polynomials is a complete problem for one clean qubit, Quantum Information & Computation 8, 681 (2008).
http://www.rintonpress.com/xxqic8/qic-8-89/0681-0714.pdf

[45] IBM Q 5 Tenerife backend specification, (2018a).
https://github.com/QISKit/qiskit-backend-information/tree/master/backends/tenerife/V1

[46] IBM Q 16 Rueschlikon backend specification, (2018b).
https://github.com/Qiskit/qiskit-backend-information/tree/master/backends/rueschlikon/V1

[47] Rigetti 8Q-Agave specification v.2.0.0.dev0, (2018).
http://docs.rigetti.com/en/latest/qpu.html

[48] J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature Communications 9, 4812 (2018).
https://doi.org/10.1038/s41467-018-07090-4

[49] A. G. R. Day, M. Bukov, P. Weinberg, P. Mehta, and D. Sels, Glassy phase of optimal quantum control, Physical Review Letters 122, 020601 (2019).
https://doi.org/10.1103/PhysRevLett.122.020601

[50] X. Glorot and Y. Bengio, in In Proceedings of the International Conference on Artificial Intelligence and Statistics (2010) pp. 249–256.
http://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf?hc_location=ufi

[51] M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, A generative modeling approach for benchmarking and training shallow quantum circuits, arXiv:1801.07686 (2018b).
arXiv:1801.07686

[52] R. LaRose, A. Tikku, É. O'Neel-Judy, L. Cincio, and P. J. Coles, Variational quantum state diagonalization, arXiv:1810.10506 (2018).
arXiv:1810.10506

[53] A. Kandala, K. Temme, A. D. Corcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Extending the computational reach of a noisy superconducting quantum processor, Nature 567, 491 (2018).
https://doi.org/10.1038/s41586-019-1040-7

[54] Scikit-optimize, (2018a).
https://github.com/scikit-optimize/scikit-optimize

[55] J. Močkus, in Optimization Techniques IFIP Technical Conference Novosibirsk, July 1–7, 1974 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1975) pp. 400–404.
https://doi.org/10.1007/978-3-662-38527-2_55

[56] M. A. Osborne, R. Garnett, and S. J. Roberts, in 3rd International Conference on Learning and Intelligent Optimization (LION3) 2009 (2009).
https://www.cse.wustl.edu/~garnett/files/papers/osborne_et_al_lion_2009.pdf

[57] P. Rebentrost, M. Schuld, L. Wossnig, F. Petruccione, and S. Lloyd, Quantum gradient descent and Newton's method for constrained polynomial optimization, arXiv:1612.01789 (2016).
arXiv:1612.01789

[58] I. Kerenidis and A. Prakash, Quantum gradient descent for linear systems and least squares, arXiv:1704.04992 (2017).
arXiv:1704.04992

[59] A. Gilyén, S. Arunachalam, and N. Wiebe, Optimizing quantum optimization algorithms via faster quantum gradient computation, in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1425–1444.
https://doi.org/10.1137/1.9781611975482.87

[60] P. B. M. Sousa and R. V. Ramos, Universal quantum circuit for $n$-qubit quantum gate: A programmable quantum gate, Quantum Information and Computation 7, 228 (2007).
http://dl.acm.org/citation.cfm?id=2011717.2011721

[61] F. Vatan and C. Williams, Optimal quantum circuits for general two-qubit gates, Physical Review A 69, 032315 (2004).
https://doi.org/10.1103/PhysRevA.69.032315

[62] Scipy optimization and root finding, (2018b).
https://docs.scipy.org/doc/scipy/reference/optimize.html

[63] X.-Q. Zhou, T. C. Ralph, P. Kalasuwan, M. Zhang, A. Peruzzo, B. P. Lanyon, and J. L. O'Brien, Adding control to arbitrary unknown quantum operations, Nature Communications 2, 413 (2011).
https://doi.org/10.1038/ncomms1392

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[11] Lukasz Cincio, Yiğit Subaşı, Andrew T. Sornborger, and Patrick J. Coles, "Learning the quantum algorithm for state overlap", New Journal of Physics 20 11, 113022 (2018).

[12] Tianqi Chen, Ruizhe Shen, Ching Hua Lee, and Bo Yang, "High-fidelity realization of the AKLT state on a NISQ-era quantum processor", SciPost Physics 15 4, 170 (2023).

[13] Shuo Liu, Shi-Xin Zhang, Chang-Yu Hsieh, Shengyu Zhang, and Hong Yao, "Probing many-body localization by excited-state variational quantum eigensolver", Physical Review B 107 2, 024204 (2023).

[14] Arthur Pesah, M. Cerezo, Samson Wang, Tyler Volkoff, Andrew T. Sornborger, and Patrick J. Coles, "Absence of Barren Plateaus in Quantum Convolutional Neural Networks", Physical Review X 11 4, 041011 (2021).

[15] Kunal Sharma, Sumeet Khatri, M. Cerezo, and Patrick J. Coles, "Noise resilience of variational quantum compiling", New Journal of Physics 22 4, 043006 (2020).

[16] Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio, "Error mitigation with Clifford quantum-circuit data", Quantum 5, 592 (2021).

[17] Ryan LaRose and Brian Coyle, "Robust data encodings for quantum classifiers", Physical Review A 102 3, 032420 (2020).

[18] Matthias C. Caro, Hsin-Yuan Huang, M. Cerezo, Kunal Sharma, Andrew Sornborger, Lukasz Cincio, and Patrick J. Coles, "Generalization in quantum machine learning from few training data", Nature Communications 13, 4919 (2022).

[19] Bálint Koczor, "Exponential Error Suppression for Near-Term Quantum Devices", Physical Review X 11 3, 031057 (2021).

[20] Tyler Volkoff and Patrick J. Coles, "Large gradients via correlation in random parameterized quantum circuits", Quantum Science and Technology 6 2, 025008 (2021).

[21] A. V. Uvarov and J. D. Biamonte, "On barren plateaus and cost function locality in variational quantum algorithms", Journal of Physics A Mathematical General 54 24, 245301 (2021).

[22] M. Cerezo and Patrick J. Coles, "Higher order derivatives of quantum neural networks with barren plateaus", Quantum Science and Technology 6 3, 035006 (2021).

[23] Kaoru Mizuta, Yuya O. Nakagawa, Kosuke Mitarai, and Keisuke Fujii, "Local Variational Quantum Compilation of Large-Scale Hamiltonian Dynamics", PRX Quantum 3 4, 040302 (2022).

[24] Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone, Patrick J. Coles, Frédéric Sauvage, Martín Larocca, and M. Cerezo, "Theory for Equivariant Quantum Neural Networks", PRX Quantum 5 2, 020328 (2024).

[25] Juan Miguel Arrazola, Thomas R. Bromley, Josh Izaac, Casey R. Myers, Kamil Brádler, and Nathan Killoran, "Machine learning method for state preparation and gate synthesis on photonic quantum computers", Quantum Science and Technology 4 2, 024004 (2019).

[26] Martin Larocca, Piotr Czarnik, Kunal Sharma, Gopikrishnan Muraleedharan, Patrick J. Coles, and M. Cerezo, "Diagnosing Barren Plateaus with Tools from Quantum Optimal Control", Quantum 6, 824 (2022).

[27] Matthias C. Caro, Hsin-Yuan Huang, Nicholas Ezzell, Joe Gibbs, Andrew T. Sornborger, Lukasz Cincio, Patrick J. Coles, and Zoë Holmes, "Out-of-distribution generalization for learning quantum dynamics", Nature Communications 14, 3751 (2023).

[28] Andrew Arrasmith, Zoë Holmes, M. Cerezo, and Patrick J. Coles, "Equivalence of quantum barren plateaus to cost concentration and narrow gorges", Quantum Science and Technology 7 4, 045015 (2022).

[29] Shi-Xin Zhang, Chang-Yu Hsieh, Shengyu Zhang, and Hong Yao, "Differentiable quantum architecture search", Quantum Science and Technology 7 4, 045023 (2022).

[30] Jonas M. Kübler, Andrew Arrasmith, Lukasz Cincio, and Patrick J. Coles, "An Adaptive Optimizer for Measurement-Frugal Variational Algorithms", Quantum 4, 263 (2020).

[31] Eric R. Anschuetz and Bobak T. Kiani, "Quantum variational algorithms are swamped with traps", Nature Communications 13, 7760 (2022).

[32] Brian Coyle, Daniel Mills, Vincent Danos, and Elham Kashefi, "The Born supremacy: quantum advantage and training of an Ising Born machine", npj Quantum Information 6, 60 (2020).

[33] Kentaro Heya, Yasunari Suzuki, Yasunobu Nakamura, and Keisuke Fujii, "Variational Quantum Gate Optimization", arXiv:1810.12745, (2018).

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[39] Shiro Tamiya and Hayata Yamasaki, "Stochastic gradient line Bayesian optimization for efficient noise-robust optimization of parameterized quantum circuits", npj Quantum Information 8, 90 (2022).

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[48] M. Cerezo, Kunal Sharma, Andrew Arrasmith, and Patrick J. Coles, "Variational quantum state eigensolver", npj Quantum Information 8, 113 (2022).

[49] Christophe Piveteau, David Sutter, and Stefan Woerner, "Quasiprobability decompositions with reduced sampling overhead", npj Quantum Information 8, 12 (2022).

[50] Enrico Fontana, Nathan Fitzpatrick, David Muñoz Ramo, Ross Duncan, and Ivan Rungger, "Evaluating the noise resilience of variational quantum algorithms", Physical Review A 104 2, 022403 (2021).

[51] Cheng Xue, Zhao-Yun Chen, Yu-Chun Wu, and Guo-Ping Guo, "Effects of Quantum Noise on Quantum Approximate Optimization Algorithm", Chinese Physics Letters 38 3, 030302 (2021).

[52] Lorenzo Pastori, Tobias Olsacher, Christian Kokail, and Peter Zoller, "Characterization and Verification of Trotterized Digital Quantum Simulation Via Hamiltonian and Liouvillian Learning", PRX Quantum 3 3, 030324 (2022).

[53] Laura Gentini, Alessandro Cuccoli, Stefano Pirandola, Paola Verrucchi, and Leonardo Banchi, "Noise-resilient variational hybrid quantum-classical optimization", Physical Review A 102 5, 052414 (2020).

[54] Benedikt Fauseweh, "Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges", Nature Communications 15, 2123 (2024).

[55] Ludmila Botelho, Adam Glos, Akash Kundu, Jarosław Adam Miszczak, Özlem Salehi, and Zoltán Zimborás, "Error mitigation for variational quantum algorithms through mid-circuit measurements", Physical Review A 105 2, 022441 (2022).

[56] Daniel Bultrini, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Patrick J. Coles, and Lukasz Cincio, "Unifying and benchmarking state-of-the-art quantum error mitigation techniques", arXiv:2107.13470, (2021).

[57] Jin Ming Koh, Tommy Tai, Yong Han Phee, Wei En Ng, and Ching Hua Lee, "Stabilizing multiple topological fermions on a quantum computer", npj Quantum Information 8, 16 (2022).

[58] Ryo Watanabe, Keisuke Fujii, and Hiroshi Ueda, "Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz", Physical Review Research 6 2, 023009 (2024).

[59] Patrick J. Coles, M. Cerezo, and Lukasz Cincio, "Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states", Physical Review A 100 2, 022103 (2019).

[60] Péter Rakyta and Zoltán Zimborás, "Approaching the theoretical limit in quantum gate decomposition", Quantum 6, 710 (2022).

[61] Lindsay Bassman, Roel Van Beeumen, Ed Younis, Ethan Smith, Costin Iancu, and Wibe A. de Jong, "Constant-depth circuits for dynamic simulations of materials on quantum computers", Materials Theory 6 1, 13 (2022).

[62] Lukas Broers and Ludwig Mathey, "Mitigated barren plateaus in the time-nonlocal optimization of analog quantum-algorithm protocols", Physical Review Research 6 1, 013076 (2024).

[63] Matteo G. Pozzi, Steven J. Herbert, Akash Sengupta, and Robert D. Mullins, "Using Reinforcement Learning to Perform Qubit Routing in Quantum Compilers", arXiv:2007.15957, (2020).

[64] Tyson Jones and Simon C. Benjamin, "Robust quantum compilation and circuit optimisation via energy minimisation", Quantum 6, 628 (2022).

[65] Riccardo Porotti, Vittorio Peano, and Florian Marquardt, "Gradient-Ascent Pulse Engineering with Feedback", PRX Quantum 4 3, 030305 (2023).

[66] Xiaosi Xu, Simon C. Benjamin, and Xiao Yuan, "Variational Circuit Compiler for Quantum Error Correction", Physical Review Applied 15 3, 034068 (2021).

[67] B. Jaderberg, A. Agarwal, K. Leonhardt, M. Kiffner, and D. Jaksch, "Minimum hardware requirements for hybrid quantum-classical DMFT", Quantum Science and Technology 5 3, 034015 (2020).

[68] Gregory Boyd and Bálint Koczor, "Training Variational Quantum Circuits with CoVaR: Covariance Root Finding with Classical Shadows", Physical Review X 12 4, 041022 (2022).

[69] Brian Coyle, Mina Doosti, Elham Kashefi, and Niraj Kumar, "Progress toward practical quantum cryptanalysis by variational quantum cloning", Physical Review A 105 4, 042604 (2022).

[70] Ed Younis, Koushik Sen, Katherine Yelick, and Costin Iancu, "QFAST: Quantum Synthesis Using a Hierarchical Continuous Circuit Space", arXiv:2003.04462, (2020).

[71] Jacob L. Beckey, M. Cerezo, Akira Sone, and Patrick J. Coles, "Variational quantum algorithm for estimating the quantum Fisher information", Physical Review Research 4 1, 013083 (2022).

[72] Sanjib Ghosh, Tanjung Krisnanda, Tomasz Paterek, and Timothy C. H. Liew, "Realising and compressing quantum circuits with quantum reservoir computing", Communications Physics 4 1, 105 (2021).

[73] Marc Grau Davis, Ethan Smith, Ana Tudor, Koushik Sen, Irfan Siddiqi, and Costin Iancu, "Heuristics for Quantum Compiling with a Continuous Gate Set", arXiv:1912.02727, (2019).

[74] Shota Kanasugi, Shoichiro Tsutsui, Yuya O. Nakagawa, Kazunori Maruyama, Hirotaka Oshima, and Shintaro Sato, "Computation of Green's function by local variational quantum compilation", Physical Review Research 5 3, 033070 (2023).

[75] Tariq M. Khan and Antonio Robles-Kelly, "Machine Learning: Quantum vs Classical", IEEE Access 8, 219275 (2020).

[76] Alistair Letcher, Stefan Woerner, and Christa Zoufal, "Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits", arXiv:2309.12681, (2023).

[77] Shichuan Xue, Yong Liu, Yang Wang, Pingyu Zhu, Chu Guo, and Junjie Wu, "Variational quantum process tomography of unitaries", Physical Review A 105 3, 032427 (2022).

[78] Lingling Lao and Carmen G. Almudever, "Fault-tolerant quantum error correction on near-term quantum processors using flag and bridge qubits", Physical Review A 101 3, 032333 (2020).

[79] Ryan Shaffer, Eli Megidish, Joseph Broz, Wei-Ting Chen, and Hartmut Häffner, "Practical verification protocols for analog quantum simulators", npj Quantum Information 7, 46 (2021).

[80] Zhenhuan Liu, Pei Zeng, You Zhou, and Mile Gu, "Characterizing correlation within multipartite quantum systems via local randomized measurements", Physical Review A 105 2, 022407 (2022).

[81] Nikita A. Nemkov, Evgeniy O. Kiktenko, Ilia A. Luchnikov, and Aleksey K. Fedorov, "Efficient variational synthesis of quantum circuits with coherent multi-start optimization", Quantum 7, 993 (2023).

[82] Zhimin He, Lvzhou Li, Shenggen Zheng, Yongyao Li, and Haozhen Situ, "Variational quantum compiling with double Q-learning", New Journal of Physics 23 3, 033002 (2021).

[83] Péter Rakyta, Gregory Morse, Jakab Nádori, Zita Majnay-Takács, Oskar Mencer, and Zoltán Zimborás, "Highly optimized quantum circuits synthesized via data-flow engines", Journal of Computational Physics 500, 112756 (2024).

[84] Tyler Volkoff, Zoë Holmes, and Andrew Sornborger, "Universal Compiling and (No-)Free-Lunch Theorems for Continuous-Variable Quantum Learning", PRX Quantum 2 4, 040327 (2021).

[85] David Linteau, Stefano Barison, Netanel H. Lindner, and Giuseppe Carleo, "Adaptive projected variational quantum dynamics", Physical Review Research 6 2, 023130 (2024).

[86] S. X. Li, W. L. Mu, J. B. You, and X. Q. Shao, "Simulation of a feedback-based algorithm for quantum optimization for a realistic neutral-atom system with an optimized small-angle controlled-phase gate", Physical Review A 109 6, 062603 (2024).

[87] Ed Younis, Koushik Sen, Katherine Yelick, and Costin Iancu, "QFAST: Conflating Search and Numerical Optimization for Scalable Quantum Circuit Synthesis", arXiv:2103.07093, (2021).

[88] Evan Peters, Prasanth Shyamsundar, Andy C. Y. Li, and Gabriel Perdue, "Qubit Assignment Using Time Reversal", PRX Quantum 3 4, 040333 (2022).

[89] Ethan Smith, Marc G. Davis, Jeffrey Larson, Ed Younis, Costin Iancu, and Wim Lavrijsen, "LEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach", arXiv:2106.11246, (2021).

[90] Michael R. Geller, Zoë Holmes, Patrick J. Coles, and Andrew Sornborger, "Experimental quantum learning of a spectral decomposition", Physical Review Research 3 3, 033200 (2021).

[91] Corey Jason Trahan, Mark Loveland, Noah Davis, and Elizabeth Ellison, "A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods", Entropy 25 4, 580 (2023).

[92] Richard Meister, Cica Gustiani, and Simon C. Benjamin, "Exploring ab initio machine synthesis of quantum circuits", New Journal of Physics 25 7, 073018 (2023).

[93] Kok Chuan Tan and Tyler Volkoff, "Variational quantum algorithms to estimate rank, quantum entropies, fidelity, and Fisher information via purity minimization", Physical Review Research 3 3, 033251 (2021).

[94] Daan Camps and Roel Van Beeumen, "Approximate quantum circuit synthesis using block encodings", Physical Review A 102 5, 052411 (2020).

[95] Enrico Fontana, M. Cerezo, Andrew Arrasmith, Ivan Rungger, and Patrick J. Coles, "Non-trivial symmetries in quantum landscapes and their resilience to quantum noise", Quantum 6, 804 (2022).

[96] Xinbiao Wang, Yuxuan Du, Zhuozhuo Tu, Yong Luo, Xiao Yuan, and Dacheng Tao, "Transition role of entangled data in quantum machine learning", Nature Communications 15, 3716 (2024).

[97] Zhimin He, Junjian Su, Chuangtao Chen, Minghua Pan, and Haozhen Situ, "Search space pruning for quantum architecture search", European Physical Journal Plus 137 4, 491 (2022).

[98] Daniel Bultrini, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Patrick J. Coles, and Lukasz Cincio, "Unifying and benchmarking state-of-the-art quantum error mitigation techniques", Quantum 7, 1034 (2023).

[99] Simon Cichy, Paul K. Faehrmann, Sumeet Khatri, and Jens Eisert, "Perturbative gadgets for gate-based quantum computing: Nonrecursive constructions without subspace restrictions", Physical Review A 109 5, 052624 (2024).

[100] Daniel Mills, Seyon Sivarajah, Travis L. Scholten, and Ross Duncan, "Application-Motivated, Holistic Benchmarking of a Full Quantum Computing Stack", Quantum 5, 415 (2021).

[101] Evan Peters, Andy C. Y. Li, and Gabriel N. Perdue, "Perturbative readout-error mitigation for near-term quantum computers", Physical Review A 107 6, 062426 (2023).

[102] Ryan Shaffer, Hang Ren, Emiliia Dyrenkova, Christopher G. Yale, Daniel S. Lobser, Ashlyn D. Burch, Matthew N. H. Chow, Melissa C. Revelle, Susan M. Clark, and Hartmut Häffner, "Sample-efficient verification of continuously-parameterized quantum gates for small quantum processors", Quantum 7, 997 (2023).

[103] Naoki Mitsuda, Tatsuhiro Ichimura, Kouhei Nakaji, Yohichi Suzuki, Tomoki Tanaka, Rudy Raymond, Hiroyuki Tezuka, Tamiya Onodera, and Naoki Yamamoto, "Approximate complex amplitude encoding algorithm and its application to data classification problems", Physical Review A 109 5, 052423 (2024).

[104] Santosh Kumar, "Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance", Physical Review A 102 1, 012405 (2020).

[105] Cica Gustiani, Richard Meister, and Simon C. Benjamin, "Exploiting subspace constraints and ab initio variational methods for quantum chemistry", New Journal of Physics 25 7, 073019 (2023).

[106] Shichuan Xue, Guangyao Huang, Yong Liu, Dongyang Wang, Weixu Shi, Yingwen Liu, Xiang Fu, Anqi Huang, Mingtang Deng, and Junjie Wu, "Efficient quantum process tomography for Clifford circuits", Physical Review A 108 3, 032419 (2023).

[107] Vu Tuan Hai and Le Bin Ho, "Universal compilation for quantum state tomography", Scientific Reports 13, 3750 (2023).

[108] Mark M. Wilde, "Coherent Quantum Channel Discrimination", arXiv:2001.02668, (2020).

[109] Peter Nimbe, Benjamin Asubam Weyori, and Prosper Kandabongee Yeng, "A Framework for Quantum-Classical Cryptographic Translation", International Journal of Theoretical Physics 60 3, 793 (2021).

[110] Wonho Jang, Koji Terashi, Masahiko Saito, Christian W. Bauer, Benjamin Nachman, Yutaro Iiyama, Ryunosuke Okubo, and Ryu Sawada, "Initial-State Dependent Optimization of Controlled Gate Operations with Quantum Computer", Quantum 6, 798 (2022).

[111] Xinyu Fei, Lucas T. Brady, Jeffrey Larson, Sven Leyffer, and Siqian Shen, "Binary Control Pulse Optimization for Quantum Systems", Quantum 7, 892 (2023).

[112] Sean Greenaway, Frédéric Sauvage, Kiran E. Khosla, and Florian Mintert, "Efficient assessment of process fidelity", Physical Review Research 3 3, 033031 (2021).

[113] Lea M. Trenkwalder, Eleanor Scerri, Thomas E. O'Brien, and Vedran Dunjko, "Compilation of product-formula Hamiltonian simulation via reinforcement learning", arXiv:2311.04285, (2023).

[114] Grzegorz Czelusta and Jakub Mielczarek, "Quantum circuits for the Ising spin networks", Physical Review D 108 8, 086027 (2023).

[115] Shunsuke Daimon, Kakeru Tsunekawa, Ryoto Takeuchi, Takahiro Sagawa, Naoki Yamamoto, and Eiji Saitoh, "Quantum circuit distillation and compression", Japanese Journal of Applied Physics 63 3, 032003 (2024).

[116] Thomas J. Maldonado, Johannes Flick, Stefan Krastanov, and Alexey Galda, "Error rate reduction of single-qubit gates via noise-aware decomposition into native gates", Scientific Reports 12, 6379 (2022).

[117] Shichuan Xue, Yizhi Wang, Junwei Zhan, Yaxuan Wang, Ru Zeng, Jiangfang Ding, Weixu Shi, Yong Liu, Yingwen Liu, Anqi Huang, Guangyao Huang, Chunlin Yu, Dongyang Wang, Xiang Fu, Xiaogang Qiang, Ping Xu, Mingtang Deng, Xuejun Yang, and Junjie Wu, "Variational Entanglement-Assisted Quantum Process Tomography with Arbitrary Ancillary Qubits", Physical Review Letters 129 13, 133601 (2022).

[118] Aritra Laha, Agrim Aggarwal, and Santosh Kumar, "Random density matrices: Analytical results for mean root fidelity and the mean-square Bures distance", Physical Review A 104 2, 022438 (2021).

[119] Jin-Min Liang, Qiao-Qiao Lv, Zhi-Xi Wang, and Shao-Ming Fei, "Assisted quantum simulation of open quantum systems", iScience 26 4, 106306 (2023).

[120] Aritra Laha and Santosh Kumar, "Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance", Physical Review E 107 3, 034206 (2023).

[121] Yuxuan Zhang, "Straddling-gates problem in multipartite quantum systems", Physical Review A 105 6, 062430 (2022).

[122] Yongyan Hou, Baiyang Dong, Wenqiang Guo, Xin Wang, and Qinkun Xiao, "A Triple Unlocking Mechanism Model Against Forging Signature Attack Based on Multivariate Polynomial Public Key Cryptosystem", IEEE Access 11, 134614 (2023).

[123] Noah Linden and Ronald de Wolf, "Lightweight Detection of a Small Number of Large Errors in a Quantum Circuit", Quantum 5, 436 (2021).

[124] David A. Herrera-Martí, "Policy Gradient Approach to Compilation of Variational Quantum Circuits", Quantum 6, 797 (2022).

[125] Shichuan Xue, Yizhi Wang, Yong Liu, Weixu Shi, and Junjie Wu, "Variational Quantum Process Tomography of Non-Unitaries", Entropy 25 1, 90 (2023).

[126] Samson Wang, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Lukasz Cincio, and Patrick J. Coles, "Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?", Quantum 8, 1287 (2024).

[127] Yihui Quek, Eneet Kaur, and Mark M. Wilde, "Multivariate trace estimation in constant quantum depth", Quantum 8, 1220 (2024).

[128] Sean Greenaway, Francesco Petiziol, Zhao Hongzheng, and Florian Mintert, "Variational quantum gate optimization at the pulse level", SciPost Physics 16 3, 082 (2024).

[129] Yudai Suzuki, Hideaki Kawaguchi, and Naoki Yamamoto, "Quantum Fisher kernel for mitigating the vanishing similarity issue", Quantum Science and Technology 9 3, 035050 (2024).

[130] L. Zambrano, A. D. Muñoz-Moller, M. Muñoz, L. Pereira, and A. Delgado, "Avoiding barren plateaus in the variational determination of geometric entanglement", Quantum Science and Technology 9 2, 025016 (2024).

[131] Francesco Preti, Michael Schilling, Sofiene Jerbi, Lea M. Trenkwalder, Hendrik Poulsen Nautrup, Felix Motzoi, and Hans J. Briegel, "Hybrid discrete-continuous compilation of trapped-ion quantum circuits with deep reinforcement learning", Quantum 8, 1343 (2024).

[132] Julien Gacon, "Scalable Quantum Algorithms for Noisy Quantum Computers", arXiv:2403.00940, (2024).

[133] Daniel Tandeitnik and Thiago Guerreiro, "Evolving quantum circuits", Quantum Information Processing 23 3, 109 (2024).

[134] Nikita A. Nemkov, Evgeniy O. Kiktenko, and Aleksey K. Fedorov, "Barren plateaus are swamped with traps", arXiv:2405.05332, (2024).

[135] Aby Philip, Soorya Rethinasamy, Vincent Russo, and Mark M. Wilde, "Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering", Quantum 8, 1366 (2024).

[136] Vu Tuan Hai, Nguyen Tan Viet, and Le Bin Ho, "〈qo|op〉: A quantum object optimizer", SoftwareX 26, 101726 (2024).

[137] Evan Peters, "Bounds and guarantees for learning and entanglement", arXiv:2404.07277, (2024).

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