Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design

Xiu-Zhe Luo; Jin-Guo Liu; Pan Zhang; Lei Wang

doi:10.22331/q-2020-10-11-341

Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design

Xiu-Zhe Luo^1,2,3,4, Jin-Guo Liu¹, Pan Zhang², and Lei Wang^1,5

¹Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
³Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada
⁴Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
⁵Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

Published:	2020-10-11, volume 4, page 341
Eprint:	arXiv:1912.10877v3
Doi:	https://doi.org/10.22331/q-2020-10-11-341
Citation:	Quantum 4, 341 (2020).

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Abstract

We introduce $\texttt{Yao}$, an extensible, efficient open-source framework for quantum algorithm design. $\texttt{Yao}$ features generic and differentiable programming of quantum circuits. It achieves state-of-the-art performance in simulating small to intermediate-sized quantum circuits that are relevant to near-term applications. We introduce the design principles and critical techniques behind $\texttt{Yao}$. These include the quantum block intermediate representation of quantum circuits, a builtin automatic differentiation engine optimized for reversible computing, and batched quantum registers with GPU acceleration. The extensibility and efficiency of $\texttt{Yao}$ help boost innovation in quantum algorithm design.

► BibTeX data

@article{Luo2020yaojlextensible,
  doi = {10.22331/q-2020-10-11-341},
  url = {https://doi.org/10.22331/q-2020-10-11-341},
  title = {Yao.jl: {E}xtensible, {E}fficient {F}ramework for {Q}uantum {A}lgorithm {D}esign},
  author = {Luo, Xiu-Zhe and Liu, Jin-Guo and Zhang, Pan and Wang, Lei},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {341},
  month = oct,
  year = {2020}
}

► References

[1] John Preskill. Quantum computing in the nisq era and beyond. Quantum, 2: 79, 2018. 10.22331/q-2018-08-06-79.
https://doi.org/10.22331/q-2018-08-06-79

[2] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien. A variational eigenvalue solver on a photonic quantum processor. Nature communications, 5: 4213, 2014a. 10.1038/ncomms5213.
https://doi.org/10.1038/ncomms5213

[3] Dave Wecker, Matthew B Hastings, and Matthias Troyer. Progress towards practical quantum variational algorithms. Physical Review A, 92 (4): 042303, 2015. 10.1103/physreva.92.042303.
https://doi.org/10.1103/physreva.92.042303

[4] Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. New Journal of Physics, 18 (2): 023023, 2016. 10.1088/1367-2630/18/2/023023.
https://doi.org/10.1088/1367-2630/18/2/023023

[5] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028, 2014.
arXiv:1411.4028

[6] Edward Farhi and Hartmut Neven. Classification with Quantum Neural Networks on Near Term Processors. arXiv e-prints, art. arXiv:1802.06002, February 2018.
arXiv:1802.06002

[7] Kosuke Mitarai, Makoto Negoro, Masahiro Kitagawa, and Keisuke Fujii. Quantum circuit learning. Physical Review A, 98 (3): 032309, 2018. 10.1103/physreva.98.032309.
https://doi.org/10.1103/physreva.98.032309

[8] Marcello Benedetti, Delfina Garcia-Pintos, Oscar Perdomo, Vicente Leyton-Ortega, Yunseong Nam, and Alejandro Perdomo-Ortiz. A generative modeling approach for benchmarking and training shallow quantum circuits. npj Quantum Information, 5 (1), May 2019a. ISSN 2056-6387. 10.1038/s41534-019-0157-8. URL http://dx.doi.org/10.1038/s41534-019-0157-8.
https://doi.org/10.1038/s41534-019-0157-8

[9] Jin-Guo Liu and Lei Wang. Differentiable learning of quantum circuit born machines. Physical Review A, 98 (6): 062324, 2018. 10.1103/physreva.98.062324.
https://doi.org/10.1103/physreva.98.062324

[10] Peter JJ O’Malley et al. Scalable quantum simulation of molecular energies. Physical Review X, 6 (3): 031007, 2016. 10.21236/ada387360.
https://doi.org/10.21236/ada387360

[11] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549 (7671): 242, 2017a. 10.1038/nature23879. URL https://www.nature.com/articles/nature23879.
https://doi.org/10.1038/nature23879
https://www.nature.com/articles/nature23879

[12] Vojtěch Havlíček, Antonio D Córcoles, 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. 10.1038/s41586-019-0980-2.
https://doi.org/10.1038/s41586-019-0980-2

[13] Daiwei Zhu et al. Training of quantum circuits on a hybrid quantum computer. Science Advances, 5 (10): eaaw9918, 2019. 10.1126/sciadv.aaw9918.
https://doi.org/10.1126/sciadv.aaw9918

[14] G. Pagano, A. Bapat, P. Becker, K. S. Collins, A. De, P. W. Hess, H. B. Kaplan, A. Kyprianidis, W. L. Tan, C Baldwin, L T Brady, A Deshpande, F Liu, S Jordan, A V Gorshkov, and C Monroe. Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator. 2019. URL http://arxiv.org/abs/1906.02700.
arXiv:1906.02700

[15] Vicente Leyton-Ortega, Alejandro Perdomo-Ortiz, and Oscar Perdomo. Robust implementation of generative modeling with parametrized quantum circuits. arXiv preprint arXiv:1901.08047, 2019.
arXiv:1901.08047

[16] Jarrod R. McClean, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, and Hartmut Neven. Barren plateaus in quantum neural network training landscapes. Nat. Commun., 9 (1): 4812, 2018. ISSN 2041-1723. 10.1038/s41467-018-07090-4. URL https://doi.org/10.1038/s41467-018-07090-4.
https://doi.org/10.1038/s41467-018-07090-4

[17] Tim Besard, Christophe Foket, and Bjorn De Sutter. Effective extensible programming: Unleashing julia on gpus. CoRR, abs/1712.03112, 2017. 10.1109/tpds.2018.2872064. URL http://arxiv.org/abs/1712.03112.
https://doi.org/10.1109/tpds.2018.2872064
arXiv:1712.03112

[18] Guillermo García-Pérez, Matteo A. C. Rossi, and Sabrina Maniscalco. Ibm q experience as a versatile experimental testbed for simulating open quantum systems, 2019. URL https://arxiv.org/abs/1906.07099. 10.1038/s41534-019-0235-y.
https://doi.org/10.1038/s41534-019-0235-y
arXiv:1906.07099

[19] Differentiable Programming. https://en.wikipedia.org/wiki/Differentiable_programming, a.
https://en.wikipedia.org/wiki/Differentiable_programming

[20] Karpathy, Andrej. Software 2.0. https://medium.com/@karpathy/software-2-0-a64152b37c35.
https://medium.com/@karpathy/software-2-0-a64152b37c35

[21] Tianqi Chen et al. Mxnet: A flexible and efficient machine learning library for heterogeneous distributed systems. arXiv preprint arXiv:1512.01274, 2015.
arXiv:1512.01274

[22] Martín Abadi et al. Tensorflow: A system for large-scale machine learning. In 12th $\{$USENIX$\}$ Symposium on Operating Systems Design and Implementation ($\{$OSDI$\}$ 16), pages 265–283, 2016.

[23] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-performance deep learning library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d' Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems 32, pages 8024–8035. Curran Associates, Inc., 2019. https://arxiv.org/abs/1912.01703.
arXiv:1912.01703

[24] Dougal Maclaurin, David Duvenaud, and Ryan P Adams. Autograd: Effortless gradients in numpy. In ICML 2015 AutoML Workshop, volume 238, 2015.

[25] Michael Innes, Elliot Saba, Keno Fischer, Dhairya Gandhi, Marco Concetto Rudilosso, Neethu Mariya Joy, Tejan Karmali, Avik Pal, and Viral Shah. Fashionable modelling with flux. CoRR, abs/1811.01457, 2018. URL http://arxiv.org/abs/1811.01457.
arXiv:1811.01457

[26] Mike Innes, Alan Edelman, Keno Fischer, Chris Rackauckus, Elliot Saba, Viral B Shah, and Will Tebbutt. Zygote: A differentiable programming system to bridge machine learning and scientific computing. arXiv preprint arXiv:1907.07587, 2019.
arXiv:1907.07587

[27] C. H. Bennett. Logical reversibility of computation. IBM Journal of Research and Development, 17 (6): 525–532, Nov 1973. ISSN 0018-8646. 10.1147/rd.176.0525.
https://doi.org/10.1147/rd.176.0525

[28] Jin-Guo Liu, Yi-Hong Zhang, Yuan Wan, and Lei Wang. Variational quantum eigensolver with fewer qubits. Phys. Rev. Research, 1: 023025, Sep 2019a. 10.1103/PhysRevResearch.1.023025. URL https://link.aps.org/doi/10.1103/PhysRevResearch.1.023025.
https://doi.org/10.1103/PhysRevResearch.1.023025

[29] Alexander S Green, Peter LeFanu Lumsdaine, Neil J Ross, Peter Selinger, and Benoı̂t Valiron. Quipper: a scalable quantum programming language. In ACM SIGPLAN Notices, volume 48, pages 333–342. ACM, 2013. 10.1145/2491956.2462177.
https://doi.org/10.1145/2491956.2462177

[30] Damian S Steiger, Thomas Häner, and Matthias Troyer. Projectq: an open source software framework for quantum computing. arXiv preprint arXiv:1612.08091, 2016. 10.22331/q-2018-01-31-49.
https://doi.org/10.22331/q-2018-01-31-49
arXiv:1612.08091

[31] Krysta Svore, Martin Roetteler, Alan Geller, Matthias Troyer, John Azariah, Christopher Granade, Bettina Heim, Vadym Kliuchnikov, Mariia Mykhailova, and Andres Paz. Q#: Enabling scalable quantum computing and development with a high-level dsl. Proceedings of the Real World Domain Specific Languages Workshop 2018 on - RWDSL2018, 2018. 10.1145/3183895.3183901. URL http://dx.doi.org/10.1145/3183895.3183901.
https://doi.org/10.1145/3183895.3183901

[32] Cirq: A Python framework for creating, editing, and invoking noisy intermediate scale quantum (NISQ) circuits. https://github.com/quantumlib/Cirq.
https://github.com/quantumlib/Cirq

[33] qulacs: Variational Quantum Circuit Simulator for Quantum Computation Research. https://github.com/qulacs/qulacs.
https://github.com/qulacs/qulacs

[34] Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, and Nathan Killoran. Pennylane: Automatic differentiation of hybrid quantum-classical computations. arXiv preprint arXiv:1811.04968, 2018.
arXiv:1811.04968

[35] Héctor Abraham et al. Qiskit: An open-source framework for quantum computing, 2019.

[36] Tyson Jones, Anna Brown, Ian Bush, and Simon C. Benjamin. Quest and high performance simulation of quantum computers. Scientific Reports, 9 (1), Jul 2019. ISSN 2045-2322. 10.1038/s41598-019-47174-9. URL http://dx.doi.org/10.1038/s41598-019-47174-9.
https://doi.org/10.1038/s41598-019-47174-9

[37] Mark Fingerhuth, Tomáš Babej, and Peter Wittek. Open source software in quantum computing. PloS one, 13 (12): e0208561, 2018. 10.1371/journal.pone.0208561.
https://doi.org/10.1371/journal.pone.0208561

[38] Ryan LaRose. Overview and Comparison of Gate Level Quantum Software Platforms. Quantum, 3: 130, March 2019. ISSN 2521-327X. 10.22331/q-2019-03-25-130. URL https://doi.org/10.22331/q-2019-03-25-130.
https://doi.org/10.22331/q-2019-03-25-130

[39] Marcello Benedetti, Erika Lloyd, Stefan Sack, and Mattia Fiorentini. Parameterized quantum circuits as machine learning models. Quantum Science and Technology, 4 (4): 043001, nov 2019b. 10.1088/2058-9565/ab4eb5. URL https://doi.org/10.1088.
https://doi.org/10.1088/2058-9565/ab4eb5

[40] J. Bezanson. “Why is Julia fast? Can it be faster?” 2015, JuliaCon India. https://www.youtube.com/watch?v=xUP3cSKb8sI.
https://www.youtube.com/watch?v=xUP3cSKb8sI

[41] Jeff Bezanson, Stefan Karpinski, Viral B Shah, and Alan Edelman. Julia: A fast dynamic language for technical computing. arXiv preprint arXiv:1209.5145, 2012.
arXiv:1209.5145

[42] Jarrod R. McClean et al. Openfermion: The electronic structure package for quantum computers, jun 2020. URL https://doi.org/10.1088/2058-9565/ab8ebc.
https://doi.org/10.1088/2058-9565/ab8ebc

[43] D Coppersmith. An approximate fourier transform useful in quantum computing. Technical report, Technical report, IBM Research Division, 1994. https://arxiv.org/abs/quant-ph/0201067.
arXiv:quant-ph/0201067

[44] Artur Ekert and Richard Jozsa. Quantum computation and shor's factoring algorithm. Reviews of Modern Physics, 68 (3): 733, 1996. 10.1103/RevModPhys.68.733.
https://doi.org/10.1103/RevModPhys.68.733

[45] Richard Jozsa. Quantum algorithms and the fourier transform. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454 (1969): 323–337, 1998. 10.1098/rspa.1998.0163.
https://doi.org/10.1098/rspa.1998.0163

[46] Peter J Karalekas, Nikolas A Tezak, Eric C Peterson, Colm A Ryan, Marcus P da Silva, and Robert S Smith. A quantum-classical cloud platform optimized for variational hybrid algorithms. Quantum Science and Technology, 5 (2): 024003, apr 2020. 10.1088/2058-9565/ab7559. URL https://doi.org/10.1088.
https://doi.org/10.1088/2058-9565/ab7559

[47] Krylovkit.jl: Krylov methods for linear problems, eigenvalues, singular values and matrix functions. https://github.com/Jutho/KrylovKit.jl.
https://github.com/Jutho/KrylovKit.jl

[48] Christopher Rackauckas and Qing Nie. Differentialequations.jl – a performant and feature-rich ecosystem for solving differential equations in julia. The Journal of Open Research Software, 5 (1), 2017. 10.5334/jors.151. URL https://app.dimensions.ai/details/publication/pub.1085583166 and http://openresearchsoftware.metajnl.com/articles/10.5334/jors.151/galley/245/download/. Exported from https://app.dimensions.ai on 2019/05/05.
https://doi.org/10.5334/jors.151

[49] Atilim Gunes Baydin, Barak A Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind. Automatic differentiation in machine learning: a survey. Journal of machine learning research, 18 (153), 2018. https://arxiv.org/abs/1502.05767.
arXiv:1502.05767

[50] Andreas Griewank and Andrea Walther. Evaluating Derivatives. Society for Industrial and Applied Mathematics, jan 2008. 10.1137/1.9780898717761. URL https://doi.org/10.1137.
https://doi.org/10.1137/1.9780898717761

[51] Aidan N Gomez, Mengye Ren, Raquel Urtasun, and Roger B Grosse. The reversible residual network: Backpropagation without storing activations. In Advances in neural information processing systems, pages 2214–2224, 2017.

[52] Tian Qi Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. Neural ordinary differential equations. In Advances in neural information processing systems, pages 6571–6583, 2018a.

[53] Akira Hirose. Complex-valued neural networks: theories and applications, volume 5. World Scientific, 2003. 10.1142/5345.
https://doi.org/10.1142/5345

[54] Mike Giles. An extended collection of matrix derivative results for forward and reverse mode algorithmic differentiation. Technical report, 2008. URL https://people.maths.ox.ac.uk/gilesm/files/NA-08-01.pdf.
https://people.maths.ox.ac.uk/gilesm/files/NA-08-01.pdf

[55] Jin-Guo Liu, Liang Mao, Pan Zhang, and Lei Wang. Solving quantum statistical mechanics with variational autoregressive networks and quantum circuits. 2019b. URL http://arxiv.org/abs/1912.11381.
arXiv:1912.11381

[56] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun., 5: 4213, 2014b. 10.1038/ncomms5213. URL https://www.nature.com/articles/ncomms5213.
https://doi.org/10.1038/ncomms5213
https://www.nature.com/articles/ncomms5213

[57] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549 (7671): 242, 2017b. 10.1038/nature23879.
https://doi.org/10.1038/nature23879

[58] Gavin E Crooks. Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition. URL https://arxiv.org/abs/1905.13311.
arXiv:1905.13311

[59] Jun Li, Xiaodong Yang, Xinhua Peng, and Chang-Pu Sun. Hybrid quantum-classical approach to quantum optimal control. Phys. Rev. Lett., 118: 150503, Apr 2017. 10.1103/physrevlett.118.150503. URL https://link.aps.org/doi/10.1103/PhysRevLett.118.150503.
https://doi.org/10.1103/physrevlett.118.150503
https://link.aps.org/doi/10.1103/PhysRevLett.118.150503

[60] Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran. Evaluating analytic gradients on quantum hardware. Phys. Rev. A, 99 (3): 032331, 2019. ISSN 24699934. 10.1103/PhysRevA.99.032331.
https://doi.org/10.1103/PhysRevA.99.032331

[61] Ken M Nakanishi, Keisuke Fujii, and Synge Todo. Sequential minimal optimization for quantum-classical hybrid algorithms. 10.21236/ada212800. URL https://arxiv.org/abs/1903.12166.
https://doi.org/10.21236/ada212800
arXiv:1903.12166

[62] Shakir Mohamed, Mihaela Rosca, Michael Figurnov, and Andriy Mnih. Monte carlo gradient estimation in machine learning. URL https://arxiv.org/abs/1906.10652.
arXiv:1906.10652

[63] Chun-Liang Li, Wei-Cheng Chang, Yu Cheng, Yiming Yang, and Barnabás Póczos. MMD GAN: Towards Deeper Understanding of Moment Matching Network. URL http://arxiv.org/abs/1705.08584.
arXiv:1705.08584

[64] Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola. A kernel two-sample test. Journal of Machine Learning Research, 13 (Mar): 723–773, 2012. URL http://www.jmlr.org/papers/v13/gretton12a.html.
http://www.jmlr.org/papers/v13/gretton12a.html

[65] Michael A Nielsen and Isaac L Chuang. Quantum Computation and Quantum Information. Cambridge university press, 2010. 10.1017/cbo9780511976667.016.
https://doi.org/10.1017/cbo9780511976667.016

[66] William James Huggins, Piyush Patil, Bradley Mitchell, K Birgitta Whaley, and Miles Stoudenmire. Towards quantum machine learning with tensor networks. Quantum Science and Technology, 2018. 10.1088/2058-9565/aaea94.
https://doi.org/10.1088/2058-9565/aaea94

[67] Frederica Darema, David A George, V Alan Norton, and Gregory F Pfister. A single-program-multiple-data computational model for epex/fortran. Parallel Computing, 7 (1): 11–24, 1988. 10.1016/0167-8191(88)90094-4.
https://doi.org/10.1016/0167-8191(88)90094-4

[68] Statically sized arrays for Julia. https://github.com/JuliaArrays/StaticArrays.jl.
https://github.com/JuliaArrays/StaticArrays.jl

[69] A luxury sparse matrix package for julia. https://github.com/QuantumBFS/LuxurySparse.jl.
https://github.com/QuantumBFS/LuxurySparse.jl

[70] Thomas Häner and Damian S Steiger. 0.5 petabyte simulation of a 45-qubit quantum circuit. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, page 33. ACM, 2017. 10.1145/3126908.3126947.
https://doi.org/10.1145/3126908.3126947

[71] Igor L Markov and Yaoyun Shi. Simulating quantum computation by contracting tensor networks. SIAM Journal on Computing, 38 (3): 963–981, 2008. 10.1137/050644756.
https://doi.org/10.1137/050644756

[72] Edwin Pednault, John A Gunnels, Giacomo Nannicini, Lior Horesh, Thomas Magerlein, Edgar Solomonik, and Robert Wisnieff. Breaking the 49-qubit barrier in the simulation of quantum circuits. arXiv preprint arXiv:1710.05867, 2017.
arXiv:1710.05867

[73] Fang Zhang et al. Alibaba cloud quantum development kit: Large-scale classical simulation of quantum circuits. arXiv preprint arXiv:1907.11217, 2019.
arXiv:1907.11217

[74] Pyquest-cffi: A python interface to the quest quantum simulator (cffi based). https://github.com/HQSquantumsimulations/PyQuEST-cffi.
https://github.com/HQSquantumsimulations/PyQuEST-cffi

[75] PennyLane is a cross-platform Python library for quantum machine learning, automatic differentiation, and optimization of hybrid quantum-classical computations. https://github.com/XanaduAI/pennylane, a.
https://github.com/XanaduAI/pennylane

[76] Review of PennyLane benchmark. https://github.com/Roger-luo/quantum-benchmarks/pull/7, b.
https://github.com/Roger-luo/quantum-benchmarks/pull/7

[77] Aer is a high performance simulator for quantum circuits that includes noise models. https://github.com/Qiskit/qiskit-aer, a.
https://github.com/Qiskit/qiskit-aer

[78] Terra provides the foundations for Qiskit. It allows the user to write quantum circuits easily, and takes care of the constraints of real hardware. https://github.com/Qiskit/qiskit-terra, b.
https://github.com/Qiskit/qiskit-terra

[79] py.test fixture for benchmarking code. https://github.com/ionelmc/pytest-benchmark.
https://github.com/ionelmc/pytest-benchmark

[80] Jiahao Chen and Jarrett Revels. Robust benchmarking in noisy environments. arXiv preprint arXiv:1608.04295, 2016.
arXiv:1608.04295

[81] Benchmarking Quantum Circuit Emulators For Your Daily Research Usage. https://github.com/Roger-luo/quantum-benchmarks.
https://github.com/Roger-luo/quantum-benchmarks

[82] Frank Arute et al. Quantum supremacy using a programmable superconducting processor. Nature, 574 (7779): 505–510, 2019. 10.1038/s41586-019-1666-5.
https://doi.org/10.1038/s41586-019-1666-5

[83] CuYao.jl: CUDA extension for Yao.jl. https://github.com/QuantumBFS/CuYao.jl.
https://github.com/QuantumBFS/CuYao.jl

[84] Jinfeng Zeng, Yufeng Wu, Jin-Guo Liu, Lei Wang, and Jiangping Hu. Learning and inference on generative adversarial quantum circuits. Physical Review A, 99 (5): 052306, 2019. 10.1103/physreva.99.052306.
https://doi.org/10.1103/physreva.99.052306

[85] Weishi Wang, Jin-Guo Liu, and Lei Wang. A variational quantum state compression algorithm. to appear.

[86] Vivek V. Shende, Igor L. Markov, and Stephen S. Bullock. Minimal universal two-qubit controlled-not-based circuits. Phys. Rev. A, 69: 062321, Jun 2004. 10.1103/PhysRevA.69.062321. URL https://link.aps.org/doi/10.1103/PhysRevA.69.062321.
https://doi.org/10.1103/PhysRevA.69.062321

[87] Michael Innes. Don't unroll adjoint: Differentiating ssa-form programs. CoRR, abs/1810.07951, 2018. URL http://arxiv.org/abs/1810.07951.
arXiv:1810.07951

[88] Andrew W Cross, Lev S Bishop, John A Smolin, and Jay M Gambetta. Open quantum assembly language. arXiv preprint arXiv:1707.03429, 2017.
arXiv:1707.03429

[89] Xiang Fu et al. eqasm: An executable quantum instruction set architecture. In 2019 IEEE International Symposium on High Performance Computer Architecture (HPCA), pages 224–237. IEEE, 2019. 10.1109/hpca.2019.00040.
https://doi.org/10.1109/hpca.2019.00040

[90] Robert S Smith, Michael J Curtis, and William J Zeng. A practical quantum instruction set architecture. arXiv preprint arXiv:1608.03355, 2016.
arXiv:1608.03355

[91] RBNF: A DSL for modern parsing. https://github.com/thautwarm/RBNF.jl.
https://github.com/thautwarm/RBNF.jl

[92] Bidirectional transformation between Yao Quantum Block IR and QASM. https://github.com/QuantumBFS/YaoQASM.jl, a.
https://github.com/QuantumBFS/YaoQASM.jl

[93] YaoLang: The next DSL for Yao and quantum programs. https://github.com/QuantumBFS/YaoLang.jl, b.
https://github.com/QuantumBFS/YaoLang.jl

[94] ZXCalculus.jl: An implementation of ZX-calculus in Julia. https://github.com/QuantumBFS/ZXCalculus.jl, c.
https://github.com/QuantumBFS/ZXCalculus.jl

[95] Aleks Kissinger and John van de Wetering. PyZX: Large Scale Automated Diagrammatic Reasoning. In Bob Coecke and Matthew Leifer, editors, Proceedings 16th International Conference on Quantum Physics and Logic, Chapman University, Orange, CA, USA., 10-14 June 2019, volume 318 of Electronic Proceedings in Theoretical Computer Science, pages 229–241. Open Publishing Association, 2020. 10.4204/EPTCS.318.14.
https://doi.org/10.4204/EPTCS.318.14

[96] Raban Iten, David Sutter, and Stefan Woerner. Efficient template matching in quantum circuits. arXiv preprint arXiv:1909.05270, 2019.
arXiv:1909.05270

[97] Dmitri Maslov, Gerhard W Dueck, D Michael Miller, and Camille Negrevergne. Quantum circuit simplification and level compaction. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 27 (3): 436–444, 2008. 10.1109/tcad.2007.911334.
https://doi.org/10.1109/tcad.2007.911334

[98] Aleks Kissinger and John van de Wetering. Reducing T-count with the ZX-calculus. arXiv preprint arXiv:1903.10477, 2019. 10.1103/PhysRevA.102.022406.
https://doi.org/10.1103/PhysRevA.102.022406
arXiv:1903.10477

[99] Piotr Gawron, Dariusz Kurzyk, and Łukasz Pawela. Quantuminformation.jl—a julia package for numerical computation in quantum information theory. PLOS ONE, 13 (12): e0209358, Dec 2018. ISSN 1932-6203. 10.1371/journal.pone.0209358. URL http://dx.doi.org/10.1371/journal.pone.0209358.
https://doi.org/10.1371/journal.pone.0209358

[100] Sergio Boixo, Sergei V Isakov, Vadim N Smelyanskiy, and Hartmut Neven. Simulation of low-depth quantum circuits as complex undirected graphical models. arXiv preprint arXiv:1712.05384, 2017.
arXiv:1712.05384

[101] Jianxin Chen, Fang Zhang, Mingcheng Chen, Cupjin Huang, Michael Newman, and Yaoyun Shi. Classical simulation of intermediate-size quantum circuits. arXiv preprint arXiv:1805.01450, 2018b.
arXiv:1805.01450

[102] Chu Guo, Yong Liu, Min Xiong, Shichuan Xue, Xiang Fu, Anqi Huang, Xiaogang Qiang, Ping Xu, Junhua Liu, Shenggen Zheng, He-Liang Huang, Mingtang Deng, Dario Poletti, Wan-Su Bao, and Junjie Wu. General-purpose quantum circuit simulator with projected entangled-pair states and the quantum supremacy frontier. Phys. Rev. Lett., 123: 190501, Nov 2019. 10.1103/PhysRevLett.123.190501. URL https://link.aps.org/doi/10.1103/PhysRevLett.123.190501.
https://doi.org/10.1103/PhysRevLett.123.190501

[103] Feng Pan, Pengfei Zhou, Sujie Li, and Pan Zhang. Contracting arbitrary tensor networks: general approximate algorithm and applications in graphical models and quantum circuit simulations. Phys. Rev. Lett., 2020. 10.1103/PhysRevLett.125.060503.
https://doi.org/10.1103/PhysRevLett.125.060503

[104] Edwin Stoudenmire and David J Schwab. Supervised learning with tensor networks. pages 4799–4807, 2016. URL http://papers.nips.cc/paper/6211-supervised-learning-with-tensor-networks.pdf.
http://papers.nips.cc/paper/6211-supervised-learning-with-tensor-networks.pdf

[105] Zhao-Yu Han, Jun Wang, Heng Fan, Lei Wang, and Pan Zhang. Unsupervised generative modeling using matrix product states. Phys. Rev. X, 8: 031012, Jul 2018. 10.1103/PhysRevX.8.031012. URL https://link.aps.org/doi/10.1103/PhysRevX.8.031012.
https://doi.org/10.1103/PhysRevX.8.031012

[106] Song Cheng, Lei Wang, Tao Xiang, and Pan Zhang. Tree tensor networks for generative modeling. Phys. Rev. B, 99: 155131, Apr 2019. 10.1103/PhysRevB.99.155131. URL https://link.aps.org/doi/10.1103/PhysRevB.99.155131.
https://doi.org/10.1103/PhysRevB.99.155131

[107] Ivan Glasser, Ryan Sweke, Nicola Pancotti, Jens Eisert, and Ignacio Cirac. Expressive power of tensor-network factorizations for probabilistic modeling. In Advances in Neural Information Processing Systems, pages 1496–1508, 2019.

[108] Tai-Danae Bradley, E M Stoudenmire, and John Terilla. Modeling sequences with quantum states: a look under the hood. Machine Learning: Science and Technology, 1 (3): 035008, jul 2020. 10.1088/2632-2153/ab8731. URL https://doi.org/10.1088.
https://doi.org/10.1088/2632-2153/ab8731

[109] YaoTensorNetwork: Dump a quantum circuit in Yao to a tensor network graph model. https://github.com/QuantumBFS/YaoTensorNetwork.jl, d.
https://github.com/QuantumBFS/YaoTensorNetwork.jl

[110] Sergio Boixo, Sergei V Isakov, Vadim N Smelyanskiy, Ryan Babbush, Nan Ding, Zhang Jiang, Michael J Bremner, John M Martinis, and Hartmut Neven. Characterizing quantum supremacy in near-term devices. Nature Physics, 14 (6): 595, 2018. 10.1038/s41567-018-0124-x.
https://doi.org/10.1038/s41567-018-0124-x

[111] Miriam Backens. The ZX-calculus is complete for stabilizer quantum mechanics. New Journal of Physics, 16 (9): 093021, sep 2014. 10.1088/1367-2630/16/9/093021. URL https://doi.org/10.1088.
https://doi.org/10.1088/1367-2630/16/9/093021

[112] Multi-language suite for high-performance solvers of differential equations. https://github.com/JuliaDiffEq/DifferentialEquations.jl, b.
https://github.com/JuliaDiffEq/DifferentialEquations.jl

[113] General Permutation Matrix. https://en.wikipedia.org/wiki/Generalized_permutation_matrix.
https://en.wikipedia.org/wiki/Generalized_permutation_matrix

[114] Thomas Häner, Damian S Steiger, Mikhail Smelyanskiy, and Matthias Troyer. High performance emulation of quantum circuits. In SC'16: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, pages 866–874. IEEE, 2016. 10.1109/sc.2016.73.
https://doi.org/10.1109/sc.2016.73

[115] Ryan LaRose, Arkin Tikku, Étude O’Neel-Judy, Lukasz Cincio, and Patrick J. Coles. Variational quantum state diagonalization. npj Quantum Information, 5 (1), Jun 2019. ISSN 2056-6387. 10.1038/s41534-019-0167-6. URL http://dx.doi.org/10.1038/s41534-019-0167-6.
https://doi.org/10.1038/s41534-019-0167-6

[116] Cristina Cirstoiu, Zoe Holmes, Joseph Iosue, Lukasz Cincio, Patrick J. Coles, and Andrew Sornborger. Variational fast forwarding for quantum simulation beyond the coherence time, 2019. 10.1038/s41534-020-00302-0.
https://doi.org/10.1038/s41534-020-00302-0

[117] 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, Nov 2018. ISSN 1367-2630. 10.1088/1367-2630/aae94a. URL http://dx.doi.org/10.1088/1367-2630/aae94a.
https://doi.org/10.1088/1367-2630/aae94a

[118] Xiaoguang Wang, Zhe Sun, and Z. D. Wang. Operator fidelity susceptibility: An indicator of quantum criticality. Physical Review A, 79 (1), Jan 2009. ISSN 1094-1622. 10.1103/physreva.79.012105. URL http://dx.doi.org/10.1103/PhysRevA.79.012105.
https://doi.org/10.1103/physreva.79.012105

[119] Richard H Byrd, Peihuang Lu, Jorge Nocedal, and Ciyou Zhu. A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing, 16 (5): 1190–1208, 1995. 10.2172/204262. URL https://doi.org/10.1137/0916069.
https://doi.org/10.2172/204262

[120] Patrick Kofod Mogensen and Asbjørn Nilsen Riseth. Optim: A mathematical optimization package for Julia. Journal of Open Source Software, 3 (24): 615, 2018. 10.21105/joss.00615.
https://doi.org/10.21105/joss.00615

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[4] Maren Hackenberg, Marlon Grodd, Clemens Kreutz, Martina Fischer, Janina Esins, Linus Grabenhenrich, Christian Karagiannidis, and Harald Binder, "Using Differentiable Programming for Flexible Statistical Modeling", The American Statistician 76 3, 270 (2022).

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[7] Vincent Paul Su, "Variational preparation of the thermofield double state of the Sachdev-Ye-Kitaev model", Physical Review A 104 1, 012427 (2021).

[8] Tong Dou, Guofeng Zhang, and Wei Cui, "Efficient quantum feature extraction for CNN-based learning", Journal of the Franklin Institute 360 11, 7438 (2023).

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[10] Tuyen Nguyen, Incheon Paik, Yutaka Watanobe, and Truong Cong Thang, "An Evaluation of Hardware-Efficient Quantum Neural Networks for Image Data Classification", Electronics 11 3, 437 (2022).

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[14] Qunsheng Huang and Christian B. Mendl, "Classical simulation of quantum circuits using a multiqubit Bloch vector representation of density matrices", Physical Review A 105 2, 022409 (2022).

[15] Chen Zhang, Haojie Wang, Zixuan Ma, Lei Xie, Zeyu Song, and Jidong Zhai, SC22: International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2022) ISBN:978-1-6654-5444-5.

[16] Mahabubul Alam and Swaroop Ghosh, "QNet: A Scalable and Noise-Resilient Quantum Neural Network Architecture for Noisy Intermediate-Scale Quantum Computers", Frontiers in Physics 9, 755139 (2022).

[17] Weitang Li, Jonathan Allcock, Lixue Cheng, Shi-Xin Zhang, Yu-Qin Chen, Jonathan P. Mailoa, Zhigang Shuai, and Shengyu Zhang, "TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era", Journal of Chemical Theory and Computation 19 13, 3966 (2023).

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[20] Stavros Efthymiou, Alvaro Orgaz-Fuertes, Rodolfo Carobene, Juan Cereijo, Andrea Pasquale, Sergi Ramos-Calderer, Simone Bordoni, David Fuentes-Ruiz, Alessandro Candido, Edoardo Pedicillo, Matteo Robbiati, Yuanzheng Paul Tan, Jadwiga Wilkens, Ingo Roth, José Ignacio Latorre, and Stefano Carrazza, "Qibolab: an open-source hybrid quantum operating system", Quantum 8, 1247 (2024).

[21] Arsenii Senokosov, Alexandr Sedykh, Asel Sagingalieva, Basil Kyriacou, and Alexey Melnikov, "Quantum machine learning for image classification", Machine Learning: Science and Technology 5 1, 015040 (2024).

[22] David Plankensteiner, Christoph Hotter, and Helmut Ritsch, "QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems", Quantum 6, 617 (2022).

[23] Tatiana A. Bespalova and Oleksandr Kyriienko, "Hamiltonian Operator Approximation for Energy Measurement and Ground-State Preparation", PRX Quantum 2 3, 030318 (2021).

[24] Sachin Kasture, Oleksandr Kyriienko, and Vincent E. Elfving, "Protocols for classically training quantum generative models on probability distributions", Physical Review A 108 4, 042406 (2023).

[25] Yasunari Suzuki, Yoshiaki Kawase, Yuya Masumura, Yuria Hiraga, Masahiro Nakadai, Jiabao Chen, Ken M. Nakanishi, Kosuke Mitarai, Ryosuke Imai, Shiro Tamiya, Takahiro Yamamoto, Tennin Yan, Toru Kawakubo, Yuya O. Nakagawa, Yohei Ibe, Youyuan Zhang, Hirotsugu Yamashita, Hikaru Yoshimura, Akihiro Hayashi, and Keisuke Fujii, "Qulacs: a fast and versatile quantum circuit simulator for research purpose", Quantum 5, 559 (2021).

[26] Jan Lukas Bosse, Raul A Santos, and Ashley Montanaro, "Sketching phase diagrams using low-depth variational quantum algorithms", Quantum Science and Technology 9 3, 035034 (2024).

[27] Alan Morningstar, Markus Hauru, Jackson Beall, Martin Ganahl, Adam G.M. Lewis, Vedika Khemani, and Guifre Vidal, "Simulation of Quantum Many-Body Dynamics with Tensor Processing Units: Floquet Prethermalization", PRX Quantum 3 2, 020331 (2022).

[28] Chen Zhang, Zeyu Song, Haojie Wang, Kaiyuan Rong, and Jidong Zhai, Proceedings of the ACM International Conference on Supercomputing 443 (2021) ISBN:9781450383356.

[29] Jin-Guo Liu and Kai-Lai Xu, "Automatic differentiation and its applications in physics simulation", Acta Physica Sinica 70 14, 149402 (2021).

[30] Asel Sagingalieva, Mohammad Kordzanganeh, Nurbolat Kenbayev, Daria Kosichkina, Tatiana Tomashuk, and Alexey Melnikov, "Hybrid Quantum Neural Network for Drug Response Prediction", Cancers 15 10, 2705 (2023).

[31] Zhenyu Li, Jie Liu, Xiangjian Shen, and Feixue Gao, "Challenges and opportunities of quantum-computational chemistry", SCIENTIA SINICA Chimica 53 2, 119 (2023).

[32] Arvindhan Muthusamy, Advances in Computer and Electrical Engineering 22 (2023) ISBN:9781668475355.

[33] Marc Illa, Caroline E. P. Robin, and Martin J. Savage, "Quantum simulations of SO(5) many-fermion systems using qudits", Physical Review C 108 6, 064306 (2023).

[34] Jarosław Adam Miszczak, Companion Proceedings of the 7th International Conference on the Art, Science, and Engineering of Programming 101 (2023) ISBN:9798400707551.

[35] Daniel Huerga, "Variational Quantum Simulation of Valence-Bond Solids", Quantum 6, 874 (2022).

[36] Jakob S Kottmann, Sumner Alperin-Lea, Teresa Tamayo-Mendoza, Alba Cervera-Lierta, Cyrille Lavigne, Tzu-Ching Yen, Vladyslav Verteletskyi, Philipp Schleich, Abhinav Anand, Matthias Degroote, Skylar Chaney, Maha Kesibi, Naomi Grace Curnow, Brandon Solo, Georgios Tsilimigkounakis, Claudia Zendejas-Morales, Artur F Izmaylov, and Alán Aspuru-Guzik, "TEQUILA: a platform for rapid development of quantum algorithms", Quantum Science and Technology 6 2, 024009 (2021).

[37] Oleksandr Kyriienko, Annie E. Paine, and Vincent E. Elfving, "Solving nonlinear differential equations with differentiable quantum circuits", Physical Review A 103 5, 052416 (2021).

[38] Hasitha Muthumala Waidyasooriya, Hiroki Oshiyama, Yuya Kurebayashi, Masanori Hariyama, and Masayuki Ohzeki, "A Scalable Emulator for Quantum Fourier Transform Using Multiple-FPGAs With High-Bandwidth-Memory", IEEE Access 10, 65103 (2022).

[39] Andrea Mari, Thomas R. Bromley, and Nathan Killoran, "Estimating the gradient and higher-order derivatives on quantum hardware", Physical Review A 103 1, 012405 (2021).

[40] Saad Yalouz, Martin Rafael Gullin, and Sajanthan Sekaran, "QuantNBody: a Python package for quantum chemistry and physics to build and manipulate many-body operators and wave functions.", Journal of Open Source Software 7 80, 4759 (2022).

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[42] Weiyuan Gong, Dong Yuan, Weikang Li, and Dong-Ling Deng, "Enhancing quantum adversarial robustness by randomized encodings", Physical Review Research 6 2, 023020 (2024).

[43] Zhide Lu, Pei-Xin Shen, and Dong-Ling Deng, "Markovian Quantum Neuroevolution for Machine Learning", Physical Review Applied 16 4, 044039 (2021).

[44] John Brennan, Lee O’Riordan, Kenneth Hanley, Myles Doyle, Momme Allalen, David Brayford, Luigi Iapichino, and Niall Moran, "QXTools: A Julia framework for distributed quantum circuit simulation", Journal of Open Source Software 7 70, 3711 (2022).

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[46] Yun-Zhong Qiu, "Universal adversarial perturbations for multiple classification tasks with quantum classifiers", Machine Learning: Science and Technology 4 4, 045009 (2023).

[47] Yi-Te Huang, Po-Chen Kuo, Neill Lambert, Mauro Cirio, Simon Cross, Shen-Liang Yang, Franco Nori, and Yueh-Nan Chen, "An efficient Julia framework for hierarchical equations of motion in open quantum systems", Communications Physics 6 1, 313 (2023).

[48] Jin-Guo Liu, Lei Wang, and Pan Zhang, "Tropical Tensor Network for Ground States of Spin Glasses", Physical Review Letters 126 9, 090506 (2021).

[49] Nicholas H. Stair and Francesco A. Evangelista, "QForte: An Efficient State-Vector Emulator and Quantum Algorithms Library for Molecular Electronic Structure", Journal of Chemical Theory and Computation 18 3, 1555 (2022).

[50] Jan Lukas Bosse and Ashley Montanaro, "Probing ground-state properties of the kagome antiferromagnetic Heisenberg model using the variational quantum eigensolver", Physical Review B 105 9, 094409 (2022).

[51] Nguyen Tan Viet, Nguyen Thi Chuong, Vu Thi Ngoc Huyen, and Le Bin Ho, "tqix.pis: A toolbox for quantum dynamics simulation of spin ensembles in Dicke basis", Computer Physics Communications 286, 108686 (2023).

[52] Chu Guo, Yi Fan, Zhiqian Xu, and Honghui Shang, "Differentiable matrix product states for simulating variational quantum computational chemistry", Quantum 7, 1192 (2023).

[53] Madhav Krishnan Vijayan, Alexandru Paler, Jason Gavriel, Casey R Myers, Peter P Rohde, and Simon J Devitt, "Compilation of algorithm-specific graph states for quantum circuits", Quantum Science and Technology 9 2, 025005 (2024).

[54] Tobias Haug and M. S. Kim, "Natural parametrized quantum circuit", Physical Review A 106 5, 052611 (2022).

[55] Paolo Braccia, Leonardo Banchi, and Filippo Caruso, "Quantum Noise Sensing by Generating Fake Noise", Physical Review Applied 17 2, 024002 (2022).

[56] Gian Giacomo Guerreschi, "Fast simulation of quantum algorithms using circuit optimization", Quantum 6, 706 (2022).

[57] Kevin Mato, Stefan Hillmich, and Robert Wille, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 978 (2023) ISBN:979-8-3503-4323-6.

[58] B Jaderberg, L W Anderson, W Xie, S Albanie, M Kiffner, and D Jaksch, "Quantum self-supervised learning", Quantum Science and Technology 7 3, 035005 (2022).

[59] Aditi Misra-Spieldenner, Tim Bode, Peter K. Schuhmacher, Tobias Stollenwerk, Dmitry Bagrets, and Frank K. Wilhelm, "Mean-Field Approximate Optimization Algorithm", PRX Quantum 4 3, 030335 (2023).

[60] Honghui Shang, Li Shen, Yi Fan, Zhiqian Xu, Chu Guo, Jie Liu, Wenhao Zhou, Huan Ma, Rongfen Lin, Yuling Yang, Fang Li, Zhuoya Wang, Yunquan Zhang, and Zhenyu Li, SC22: International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2022) ISBN:978-1-6654-5444-5.

[61] Jinkai Tian, Xiaoyu Sun, Yuxuan Du, Shanshan Zhao, Qing Liu, Kaining Zhang, Wei Yi, Wanrong Huang, Chaoyue Wang, Xingyao Wu, Min-Hsiu Hsieh, Tongliang Liu, Wenjing Yang, and Dacheng Tao, "Recent Advances for Quantum Neural Networks in Generative Learning", IEEE Transactions on Pattern Analysis and Machine Intelligence 1 (2023).

[62] Junxiang Xiao, Jingwei Wen, Shijie Wei, and Guilu Long, "Reconstructing unknown quantum states using variational layerwise method", Frontiers of Physics 17 5, 51501 (2022).

[63] Stefano Barison, Filippo Vicentini, Ignacio Cirac, and Giuseppe Carleo, "Variational dynamics as a ground-state problem on a quantum computer", Physical Review Research 4 4, 043161 (2022).

[64] Gian Gentinetta, Friederike Metz, and Giuseppe Carleo, "Overhead-constrained circuit knitting for variational quantum dynamics", Quantum 8, 1296 (2024).

[65] Tobias Haug, Chris N Self, and M S Kim, "Quantum machine learning of large datasets using randomized measurements", Machine Learning: Science and Technology 4 1, 015005 (2023).

[66] Annie E. Paine, Vincent E. Elfving, and Oleksandr Kyriienko, "Quantum kernel methods for solving regression problems and differential equations", Physical Review A 107 3, 032428 (2023).

[67] Yifei Huang, Yuguo Shao, Weiluo Ren, Jinzhao Sun, and Dingshun Lv, "Efficient Quantum Imaginary Time Evolution by Drifting Real-Time Evolution: An Approach with Low Gate and Measurement Complexity", Journal of Chemical Theory and Computation 19 13, 3868 (2023).

[68] Tong Liu, Jin-Guo Liu, and Heng Fan, "Probabilistic nonunitary gate in imaginary time evolution", Quantum Information Processing 20 6, 204 (2021).

[69] Maria Schuld and Francesco Petruccione, Quantum Science and Technology 1 (2021) ISBN:978-3-030-83097-7.

[70] Chen Zhao and Xiao-Shan Gao, "QDNN: deep neural networks with quantum layers", Quantum Machine Intelligence 3 1, 15 (2021).

[71] Tim Bode, Dmitry Bagrets, Aditi Misra-Spieldenner, Tobias Stollenwerk, and Frank K. Wilhelm, "QAOA.jl: Toolkit for the Quantum and Mean-Field Approximate Optimization Algorithms", Journal of Open Source Software 8 86, 5364 (2023).

[72] Annie E. Paine, Vincent E. Elfving, and Oleksandr Kyriienko, "Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time‐Series", Advanced Quantum Technologies 6 10, 2300065 (2023).

[73] Yi Fan, Jie Liu, Xiongzhi Zeng, Zhiqian Xu, Honghui Shang, Zhenyu Li, and Jinlong Yang, "Q<sup>2</sup>Chemistry: A quantum computation platform for quantum chemistry", JUSTC 52 12, 2 (2022).

[74] Anna Dawid, Julian Arnold, Borja Requena, Alexander Gresch, Marcin Płodzień, Kaelan Donatella, Kim A. Nicoli, Paolo Stornati, Rouven Koch, Miriam Büttner, Robert Okuła, Gorka Muñoz-Gil, Rodrigo A. Vargas-Hernández, Alba Cervera-Lierta, Juan Carrasquilla, Vedran Dunjko, Marylou Gabrié, Patrick Huembeli, Evert van Nieuwenburg, Filippo Vicentini, Lei Wang, Sebastian J. Wetzel, Giuseppe Carleo, Eliška Greplová, Roman Krems, Florian Marquardt, Michał Tomza, Maciej Lewenstein, and Alexandre Dauphin, "Modern applications of machine learning in quantum sciences", arXiv:2204.04198, (2022).

[75] Sirui Lu, Lu-Ming Duan, and Dong-Ling Deng, "Quantum adversarial machine learning", Physical Review Research 2 3, 033212 (2020).

[76] Pedro Maciel Xavier, Pedro Ripper, Tiago Andrade, Joaquim Dias Garcia, Nelson Maculan, and David E. Bernal Neira, "QUBO.jl: A Julia Ecosystem for Quadratic Unconstrained Binary Optimization", arXiv:2307.02577, (2023).

[77] Nguyen Tan Viet, Nguyen Thi Chuong, Vu Thi Ngoc Huyen, and Le Bin Ho, "tqix.pis: A toolbox for quantum dynamics simulation of spin ensembles in Dicke basis", arXiv:2209.01168, (2022).

[78] Nico Meyer, Christian Ufrecht, Maniraman Periyasamy, Daniel D. Scherer, Axel Plinge, and Christopher Mutschler, "A Survey on Quantum Reinforcement Learning", arXiv:2211.03464, (2022).

[79] Stavros Efthymiou, Sergi Ramos-Calderer, Carlos Bravo-Prieto, Adrián Pérez-Salinas, Diego García-Martín, Artur Garcia-Saez, José Ignacio Latorre, and Stefano Carrazza, "Qibo: a framework for quantum simulation with hardware acceleration", Quantum Science and Technology 7 1, 015018 (2022).

[80] Feng Pan, Pengfei Zhou, Sujie Li, and Pan Zhang, "Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations", Physical Review Letters 125 6, 060503 (2020).

[81] Amit Jamadagni, Andreas M. Läuchli, and Cornelius Hempel, "Benchmarking quantum computer simulation software packages", arXiv:2401.09076, (2024).

[82] Di Luo, Jiayu Shen, Rumen Dangovski, and Marin Soljačić, "QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning", arXiv:2211.01365, (2022).

[83] Stavros Efthymiou, Sergi Ramos-Calderer, Carlos Bravo-Prieto, Adrián Pérez-Salinas, Diego García-Martín, Artur Garcia-Saez, José Ignacio Latorre, and Stefano Carrazza, "Qibo: a framework for quantum simulation with hardware acceleration", arXiv:2009.01845, (2020).

[84] Xiaosi Xu, Simon Benjamin, Jinzhao Sun, Xiao Yuan, and Pan Zhang, "A Herculean task: Classical simulation of quantum computers", arXiv:2302.08880, (2023).

[85] Jin-Guo Liu, Liang Mao, Pan Zhang, and Lei Wang, "Solving Quantum Statistical Mechanics with Variational Autoregressive Networks and Quantum Circuits", arXiv:1912.11381, (2019).

[86] Benoit Seron and Antoine Restivo, "BosonSampling.jl: A Julia package for quantum multi-photon interferometry", arXiv:2212.09537, (2022).

[87] Shane McFarthing, Anban Pillay, Ilya Sinayskiy, and Francesco Petruccione, "Classical Ensembles of Single-Qubit Quantum Variational Circuits for Classification", arXiv:2302.02964, (2023).

[88] Tyson Jones, "Efficient classical calculation of the Quantum Natural Gradient", arXiv:2011.02991, (2020).

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

[90] Jin-Guo Liu and Taine Zhao, "Differentiate Everything with a Reversible Embeded Domain-Specific Language", arXiv:2003.04617, (2020).

[91] Adrián Pérez-Salinas, "Algorithmic Strategies for seizing Quantum Computing", arXiv:2112.15175, (2021).

[92] Carsten Bauer, "Fast and stable determinant quantum Monte Carlo", SciPost Physics Core 2 2, 011 (2020).

[93] Luca Mondada, "Quantum Circuits in Additive Hilbert Space", arXiv:2111.01211, (2021).

[94] Jessie M. Henderson, Marianna Podzorova, M. Cerezo, John K. Golden, Leonard Gleyzer, Hari S. Viswanathan, and Daniel O'Malley, "Quantum Algorithms for Geologic Fracture Networks", arXiv:2210.11685, (2022).

[95] Wang Fang and Mingsheng Ying, "Symbolic Execution for Quantum Error Correction Programs", arXiv:2311.11313, (2023).

[96] Shlomo Kashani and David Zaret, "Using the Julia framework to teach quantum entanglement", arXiv:2302.12889, (2023).

[97] Rowan Pellow-Jarman, Anban Pillay, Ilya Sinayskiy, and Francesco Petruccione, "Hybrid Genetic Optimisation for Quantum Feature Map Design", arXiv:2302.02980, (2023).

[98] Jarosław Adam Miszczak, "Symbolic quantum programming for supporting applications of quantum computing technologies", arXiv:2302.09401, (2023).

[99] Jie Lin, Benjamin MacLellan, Sobhan Ghanbari, Julie Belleville, Khuong Tran, Luc Robichaud, Roger G. Melko, Hoi-Kwong Lo, and Piotr Roztocki, "GraphiQ: Quantum circuit design for photonic graph states", arXiv:2402.09285, (2024).

[100] Sara Santos, Xinyu Song, and Vincenzo Savona, "Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems", arXiv:2403.05908, (2024).

[101] John Golden, Andreas Bärtschi, Daniel O'Malley, Elijah Pelofske, and Stephan Eidenbenz, "JuliQAOA: Fast, Flexible QAOA Simulation", arXiv:2312.06451, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-22 08:23:35) and SAO/NASA ADS (last updated successfully 2024-05-22 08:23:36). The list may be incomplete as not all publishers provide suitable and complete citation data.

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