From c21198865a39183f294d053993ea50fd26900420 Mon Sep 17 00:00:00 2001 From: William Galvin Date: Fri, 29 Dec 2023 11:10:44 -0800 Subject: [PATCH] Add paper --- paper/images/results.pdf | Bin 0 -> 17010 bytes paper/main.pdf | Bin 0 -> 278251 bytes paper/main.tex | 298 +++++++++++++++++++++++++++++++++++++++ paper/references.bib | 218 ++++++++++++++++++++++++++++ 4 files changed, 516 insertions(+) create mode 100644 paper/images/results.pdf create mode 100644 paper/main.pdf create mode 100644 paper/main.tex create mode 100644 paper/references.bib diff --git a/paper/images/results.pdf b/paper/images/results.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d4983af57fef1a4ef077555cc06765f81ca6630d GIT binary patch literal 17010 zcmeHvc|29$_je?5ks*YNYaYU#?{y7DrX+J2Dzj^zT{EG9QZgoG7BZxWWU53IGG{1J znuJiP(7i_b^+ee3l+ujjAltJis*efC{v@3q!md+)W@exHPORn(+V(pZ@Awde4{ zDi{imgu7We!sO-Qh=cy_BsfCZl5FYhW(P;;TH2Ak;AlXg58u5TMsl@*2xV5hpyuXE 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journal={The Journal of Chemical Physics}, + publisher={AIP Publishing}, + author={Sun, Qiming and Zhang, Xing and Banerjee, Samragni and Bao, Peng and Barbry, Marc and Blunt, Nick S. and Bogdanov, Nikolay A. and Booth, George H. and Chen, Jia and Cui, Zhi-Hao and Eriksen, Janus J. and Gao, Yang and Guo, Sheng and Hermann, Jan and Hermes, Matthew R. and Koh, Kevin and Koval, Peter and Lehtola, Susi and Li, Zhendong and Liu, Junzi and Mardirossian, Narbe and McClain, James D. and Motta, Mario and Mussard, Bastien and Pham, Hung Q. and Pulkin, Artem and Purwanto, Wirawan and Robinson, Paul J. and Ronca, Enrico and Sayfutyarova, Elvira R. and Scheurer, Maximilian and Schurkus, Henry F. and Smith, James E. T. and Sun, Chong and Sun, Shi-Ning and Upadhyay, Shiv and Wagner, Lucas K. and Wang, Xiao and White, Alec and Whitfield, James Daniel and Williamson, Mark J. and Wouters, Sebastian and Yang, Jun and Yu, Jason M. and Zhu, Tianyu and Berkelbach, Timothy C. and Sharma, Sandeep and Sokolov, Alexander Yu. and Chan, Garnet Kin-Lic}, + year={2020}, + month=jul } + +@Article{ numpy, + title = {Array programming with {NumPy}}, + author = {Charles R. Harris and K. Jarrod Millman and St{\'{e}}fan J. + van der Walt and Ralf Gommers and Pauli Virtanen and David + Cournapeau and Eric Wieser and Julian Taylor and Sebastian + Berg and Nathaniel J. Smith and Robert Kern and Matti Picus + and Stephan Hoyer and Marten H. van Kerkwijk and Matthew + Brett and Allan Haldane and Jaime Fern{\'{a}}ndez del + R{\'{i}}o and Mark Wiebe and Pearu Peterson and Pierre + G{\'{e}}rard-Marchant and Kevin Sheppard and Tyler Reddy and + Warren Weckesser and Hameer Abbasi and Christoph Gohlke and + Travis E. Oliphant}, + year = {2020}, + month = sep, + journal = {Nature}, + volume = {585}, + number = {7825}, + pages = {357--362}, + doi = {10.1038/s41586-020-2649-2}, + publisher = {Springer Science and Business Media {LLC}}, + url = {https://doi.org/10.1038/s41586-020-2649-2} +} + +@book{Ivo, + author = {Ivo Cacelli}, + title = {Reference Module in Chemistry, Molecular Sciences and Chemical Engineering Chapter: The Hartree–Fock Method}, + publisher = {Elsevier}, + year = 2013, + url = {https://people.unipi.it/static/Cacelli/didattica/dispense.chimteo/HF_cacelli_revised.pdf} +} + +@article{complex, +title = {The Variational Quantum Eigensolver: A review of methods and best practices}, +journal = {Physics Reports}, +volume = {986}, +pages = {1-128}, +year = {2022}, +note = {The Variational Quantum Eigensolver: a review of methods and best practices}, +issn = {0370-1573}, +doi = {https://doi.org/10.1016/j.physrep.2022.08.003}, +url = {https://www.sciencedirect.com/science/article/pii/S0370157322003118}, +author = {Jules Tilly and Hongxiang Chen and Shuxiang Cao and Dario Picozzi and Kanav Setia and Ying Li and Edward Grant and Leonard Wossnig and Ivan Rungger and George H. Booth and Jonathan Tennyson}, +keywords = {Quantum computing, Variational methods, Noisy intermediate scale quantum devices, Electronic structure, Quantum chemistry, Many-body physics}, +abstract = {The variational quantum eigensolver (or VQE), first developed by Peruzzo et al. (2014), has received significant attention from the research community in recent years. It uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are constrained in their accuracy due to the computational limits facing exact modeling of the exponentially growing electronic wavefunction for these many-electron systems. The VQE may be used to model these complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. One important advantage is that variational algorithms have been shown to present some degree of resilience to the noise in the quantum hardware. Finding a path to navigate the relevant literature has rapidly become an overwhelming task, with many methods promising to improve different parts of the algorithm, but without clear descriptions of how the diverse parts fit together. The potential practical advantages of the algorithm are also widely discussed in the literature, but with varying conclusions. Despite strong theoretical underpinnings suggesting excellent scaling of individual VQE components, studies have pointed out that their various pre-factors could be too large to reach a quantum computing advantage over conventional methods. This review aims at disentangling the relevant literature to provide a comprehensive overview of the progress that has been made on the different parts of the algorithm, and to discuss future areas of research that are fundamental for the VQE to deliver on its promises. All the different components of the algorithm are reviewed in detail. These include the representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process to find ground state energies, the post processing mitigation of quantum errors, and suggested best practices. We identify four main areas of future research: (1) optimal measurement schemes for reduction of circuit repetitions required; (2) large scale parallelization across many quantum computers; (3) ways to overcome the potential appearance of vanishing gradients in the optimization process for large systems, and how the number of iterations required for the optimization scales with system size; (4) the extent to which VQE suffers for quantum noise, and whether this noise can be mitigated in a tractable manner. The answers to these open research questions will determine the routes for the VQE to achieve quantum advantage as the quantum computing hardware scales up and as the noise levels are reduced.} +} + + +