Some variational recipes for quantum field theories

Liu, Junyu; Li, Zimu; Zheng, Han; Yuan, Xiao; Sun, Jinzhao

doi:10.48550/arxiv.2109.05547

Cited by 3 publications

(8 citation statements)

References 74 publications

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“…An important outstanding challenge is to find physical applications of the scheme which exhibit an advantage compared to the best known algorithm. Aspirational targets include charged scalar fields at finite chemical potential [39] or variational calculation of scattering [22].…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

“…Starting from the definition of the loss function (42) (32). Using (22) and (31) Plug these expressions into the evolution equations (26) and consider a linear combination consisting of the θ 1 rows superposed with an imaginary unit multiplying the θ 2 rows to obtain (32).…”

Section: Appendix B Justification For Choice Of Baselinementioning

confidence: 99%

“…It is illuminating to compare and contrast the approach advocated here with proposals in the quantum computing literature for quantum field simulation. Like [19], we adopt the field amplitude basis, although we remain agnostic about the form of the regulator since it does not alter the general structure of the resulting Schrödinger operator (see [22] for a discussion of possibilities). The choice to focus on normalizing flows is motivated by their exact sampling properties and potential to exploit distributed computing using the embarrassing parallelism of Monte Carlo [29,42].…”

Section: Introductionmentioning

confidence: 99%

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Numerical and geometrical aspects of flow-based variational quantum Monte Carlo

Stokes¹,

Chen²,

Veerapaneni³

2022

Preprint

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This article aims to summarize recent and ongoing efforts to simulate continuous-variable quantum systems using flow-based variational quantum Monte Carlo techniques, focusing for pedagogical purposes on the example of bosons in the field amplitude (quadrature) basis. Particular emphasis is placed on the variational real-and imaginary-time evolution problems, carefully reviewing the stochastic estimation of the time-dependent variational principles and their relationship with information geometry. Some practical instructions are provided to guide the implementation of a PyTorch code. The review is intended to be accessible to researchers interested in machine learning and quantum information science. Contents 1. Introduction 2. Notation 3. Preliminaries 4. Information geometry 4.1. Unnormalized wavefunctions and holomorphy 5. Time-dependent variational principles 5.1. Unnormalized wavefunctions and holomorphy 6. Stochastic estimation 6.1. VMC and t-VMC 6.2. Stochastic optimization and variance reduction 7. Additional comments on quantum flows 7.1. Group equivariant dynamics from flows 7.2. Universal approximation 8. Experiments 8.1. States and Hamiltonian 8.2. Experimental setup 8.3. Results 9. Discussion and future directions 10. Acknowledgements Appendix A. McLachlan's variational principles Appendix B. Justification for choice of baseline Appendix C. Quadratic Hamiltonian in one dimension Appendix D. Derivation of time-dependent variational principles Appendix E.

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Section: Discussion and Future Directionsmentioning

confidence: 99%

Section: Appendix B Justification For Choice Of Baselinementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical and geometrical aspects of flow-based variational quantum Monte Carlo

Stokes¹,

Chen²,

Veerapaneni³

2022

Preprint

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“…[40,116,189,191] for several gauge-theory examples. They can also be taken advantage of in scattering problems as recently proposed [207]. On the other hand, classical computers may prepare non-trivial states through the use of conventional lattice-field-theory methods (as long as sign and signal-to-noise problems are not encountered) or tensor-network-inspired methods (as long as states are area-law entangled).…”

Section: Underlying Simulationsmentioning

confidence: 99%

“…While this algorithms shows the true advantage of a quantum computer, that is to enable a direct evaluation of real-time cross sections in QFTs, its resource requirement will likely prohibit its implementation for even small systems for the foreseeable future. Research is in progress to devise and benchmark less resource-intensive approaches to the scattering problem in the near term, including proposals for variational approaches [207], obtaining phase shifts in prototype spin models via time delay [448], or the use of Lüscher's method [105,106] in extracting low-energy few-body scattering parameters from energy spectra of particles in a finite volume, as is done in the conventional lattice-QCD program [107][108][109][110]. A complete resource analysis of scattering problems in gauge theories, including QCD, is still lacking and the problem is complicated by the absence of fully developed and efficient state-preparation algorithms for a range of non-trivial states in gauge theories, from the interacting vacuum to the scattering wavepackets of confined hadrons.…”

Section: Algorithmic Research For Digital Quantum Computing and Resou...mentioning

confidence: 99%

Quantum Simulation for High Energy Physics

Bauer¹,

Davoudi²,

Balantekin³

et al. 2022

Preprint

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It is for the first time that quantum simulation for High Energy Physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in Quantum Information Sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This community whitepaper is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

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mat2qubit: A lightweight pythonic package for qubit encodings of vibrational, bosonic, graph coloring, routing, scheduling, and general matrix problems

Sawaya¹

2022

Preprint

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Preparing problems for execution on quantum computers can require many compilation steps. Automated compilation software is useful not only for easier and faster problem execution, but also for facilitating the comparison between different algorithmic choices. Here we describe mat2qubit, a Python package for encoding several classes of classical and quantum problems into qubit representations. It is intended for use especially on Hamiltonians and functions defined over variables (e.g. particles) with cardinality larger than 2. More specifically, mat2qubit may be used to compile bosonic, phononic/vibrational, and spin-s problems, as well as classical problems such as graph coloring, routing, scheduling, and classical linear algebra more generally. In order to facilitate numerical analyses and ease of programmability, a built-in computer algebra system (CAS) allows for fully symbolic preparation and manipulation of problems (with symbolic operators, symbolic coefficients, and symbolic particle labels) before the final compilation into qubits is performed. We expect this code to be useful in the preparation and analysis of various classes of physics, chemistry, materials, and optimization problems for execution on digital quantum computers.

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Some variational recipes for quantum field theories

Cited by 3 publications

References 74 publications

Numerical and geometrical aspects of flow-based variational quantum Monte Carlo

Numerical and geometrical aspects of flow-based variational quantum Monte Carlo

Quantum Simulation for High Energy Physics

mat2qubit: A lightweight pythonic package for qubit encodings of vibrational, bosonic, graph coloring, routing, scheduling, and general matrix problems

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