{"title":"Encoding of linear kinetic plasma problems in quantum circuits via data compression","authors":"I. Novikau, I.Y. Dodin, E.A. Startsev","doi":"10.1017/s0022377824000795","DOIUrl":null,"url":null,"abstract":"We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation <jats:inline-formula> <jats:alternatives> <jats:tex-math>$\\boldsymbol {A}{\\boldsymbol{\\psi} } = \\boldsymbol {b}$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000795_inline1.png\"/> </jats:alternatives> </jats:inline-formula> to be solved by using the quantum signal processing algorithm. The latter requires encoding of matrix <jats:inline-formula> <jats:alternatives> <jats:tex-math>$\\boldsymbol {A}$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000795_inline2.png\"/> </jats:alternatives> </jats:inline-formula> in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode <jats:inline-formula> <jats:alternatives> <jats:tex-math>$\\boldsymbol {A}$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000795_inline3.png\"/> </jats:alternatives> </jats:inline-formula> in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Plasma Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1017/s0022377824000795","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
引用次数: 0
Abstract
We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation $\boldsymbol {A}{\boldsymbol{\psi} } = \boldsymbol {b}$ to be solved by using the quantum signal processing algorithm. The latter requires encoding of matrix $\boldsymbol {A}$ in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode $\boldsymbol {A}$ in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.
期刊介绍:
JPP aspires to be the intellectual home of those who think of plasma physics as a fundamental discipline. The journal focuses on publishing research on laboratory plasmas (including magnetically confined and inertial fusion plasmas), space physics and plasma astrophysics that takes advantage of the rapid ongoing progress in instrumentation and computing to advance fundamental understanding of multiscale plasma physics. The Journal welcomes submissions of analytical, numerical, observational and experimental work: both original research and tutorial- or review-style papers, as well as proposals for its Lecture Notes series.