◐Attested & literatureAlgorithmsQuantum differential equations · linear
Encoding of linear kinetic plasma problems in quantum circuits via data compression
Encode a linear kinetic plasma problem — modeling electrostatic linear waves, driven by a spatially localized external current, in a one-dimensional Maxwellian electron plasma — into a quantum circuit that solves the resulting linear system.
kinetic plasmavlasov-ampere systemquantum signal processingblock encodingboundary-value problem
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Encode a linear kinetic plasma problem — modeling electrostatic linear waves, driven by a spatially localized external current, in a one-dimensional Maxwellian electron plasma — into a quantum circuit that solves the resulting linear system. Novikau, Dodin and Startsev propose an algorithm for encoding linear kinetic plasma problems in quantum circuits, focusing on 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. The authors formulate this system as a boundary-value problem and cast it as a linear vector equation Aψ = b, to be solved using the quantum signal processing algorithm. Because that algorithm requires the matrix A to be encoded in a quantum circuit as a subblock of a unitary matrix, the authors propose a way to encode A in a compressed form, and discuss how the resulting circuit scales with the problem size and the desired precision.
Circuit & simulation
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What this takes and returns
TakesNothingWhat joins here
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ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
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Takes A linear PDE with its conditions, a grid over every continuous variable the problem carries, and — where the problem is posed as a boundary-value problem rather than an initial-value one — the boundary treatment that makes the resulting matrix well posed. Returns One matrix and one right-hand side over all the grid unknowns together, with the condition number that the cost of solving it will be measured against, and the discretization error that fixes how fine the grid had to be.
TakesAn access model for A — sparse-access oracles, a Pauli or LCU decomposition, a purification, or an explicit arithmetic description — plus a target precision ε.ReturnsA unitary U on s+a qubits, its subnormalization α, and its ancilla/flag count a. Because ∥U∥=1, Gilyén, Su, Low and Wiebe's Definition 43 forces ∥A∥≤α+ε.
How it works
Novikau, Dodin and Startsev propose an algorithm for encoding linear kinetic plasma problems in quantum circuits, focusing on 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. The authors formulate this system as a boundary-value problem and cast it as a linear vector equation Aψ = b, to be solved using the quantum signal processing algorithm. Because that algorithm requires the matrix A to be encoded in a quantum circuit as a subblock of a unitary matrix, the authors propose a way to encode A in a compressed form, and discuss how the resulting circuit scales with the problem size and the desired precision. The Classiq library carries this subject under applications · plasma. The sources read state no complexity bound for this record (The abstract of arXiv:2403.11989, the only source read for this record, states no complexity bound. Its closest approach to a cost claim is the closing sentence, "We propose how to encode A in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision." That sentence promises a discussion of scaling, not a scaling law: it names the two quantities the circuit scales with — problem size and desired precision — but gives no big-O expression, no exponent, and no qubit or gate count for either. The sentence before it states, "The latter requires encoding of the matrix A in a quantum circuit as a subblock of a unitary matrix." This establishes that the method is a block encoding of A, again without a size figure. The Classiq index entry this record covers, applications/plasma/vlasov_ampere, gives a directory path and a file list and states no bound. Those are the only sources read for this field, and the complexity field is left empty on purpose rather than filled with a bound written from memory.).
Implementation
Unsupported
linear-kinetic-plasma-encoding.txt
ALGORITHM: Encoding of linear kinetic plasma problems in quantum circuits via data compression
PROBLEM: Encode a linear kinetic plasma problem — modeling electrostatic linear waves, driven by a spatially localized external current, in a one-dimensional Maxwellian electron plasma — into a quantum circuit that solves the resulting linear system.
IDEA: Novikau, Dodin and Startsev propose an algorithm for encoding linear kinetic plasma problems in quantum circuits, focusing on 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. The authors formulate this system as a boundary-value problem and cast it as a linear vector equation Aψ = b, to be solved using the quantum signal processing algorithm. Because that algorithm requires the matrix A to be encoded in a quantum circuit as a subblock of a unitary matrix, the authors propose a way to encode A in a compressed form, and discuss how the resulting circuit scales with the problem size and the desired precision.
REPORTED COST: Not stated by the sources read
BASIS: The abstract of arXiv:2403.11989, the only source read for this record, states no complexity bound. Its closest approach to a cost claim is the closing sentence, "We propose how to encode $A$ in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision." That sentence promises a discussion of scaling, not a scaling law: it names the two quantities the circuit scales with — problem size and desired precision — but gives no big-O expression, no exponent, and no qubit or gate count for either. The sentence before it states, "The latter requires encoding of the matrix $A$ in a quantum circuit as a subblock of a unitary matrix." This establishes that the method is a block encoding of A, again without a size figure. The Classiq index entry this record covers, applications/plasma/vlasov_ampere, gives a directory path and a file list and states no bound. Those are the only sources read for this field, and the complexity field is left empty on purpose rather than filled with a bound written from memory.
DEMONSTRATED BY: the Classiq library entry applications/plasma/vlasov_ampere
PRIMARY SOURCE: Ivan Novikau, Ilya Y. Dodin, Edward A. Startsev (2024), Encoding of linear kinetic plasma problems in quantum circuits via data compression — https://arxiv.org/abs/2403.11989
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Quantum vs classical
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Quantum claim
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Literature & references
Encoding of linear kinetic plasma problems in quantum circuits via data compression2024 · Ivan Novikau, Ilya Y. Dodin, Edward A. Startsev
Primary source: it proposes the algorithm for encoding linear kinetic plasma problems — electrostatic linear waves in a one-dimensional Maxwellian electron plasma, described by the linearized Vlasov-Ampère system — as a linear vector equation Aψ = b solved by quantum signal processing, and proposes a compressed encoding of the matrix A. Consult it for the scaling of the resulting circuit with problem size and precision, which the abstract promises to discuss but does not itself state.