Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

Second quantization of nonlinear Vlasov-Poisson system for quantum computation

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The nonlinear Vlasov-Poisson system becomes a linear, finite, discrete quantum system under second quantization.

desk verdict A useful, honest construction of a second-quantized Vlasov–Poisson Hamiltonian; the main gap is an unproven dynamical-closure assumption in the correspondence proof, not a fatally flawed idea. read the letter →

arxiv 2506.01895 v1 pith:UONCARIM submitted 2025-06-02 physics.plasm-ph quant-ph

Michael Q. May , Hong Qin This is my paper
classification physics.plasm-phquant-ph
keywords secondquantizationVlasov-PoissonSchrödinger-PoissonquantumcomputationHamiltoniansimulationnonlinearplasmaoscillationFockspacelinearization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper shows that the nonlinear Vlasov-Poisson equations—the standard kinetic model for plasmas and self-gravitating systems—can be converted into a linear, finite-dimensional, discrete quantum system by second quantizing the mode amplitudes of the Schrödinger-Poisson form. The classical nonlinear dynamics are not discarded; they are recovered as the expectation values of the quantized system's number operators, provided the initial quantum state is a narrow Gaussian packet centered on the classical mode amplitudes with matching phases. The authors derive the correspondence conditions and simulate three- and five-mode systems showing that the quantized linear equations faithfully reproduce both linear and nonlinear plasma oscillations. The point of the exercise is practical: linear, sparse, unitary evolution is what quantum Hamiltonian simulation algorithms know how to handle efficiently, so this transformation is a candidate route to simulating nonlinear kinetic dynamics on a quantum computer.

What carries the argument

The load-bearing object is the sparse Fock-space Hamiltonian of Eq. (13), obtained by second-quantizing the mode-decomposed Schrödinger-Poisson equations. It is a many-body Hamiltonian with kinetic terms $\hat a_l^\dagger \hat a_l$ and four-operator interaction terms $\hat a_l^\dagger \hat a_p^\dagger \hat a_{l-r+p} \hat a_r$; its sparsity grows only as the cube of the number of modes. The correspondence is carried by the number operators $\hat N_l = \hat a_l^\dagger \hat a_l$: in the classical limit their expectation values and first derivatives equal the classical actions $I_l$ and their derivatives, provided the initial Fock state is the narrow Gaussian wave packet of Eq. (19) with $\mu_l = N I_l$ and $\theta_{Ql} = \arg(a_l)$. The invariant-subspace structure of $\hat H$ (it conserves total quanta and forbids single-quantum exchanges) is what makes the truncated simulations small enough to run classically.

What would settle it

Prepare the five-mode Schrödinger-Poisson system with large-amplitude asymmetric initial data (unequal $a_{\pm 2}$ and $a_{\pm 4}$) so the antisymmetric $m$ direction is not narrow; the paper's own Fig. 5 used a symmetric state with narrow $m$. If the quantized $\langle \hat N_l\rangle$ no longer tracks $I_l$ near the extrema even as $N$ and truncation widths grow, the narrow-packet assumption would be falsified.

Watch

Extended reading notes

Core claim

The central claim is that the nonlinear Schrödinger-Poisson system—obtained from Vlasov-Poisson by the standard Schrödinger substitution—can be second quantized by promoting mode amplitudes $a_l$ to creation and annihilation operators $\hat a_l^\dagger, \hat a_l$ acting on a Fock space with fixed total quanta $N$. The resulting Hamiltonian $\hat H$ of Eq. (13) is linear and sparse, with sparsity $s(n)\propto n^3$ in the maximum mode number. For an initial Fock state of the Gaussian-product form (19) with mean occupancies $\mu_l = N I_l$ and phase increments $\theta_{Ql} = \arg(a_l)$, the expected number operators $\langle \hat N_l\rangle(t)$ track the classical wave actions $I_l(t)$, and the equations of motion for their first derivatives coincide in the classical limit (Appendix I). Three-mode simulations match in both linear and nonlinear regimes; five-mode simulations capture the nonlinear plasma oscillation at the correct frequency, with deviations that shrink as the wave packet resolution improves. This is the sense in which the quantized linear system 'is' the nonlinear classical system in the classical limit.

Load-bearing premise

The load-bearing premise is that the hand-chosen Gaussian Fock state stays narrow around the classical mode amplitudes for the whole simulation; if it spreads, bifurcates, or reaches modes outside the truncated set, the matching of $\langle \hat N_l\rangle$ to $I_l$ breaks down.

Editorial extensions

If this is right

  • If the correspondence holds at larger mode counts, fault-tolerant quantum computers could integrate the Vlasov-Poisson system without resolving the nonlinearity itself; one would prepare the Gaussian Fock state and let linear Hamiltonian evolution run.
  • The effective cost scaling $\tau_{\mathrm{eff}} \propto \mathrm{dim}(\ell)^4 (w/R)^{\mathrm{dim}(\ell)}$ means the quantum advantage over the classical $\mathrm{dim}(\ell)^2$ scaling appears only when the phase-space packing fraction $w/R$ is small enough for many wave packets to be evolved simultaneously.
  • The same second-quantization pipeline—Schrödingerization, mode decomposition, operator promotion—should apply to other nonlinear kinetic or fluid equations that can be written in Hamiltonian form, with analogous correspondence conditions.
  • Simulations of the five-mode system indicate that the main practical obstacle is the resolution of the Fock wave packet near oscillation extrema; increasing $N$ and the truncation widths $j_{\max}, k_{\max}, m_{\max}$ proportionally reduces the error, so the method is convergent in the classical limit.
  • The measurable output for a quantum computer would be expectation values of number operators (mode actions) rather than full time series, matching the kind of observable quantum hardware can estimate efficiently.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural test is to initialize a multi-peaked or wide Fock state and see whether the classical limit still holds; the paper's own figures already show the approximation degrading at the oscillation extrema where the packet squeezes.
  • The scaling $\tau_{\mathrm{eff}}$ suggests a cross-over: for small mode sets the classical computation wins, but for large $\mathrm{dim}(\ell)$ the exponential factor $(w/R)^{\mathrm{dim}(\ell)}$ makes quantum simulation attractive only if the initial phase-space volume of a single trajectory is exponentially small—which is exactly the regime of collisionless kinetic theory with many weakly popula
  • A practical bottleneck the paper leaves open is state preparation: the Gaussian-product initial state of Eq. (19) has amplitude on a combinatorially large set of basis vectors, so preparing it on a quantum device may require significant overhead; future work would need a polynomial preparation circuit or a different observable that avoids full state preparation.
  • The comparison is made only through number-operator expectations on a symmetric subspace; extending to the full spatial density $|\psi_p(x,t)|^2$ will require simulating multiple non-interacting copies simultaneously, as Appendix II notes, so the practical quantum algorithm probably needs a broader observable protocol than a single run.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The manuscript proposes a route to quantum simulation of the nonlinear Vlasov-Poisson system by first approximating it with the Schrödinger-Poisson equations, decomposing the wavefunction into a finite set of Fourier modes, and then promoting the mode amplitudes to creation and annihilation operators. The resulting Hamiltonian (13) is linear, sparse, and finite on a truncated Fock space. The authors choose a Gaussian occupation-number initial state (19) whose means and phases are fixed by the classical actions and mode phases, and they claim in Appendix I that this yields correspondence between ∂_t⟨N_l⟩ and ∂_t I_l. Numerical simulations for three-mode and five-mode truncations (Figs. 3-5) show agreement over several plasma oscillations, and Section IV derives a scaling estimate τ_eff ∝ dim(l)^4 (w/R)^(dim(l)) for simultaneous simulation of many classical trajectories.

Significance. If the correspondence were rigorously established, this would be a valuable contribution to quantum algorithms for nonlinear kinetic equations: the construction is explicit, the Hamiltonian sparsity is quantified, and the invariant-subspace decomposition in Section III is a useful reduction for classical verification. The numerical examples, while limited, do demonstrate that the quantized linear system can track the finite-mode Schrödinger-Poisson dynamics in regimes where nonlinear mode coupling is present. However, the central correspondence claim is currently supported by an initial-time argument and a few trajectories, not by a proof of dynamical closure or a convergence study; the significance of the paper therefore depends on closing this gap.

major comments (4)
  1. [Appendix I, Eqs. (36)-(40)] The correspondence argument proves ∂_t⟨N_l⟩ ≈ ∂_t I_l only for the initial state (19), not for the subsequent evolution. The step from Eq. (38) to Eq. (39) uses two premises: that ψ_{j,k} is nonzero only in a narrow band around k = j = 0, and that a single-quantum change leaves the wavefunction amplitude unchanged. Neither premise follows from the quartic Hamiltonian (13), whose expectation-value hierarchy does not close. The manuscript's own Figs. 4 and 5 attribute trajectory error to the wavefunction being 'poorly resolved when it is squeezed at both the maximum and minimum of its trajectory,' which is exactly the regime where the narrow-band premise is violated. Please provide a dynamical argument that the state remains in the correspondence manifold, or a convergence study showing that increasing N and the truncation sizes drives the correspondence error to zero.
  2. [Section II, after Eq. (18)] The scale-invariance transformation is not demonstrated and appears inconsistent as written. If ⟨N_l⟩ ≈ N I_l and the four-operator expectation in Eq. (17) is of order N² times the corresponding classical product, then the interaction term in the equation for ⟨N_l⟩/N is N/δ times the classical interaction term. Direct substitution of the stated transformation ⟨N_l⟩→N⟨N_l⟩, δ→√Nδ, and t→t/√N does not remove this factor; it leaves an extra power of N in the interaction coefficient unless the Hamiltonian itself is rescaled by an additional factor not present in Eq. (13). Since all numerical comparisons depend on this scaling, please write out the explicit rescaled equations and state precisely which variables and parameters are used in Figs. 3-5.
  3. [Section III, Figs. 3-5] The numerical evidence for the central claim consists of a handful of trajectories with no error bars and no convergence study. The text asserts that increasing the total number of quanta and j_max, k_max, m_max 'will reduce the error,' but no data support this statement. Because the paper's abstract promises that the quantized linear system 'can capture nonlinear dynamics,' a quantitative convergence test (e.g., maximum trajectory error versus N at fixed physical parameters, and versus truncation size at fixed N) is needed to justify the claim.
  4. [Eqs. (4)-(5) and Figs. 3-5] The pre-quantized system being matched is the finite-mode Schrödinger-Poisson truncation, not the full Vlasov-Poisson system. The mode truncation in Eq. (5) is uncontrolled, and the initial condition (25) has non-negligible amplitudes outside the retained mode sets l={-2,0,2} and l={-4,-2,0,2,4}. The simulations therefore demonstrate correspondence with a reduced model. The abstract's claim about capturing nonlinear Vlasov-Poisson dynamics needs either a controlled truncation-error estimate or a more limited statement that the correspondence is to the finite-mode Schrödinger-Poisson system.
minor comments (4)
  1. [Section II, Eq. (19)] The symbol N is used both for the total number of quanta in Eq. (8) and for the normalization constant in Eq. (19); please disambiguate the two uses.
  2. [Section III, Eq. (27)] The fourth component of the five-mode basis vector φ_{j,k,m} is written as c4−k−m+k, which simplifies to c4−m; this appears to be a typo, and as written the basis vectors do not obviously conserve total quanta. Please correct the expression and verify the total sum.
  3. [Section II, Eqs. (5), (6), and (18)] The interaction terms use inconsistent index combinations (l−p+r versus l−r+p) and inconsistent powers of (r−l) (−2 versus 2) in the classical equations; please make these expressions mutually consistent.
  4. [Section II, Eq. (14)] The quantity s(n) is called 'sparsity' but appears to count nonzero Hamiltonian terms; this conflicts with the standard meaning of sparsity as the fraction of zero entries. Please rename it, e.g., 'number of nonzero couplings.'

Circularity Check

2 steps flagged · score 4.0 of 10

The correspondence conditions absorb the narrow-Gaussian/coherent-state ansatz, and the quantum initial state is seeded from the classical solution, so the numerical agreement is partly a consistency check; the central Vlasov demonstration retains independent dynamical content.

  1. self definitional [Appendix I, Eqs. (38)-(40); Section II, Eq. (19)]
    "In the classical limit, ψj,k will only be nonzero in a narrow band around k = j = 0, so ⟨â†l â†p âl−r+p âr + c.c.⟩ ≃ a∗l a∗p al−r+par + c.c. becomes cos(θ−4 + θ2 − θ0 − θ−2) ≃ Σj,k Re(ψ†j+1,k+1ψj,k) (38) ≃ Σj,k |ψj,k|2 cos(θQ−4 + θQ2 − θQ0 − θQ−2) (39)."

    The proof of ∂t⟨Nl⟩ ≃ ∂tIl requires the four-operator expectation value to factor into products of classical amplitudes. That factorization is inserted as the assumption that the wavefunction remains a narrow, phase-coherent packet around the classical actions and that single-quantum differences are indistinguishable. This is exactly the correspondence property to be established; the quartic Hamiltonian does not close the hierarchy of expectation values, and Figs. 4-5 show the packet becomes poorly resolved at trajectory extrema. Thus the 'derived condition' for correspondence is the ansatz itself, not a consequence obtained from the Hamiltonian.

  2. fitted input called prediction [Section II, Eq. (19); Section III, Figs. 3-5 captions]
    "For correspondence, choose µl = NIl and θQl = arg(al). An explanation of these choices may be found in Appendix I."

    The quantum initial state is constructed directly from the classical actions and phases of the solution being reproduced. Consequently ⟨Nl⟩(0)=Il(0) and the initial phase relation hold by definition. The matching of initial values in Figs. 3-5 is therefore by construction, and the subsequent agreement is a consistency check of the coherence ansatz rather than a parameter-free prediction of the nonlinear dynamics from the quantized Hamiltonian alone.

full rationale

The paper is not wholly circular: the quantized system is evolved under its own sparse linear Hamiltonian and benchmarked against an independent pre-quantized Schrödinger-Poisson calculation, with visible deviations when the wave packet is squeezed, which indicates real dynamical content. However, Appendix I's correspondence proof imports the narrow-Gaussian/coherent-state ansatz as the 'classical limit' rather than deriving its persistence from the Hamiltonian, and the quantum initial condition is seeded with the exact classical actions and phases via Eq. (19). The numerical agreement is therefore partly a demonstration that the hand-chosen packet stays approximately on the correspondence manifold, not an independent prediction. The self-citations [16,18] support the general second-quantization method but are not the load-bearing evidence for the Vlasov-Poisson result presented here. Overall, the central claim retains independent content, but one derivation step reduces to its own ansatz, giving partial circularity rather than full equivalence.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The construction promotes mode amplitudes to operators in a standard Fock space (Eq. 7), which is a mathematical representational device rather than a new particle, force, or dimension. The only model-specific objects are the Hamiltonian (Eq. 13) and the Gaussian initial condition (Eq. 19). The central computation rests on the hand-chosen parameters listed above and on the two ad hoc assumptions about wave-packet coherence and packing.

free parameters (4)
  • δ (dimensionless quantum parameter) = 0.0005 in all simulations
    Chosen by hand in Section II; it sets the scale of quantum dispersion and must be small enough to recover Vlasov-Poisson dynamics. The correspondence and the simulations depend on this value.
  • σ_l (initial Fock-space Gaussian widths per mode) = Fig. 3a: {4.0e6, 8.0e6}; Fig. 3b: {2.1e6, 4.2e6}; other runs not fully specified
    Section II states the standard deviation is chosen ad hoc. It controls the initial wave-packet width and hence the quality of the correspondence; no optimality or convergence criterion is given.
  • N (total number of quanta) = 4e7 (Fig. 3a), 3e5 (Fig. 3b), 2.43e5 (Fig. 4), 400 (Fig. 5)
    Chosen for numerical feasibility; it sets the Fock-space dimension and the classical limit. The paper does not provide a systematic convergence study in N.
  • Truncation bounds (j_max, k_max, m_max) for five-mode simulations = j_max=300, k_max=150, m_max=±17 in Fig. 4; full space in Fig. 5
    Chosen by hand to keep the basis at d'_5 ≈ 1.5e6. The paper describes them as truncations but does not study convergence in these bounds for the nonlinear regime.
assumptions (5)
  • standard math Canonical commutation relations and the Fock-space occupation-number representation (Eqs. 7 through 10).
    Standard second-quantization formalism, used without proof throughout Section II.
  • domain assumption The Wigner transform of Eq. (3) with Gaussian smoothing recovers the Vlasov distribution in the limit δ → 0.
    Invoked in Section II and supported by citations to refs. 2, 20, and 21; the paper does not re-derive or numerically verify this for its truncated mode set.
  • domain assumption A finite set of modes l = {-n, ..., n} is sufficient to represent the nonlinear plasma dynamics over the simulated time.
    Used throughout Section III; the paper notes five modes are needed for certain nonlinear interactions but does not quantify the truncation error or validate against full Vlasov-Poisson.
  • ad hoc to paper The initial state is a product of independent Gaussians in occupation number (Eq. 19) with μ_l = N I_l and θ_Ql = arg(a_l), and this state remains narrow and factorized under evolution.
    This is the core of Appendix I's correspondence proof; the simulations show deviations when the packet is squeezed, and no rigorous bound on packet spreading is given.
  • ad hoc to paper Multiple classical initial conditions can be packed as well-separated wave packets in the same Fock space with negligible interference and no packet growth, so the effective quantum time divides by (w/R)^(dim(l)).
    Assumed in Section IV to derive Eq. (28); no dynamical or numerical evidence is provided for this packing.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Second quantization of nonlinear Vlasov-Poisson system for quantum computation." pith.science (2026). https://pith.science/paper/UONCARIM

@misc{pith2026250601895,
  author       = {Pith},
  title        = {Pith review of: Second quantization of nonlinear Vlasov-Poisson system for quantum computation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UONCARIM}},
  note         = {Machine review of arXiv:2506.01895}
}
read the original abstract

The Vlasov-Poisson equations, fundamental in plasma physics and astrophysical applications, are rendered linear, finite-dimensional, and discrete by second quantization. Conditions for correspondence between the pre-quantized and quantized equations are derived, and numerical simulations demonstrating the quantized linear system can capture nonlinear dynamics are presented. Finally, encouraging scaling relations emphasizing the prospect of using quantum computers to efficiently integrate the second quantized Vlasov-Poisson equations as a model for the usual Vlasov-Poisson equations are derived.

Figures

Figures reproduced from arXiv: 2506.01895 by the authors.

Figure 1
Figure 1. Real and imaginary parts of Eq. (25) for δ = 0.0005, k0 = 4π, and with v0 = 1/(400π) = 7.96 × 10−5 (left) and v0 = 1/(40π) = 7.96 × 10−4 (right) [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Square amplitude of modes composing the initial conditions shown in Fig. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Evolution of I0 and ⟨Nˆ 0⟩ according to the three-mode pre-quantized and quantized Schrödinger–Poisson equations with initial conditions in the linear (a) and nonlinear (b) regimes. decades of magnitude difference between subsequent modes given the initial condition, Eq. (25), evident in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Evolution of I0 and ⟨Nˆ 0⟩ according to the five-mode pre-quantized and quantized Schrödinger–Poisson equations, respectively. The pre-quantized initial condition is symmetric with a−4,−2,0 = {−9.51 × 10−3 − 3.57 × 10−2 i, 3.21 × 10−4 − 6.43 × 10−2 i, 0.9945 − 7.97 × 1…
Figure 5
Figure 5. Figure 5: Evolution of I0, I2, I4, ⟨Nˆ 0⟩, ⟨Nˆ 2⟩, and ⟨Nˆ 4⟩ according to the five-mode pre-quantized and quantized Schrödinger–Poisson equations, respectively. The pre-quantized initial condition is symmetric with a−4,−2,0 = {0.36 + 0.36i, 0.29 + 0.29i, −0.29 + 0.29i}. The qua…

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum Inspiration, Classical Advantage: Dequantized particle algorithm for the nonlinear Vlasov-Poisson system

    physics.plasm-ph 2025-07 conditional novelty 4.0 of 10

    By dequantizing a truncated second-quantized Coulomb Hamiltonian, the authors obtain a structure-preserving spectral discretization of Schrödinger-Poisson that approximates Vlasov-Poisson and reproduces the two-stream...

Reference graph

Works this paper leans on

30 extracted references · 29 canonical work pages · cited by 1 Pith paper

  1. [24]

    Hong Qin and Michael Q. May. Dequantization algorithms for nonlinear vlasov–poisson sys- tems. In preparation, 2025

    work page 2025

  2. [1]

    Loureiro

    Abtin Ameri, Erika Ye, Paola Cappellaro, Hari Krovi, and Nuno F. Loureiro. Quantum algorithm for the linear vlasov equation with collisions.Phys. Rev. A, 107:062412, 2023

    work page 2023

  3. [2]

    Bertrand, Nguyen van Tuan, M

    P. Bertrand, Nguyen van Tuan, M. Gros, B. Izrar, M. Feix, and J. Gutierrez. Classical vlasov plasma description through quantum numerical methods.J. Plasma Phys., 23(3):401, 1980

    work page 1980

  4. [3]

    Random compiler for fast hamiltonian simulation.Phys

    Earl Campbell. Random compiler for fast hamiltonian simulation.Phys. Rev. Lett., 123:070503, 2019

    work page 2019

  5. [4]

    From vlasov-poisson to schrödinger-poisson: Dark matter simulation with a quantum variational time evolution algorithm.Phys

    Luca Cappelli, Francesco Tacchino, Giuseppe Murante, Stefano Borgani, and Ivano Taver- nelli. From vlasov-poisson to schrödinger-poisson: Dark matter simulation with a quantum variational time evolution algorithm.Phys. Rev. Research, 6:013282, 2024

    work page 2024

  6. [5]

    Application de la théorie des équations intégrales linéaires aux systèmes d’équations différentielles non linéaires.Acta Math, 59:63, 1932

    Torsten Carleman. Application de la théorie des équations intégrales linéaires aux systèmes d’équations différentielles non linéaires.Acta Math, 59:63, 1932

    work page 1932

  7. [6]

    Alexander Engel, Graeme Smith, and Scott E. Parker. Quantum algorithm for the vlasov equation.Phys. Rev. A, 100:062315, 2019. 17

    work page 2019

  8. [7]

    Harrow, Avinatan Hassidim, and Seth Lloyd

    Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for linear systems of equations.Phys. Rev. Lett., 103:150502, 2009

    work page 2009

Show all 30 references
  1. [8]

    Hayato Higuchi, J. W. Pedersen, K. Toyoizumi, K. Yoshikawa, C. Kiumi, and A. Yoshikawa. Quantum calculation for two-stream instability and advection test of vlasov-maxwell equa- tions: Numerical evaluation of hamiltonian simulation. arXiv, 2024

    2024

  2. [9]

    Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations.J

    Shi Jin, Nana Liu, and Yue Yu. Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations.J. Comp. Phys., 487:112149, 2023

    2023

  3. [10]

    Koopman–von neumann approach to quantum simulation of nonlinear classical dynamics.Phys

    Ilon Joseph. Koopman–von neumann approach to quantum simulation of nonlinear classical dynamics.Phys. Rev. Research, 2:043102, 2020

    2020

  4. [11]

    Hamiltonian systems and transformations in hilbert space.Proc

    B O Koopman. Hamiltonian systems and transformations in hilbert space.Proc. Nat. Acad. Sci., 17(5):315–318, 1931

    1931

  5. [12]

    Improved quantum algorithms for linear and nonlinear differential equations

    Hari Krovi. Improved quantum algorithms for linear and nonlinear differential equations. Quantum, 7:913, 2023

    2023

  6. [13]

    Krovi, Nuno F

    Jin-Peng Liu, Herman Øie Kolden, Hari K. Krovi, Nuno F. Loureiro, Konstantina Trivisa, and Andrew M. Childs. Efficient quantum algorithm for dissipative nonlinear differential equations.Proc. Natl. Acad. Sci. U.S.A., 118(35):e2026805118, 2021

    2021

  7. [14]

    Lloyd, G

    S. Lloyd, G. DePalma, C. Gokler, B Kiani, Z Liu, M Marvian, F Tennie, and T Palmer. Quantum algorithm for nonlinear differential equations. arXiv, 2020

    2020

  8. [15]

    Guang Hao Low and Isaac L. Chuang. Optimal hamiltonian simulation by quantum signal processing.Phys. Rev. Lett., 118:010501, 2017

    2017

  9. [16]

    May and Hong Qin

    Michael Q. May and Hong Qin. Quantum three-wave instability.Phys. Rev. A, 107:062204, 2023

    2023

  10. [17]

    May and Hong Qin

    Michael Q. May and Hong Qin. Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling.J. Phys. A: Math. Theor., 57(41):415304, 2024

    2024

  11. [18]

    May and Hong Qin

    Michael Q. May and Hong Qin. Nonlinear solution of classical three-wave interaction via finite dimensional quantum model.J. Plasma Phys., 90(3):805900302, 2024

    2024

  12. [19]

    Quantum algorithm for the vlasov simulation of the large-scale structure formation with mas- sive neutrinos.Phys

    Koichi Miyamoto, Soichiro Yamazaki, Fumio Uchida, Kotaro Fujisawa, and Naoki Yoshida. Quantum algorithm for the vlasov simulation of the large-scale structure formation with mas- sive neutrinos.Phys. Rev. Research, 6:013200, 2024. 18

    2024

  13. [20]

    Schrödinger-poisson–vlasov-poisson correspondence

    Philip Mocz and Lachlan Lancaster. Schrödinger-poisson–vlasov-poisson correspondence. Phys. Rev. D, 97:083519, 2018

    2018

  14. [21]

    Toward cosmological simulations of dark matter on quantum computers.ApJ, 910(1):29, 2021

    Philip Mocz and Aaron Szasz. Toward cosmological simulations of dark matter on quantum computers.ApJ, 910(1):29, 2021

    2021

  15. [22]

    Zuroperatorenmethodeinderklassischenmechanik.Annals of Mathematics, 33(3):587–642, 1932

    J.VonNeumann. Zuroperatorenmethodeinderklassischenmechanik.Annals of Mathematics, 33(3):587–642, 1932

    1932

  16. [23]

    Quantum signal processing for simulating cold plasma waves.Phys

    I Novikau, E A Startsev, and I Y Dodin. Quantum signal processing for simulating cold plasma waves.Phys. Rev. A, 105:062444, 2022

    2022

  17. [25]

    PhD thesis, Princeton University, 2018

    Yuan Shi.Plasma Physics in Strong Field Regimes. PhD thesis, Princeton University, 2018

    2018

  18. [26]

    Simulating non-native cubic interactions on noisy quantum machines.Phys

    Yuan Shi, A R Castelli, X Wu, I Joseph, V Geyko, F R Graziani, S B Libby, J B Parker, Y J Rosen, L A Martinez, and J L DuBois. Simulating non-native cubic interactions on noisy quantum machines.Phys. Rev. A, 103:062608, 2021

    2021

  19. [27]

    Yuan Shi, Hong Qin, and Nathaniel J. Fisch. Three-wave scattering in magnetized plasmas: From cold fluid to quantized lagrangian.Physical Review E, 96(2):023204, aug 2017

    2017

  20. [28]

    Yuan Shi, Hong Qin, and Nathaniel J. Fisch. Plasma physics in strong-field regimes: Theories and simulations.Physics of Plasmas, 28(4):042104, apr 2021

    2021

  21. [29]

    Hamiltonian simulation using the quantum singular-value transformation: Complexity analysis and application to the linearized vlasov-poisson equation.Phys

    Kiichiro Toyoizumi, Naoki Yamamoto, and Kazuo Hoshino. Hamiltonian simulation using the quantum singular-value transformation: Complexity analysis and application to the linearized vlasov-poisson equation.Phys. Rev. A, 109:012430, 2024

    2024

  22. [30]

    Quantum homotopy perturbation method for nonlinear dissipative ordinary differential equations.New J

    Cheng Xue, Yu-Chun Wu, and Guo-Ping Guo. Quantum homotopy perturbation method for nonlinear dissipative ordinary differential equations.New J. Phys., 23:123035, 2021. 19

    2021

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.