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arxiv: 2606.00581 · v1 · pith:QJF4TKSCnew · submitted 2026-05-30 · 🪐 quant-ph · physics.optics

Analog photonic simulator for large-scale transport

Mengyu Zhao , Xuezhi Zhu , Nikita Guseynov , Yewei Yuan , Na Wang , Meihong Wang , Yunyun Cao , Shi Jin
show 4 more authors
Nana Liu Changde Xie Kunchi Peng Xiaolong Su
This is my paper

Pith reviewed 2026-06-28 18:50 UTC · model grok-4.3

classification 🪐 quant-ph physics.optics
keywords advection equationcontinuous-variable quantum opticsphotonic simulatorcluster statessqueezed statestransport equationsanalog computinghomodyne detection
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The pith

Continuous-variable photonics encodes advection solutions into optical modes for direct analog evolution.

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

The paper establishes that constant-coefficient advection equations can be simulated on a photonic platform by mapping each of the d variables directly onto an optical mode. The partial differential equation's time evolution then reduces to programmable displacements in the quadrature phase space of those modes, implemented with squeezed-light resources and cluster states. This avoids the exponential growth in degrees of freedom that occurs when high-dimensional problems are discretized on digital grids. Experiments validate the approach on a 20,000-mode system, confirming that homodyne readout recovers first- and second-order moments of the transported field with relative errors of 0.8 percent and 0.92 percent. The method therefore supplies an analog route to large-scale transport problems that remain intractable for conventional computing.

Core claim

We demonstrate a large-scale analog photonic simulator for the constant-coefficient advection equation. The solution of a d-variable advection equation is encoded into d optical modes, so that the partial differential equation evolution maps directly to programmable phase-space displacements generated by optical quadrature momenta. Using a time-domain continuous-variable quantum photonic platform, we validate programmable control with 20,000 single-mode squeezed states and 20,000 two-mode squeezed states, and implement transport dynamics on a 20,000-mode cluster-state resource. Homodyne measurements then verify mode-resolved displacement control, which can provide first and second-order mome

What carries the argument

Encoding each variable of the d-dimensional advection equation into a separate optical mode so that PDE evolution maps to phase-space displacements controlled by quadrature momenta on a cluster-state resource.

If this is right

  • Programmable displacement control on 20,000 modes supplies first- and second-order moment data for the advection solution without spatial discretization.
  • Both single-mode and two-mode squeezed states can be used to prepare the required cluster-state resource for the simulation.
  • The same encoding converts constant-coefficient advection into linear optical operations that scale with the number of modes rather than with a grid size.
  • Homodyne detection directly extracts the observable moments that characterize the transported quantity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same phase-space displacement mechanism may apply to other linear transport or wave equations whose evolution remains affine in the field variables.
  • Hybrid quantum-classical pipelines could use the photonic output moments as initial conditions for nonlinear corrections computed on conventional hardware.
  • Error scaling with mode number could be tested by repeating the 20,000-mode experiment at successively larger cluster sizes while holding squeezing level fixed.

Load-bearing premise

The solution of a d-variable advection equation can be encoded into d optical modes such that its evolution reduces exactly to programmable phase-space displacements.

What would settle it

Homodyne readout on the 20,000-mode cluster state yielding relative error above 5 percent for first-order moment observables of the transported field.

Figures

Figures reproduced from arXiv: 2606.00581 by Changde Xie, Kunchi Peng, Meihong Wang, Mengyu Zhao, Nana Liu, Na Wang, Nikita Guseynov, Shi Jin, Xiaolong Su, Xuezhi Zhu, Yewei Yuan, Yunyun Cao.

Figure 1
Figure 1. Figure 1: Conceptual diagram and experimental procedure for simulating the advection equation on a continuous-variable quantum platform. (A) The classical advection equation is mapped to an initial quantum state under displacement operations that act on the amplitude quadrature of the quantum states. Each dimension corresponds to an independent quantum mode (qumode). (B) Experimental workflow: the experiment begins … view at source ↗
Figure 2
Figure 2. Figure 2: Experimental setup of the continuous variable photonic platform. (A) Main experimental setup. Two optical parametric oscillators (OPA A and OPA B) generate squeezed state sequences. The pump beam is modulated by cascaded acousto-optic modulators (AOMs), enabling dynamic control of the squeezing parameter. The generated squeezed states are injected into a reconfigurable optical network to generate the requi… view at source ↗
Figure 3
Figure 3. Figure 3: Measurements on time-bin-resolved single-mode and two-mode squeezed states. (A,B) Graphical representation of the single-mode (A) and two-mode (B) squeezed state sequences. (C,D) Noise power of the amplitude quadrature ˆx for the single-mode squeezed states (C) and ˆx1 + ˆx2 for the two-mode squeezed states (D) before and after displacement. All modes remain below the shot noise level. The red and blue sca… view at source ↗
Figure 4
Figure 4. Figure 4: Results of the analog photonic simulation with CV cluster state. (A) Graphical representation of the CV cluster state. (B) The quadrature output after displacement crosses 10,000 temporal modes. The green and orange lines correspond to the amplitude quadrature of the two rails. (C) Amplitude quadrature values measured by BHD A and B over five consecutive temporal modes. (D) Amplitude quadrature combination… view at source ↗
Figure 5
Figure 5. Figure 5: Experimental setup. The setup comprises three steps. First, OPA A and OPA B generate squeezed states, [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Calibration of pump power as a function of modulation voltage. The pump intensity is modulated by [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Timing sequences for dynamically modulated single-mode and two-mode squeezed states. (A) Timing [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Temporal-mode function gk(t) and quadrature trace. The red circles connected by a black line show the mode function gk(t). The gray shaded region marks the window Tw. The gray line with triangles shows the quadrature trace. Ideally, the variances of the nullifiers would be zero. However, due to finite squeeze and optical losses, the variances cannot be zero. Experimentally, we obtain ⟨Xˆ 2 k ⟩ and ⟨Pˆ2 k ⟩… view at source ↗
Figure 9
Figure 9. Figure 9: We represent the van Loock–Furusawa value as LF [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 9
Figure 9. Figure 9: Van Loock–Furusawa inseparability measurement for the time-domain CV cluster state. The seven panels [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Covariance matrix of the time-domain CV cluster state. (a) Graphical representations of the dual-rail [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Experimental implementation and modulation schemes for displacement. (a) Optical implementation. [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Impact of clock mismatch on the measured entanglement. Average nullifier noise [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Synchronization between displacement control and data acquisition. (a) Measured quadrature evolution [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Displacement performance for single-mode and two-mode squeezed states. In each panel, the lower right [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Displacement accuracy of first-order moments for the cluster state. (a) Correlation between the target [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Displacement accuracy of second-order moments for the cluster state. (a) Correlation between the target [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Displacement accuracy of cross-moments of the cluster state. (a) 2D heatmaps showing the [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: QSVT phase-modulation sequence built from the block-encoding [PITH_FULL_IMAGE:figures/full_fig_p029_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: The circuit architecture to implement the multi-mode bosonic circuit in Fig. 21 with qubits in the Fock [PITH_FULL_IMAGE:figures/full_fig_p036_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Relative error of the quadrature mean ⟨xˆ⟩ for the simulated final state across various Fock space cutoffs in the simplifed 2-mode case. The curves (red, blue, yellow and green) illustrate the error ϵx variation for displacement amplitudes α = 5, 10, 15, and 20, respectively. Markers denote the minimum cutoff photon number Np required for each mode to satisfy a target relative error threshold of 7%. As di… view at source ↗
Figure 21
Figure 21. Figure 21: Circuit used in the experiment set up from the main text, decomposed into four layers and represented as [PITH_FULL_IMAGE:figures/full_fig_p040_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Problem-specific reduction of the quantum scheme in Fig. 21. Panel (a) shows the full circuit. Panel (b) [PITH_FULL_IMAGE:figures/full_fig_p046_22.png] view at source ↗
read the original abstract

Transport equations describe how physical quantities -- such as mass, energy, momentum, concentration, probability, or fields -- are carried, propagated, or redistributed through space and time, forming a foundational class of partial differential equations across science and engineering. However, high-dimensional partial differential equations are difficult to represent on digital grids because the number of degrees of freedom grows exponentially with dimension. Continuous-variable quantum photonics on the other hand can represent and evolve these large-scale fields without first discretizing space into a discrete grid. We demonstrate a large-scale analog photonic simulator for the constant-coefficient advection equation, a transport equation that is a fundamental benchmark for scientific computing. The solution of a $d$-variable advection equation is encoded into $d$ optical modes, so that the partial differential equation evolution maps directly to programmable phase-space displacements generated by optical quadrature momenta. Using a time-domain continuous-variable quantum photonic platform, we validate programmable control with $20,000$ single-mode squeezed states and $20,000$ two-mode squeezed states, and implement transport dynamics on a $20,000$-mode cluster-state resource. Homodyne measurements then verifies mode-resolved displacement control, which can provide first and second-order moment information of the solution to the advection equation, with final achievable relative error as low as $0.8\%$ and $0.92\%$ for first and second-order moment observables respectively. Our results establish continuous-variable photonics as a suitable programmable analog platform for large-scale advection equations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript claims to demonstrate a large-scale analog photonic simulator for the constant-coefficient advection equation on a time-domain continuous-variable quantum photonic platform. The solution of a d-variable advection equation is encoded into d optical modes such that the PDE evolution maps directly to programmable phase-space displacements generated by optical quadrature momenta. Programmable control is validated using 20,000 single-mode squeezed states and 20,000 two-mode squeezed states to implement transport dynamics on a 20,000-mode cluster-state resource, with homodyne measurements verifying mode-resolved displacement control and recovering first- and second-order moment observables to relative errors as low as 0.8% and 0.92%, respectively.

Significance. If the experimental results hold, the work would establish continuous-variable photonics as a programmable analog platform capable of handling high-dimensional transport equations without exponential discretization costs. The explicit encoding of the advection equation into optical modes, the scale of the 20,000-mode resource, and the direct mapping to quadrature displacements represent a concrete advance for analog simulation of PDEs in science and engineering.

major comments (1)
  1. [Abstract] Abstract: The reported relative errors (0.8% for first-order moments and 0.92% for second-order moments) and the scale (20,000 states) are presented as concrete experimental outcomes, yet the abstract supplies no methods section, error budget, raw data, or description of calibration/post-selection procedures. This is load-bearing for the central claim because it prevents assessment of whether unstated assumptions affect the quoted precision.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and for highlighting the need for greater transparency in the abstract. We address the single major comment below and will revise the manuscript to improve accessibility of the reported results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The reported relative errors (0.8% for first-order moments and 0.92% for second-order moments) and the scale (20,000 states) are presented as concrete experimental outcomes, yet the abstract supplies no methods section, error budget, raw data, or description of calibration/post-selection procedures. This is load-bearing for the central claim because it prevents assessment of whether unstated assumptions affect the quoted precision.

    Authors: We agree that the abstract, while intended as a high-level summary, should better contextualize the quoted performance metrics. The full manuscript already contains dedicated sections on the experimental platform, homodyne detection calibration, post-selection criteria, and a complete error budget (including statistical and systematic contributions) that support the 0.8% and 0.92% relative errors. To address the referee's concern directly, we will revise the abstract to include a concise clause noting the use of calibrated homodyne readout on a time-domain cluster-state resource and that detailed error analysis appears in the main text. This revision will be kept within standard abstract length limits while improving standalone readability. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental demonstration is self-contained

full rationale

The paper reports an experimental implementation on a time-domain continuous-variable quantum photonic platform. It encodes the d-variable constant-coefficient advection equation solution into d optical modes via direct mapping to quadrature displacements, generates 20,000 single- and two-mode squeezed states, implements dynamics on a 20,000-mode cluster state, and measures first- and second-moment observables with reported relative errors of 0.8% and 0.92%. These are hardware-verified quantities, not outputs of any fitted parameter renamed as prediction, self-definitional loop, or self-citation chain. No equations in the provided text reduce the claimed results to their own inputs by construction, and the constant-coefficient restriction is stated explicitly. The derivation chain consists of physical encoding and measurement steps that remain independent of the target observables.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; no derivation details, parameter tables, or explicit assumptions beyond the stated mapping are provided.

axioms (1)
  • domain assumption The advection equation evolution maps directly to programmable phase-space displacements generated by optical quadrature momenta.
    Core encoding step stated in the abstract.

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discussion (0)

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Reference graph

Works this paper leans on

228 extracted references · 79 canonical work pages · 10 internal anchors

  1. [1]

    Feynman and computation , pages=

    Simulating physics with computers , author=. Feynman and computation , pages=. 2018 , publisher=

    2018

  2. [2]

    Gaussian quantum information , author =. Rev. Mod. Phys. , volume =. 2012 , month =. doi:10.1103/RevModPhys.84.621 , url =

    work page doi:10.1103/revmodphys.84.621 2012

  3. [3]

    Gate-Based Quantum Simulation of Gaussian Bosonic Circuits on Exponentially Many Modes , author =. Phys. Rev. Lett. , volume =. 2025 , month =. doi:10.1103/PhysRevLett.134.070604 , url =

    work page doi:10.1103/physrevlett.134.070604 2025

  4. [4]

    Quantum algorithms for solving a drift-diffusion equation: A complexity analysis , author =. Phys. Rev. A , volume =. 2025 , month =. doi:10.1103/1fw9-h14w , url =

    work page doi:10.1103/1fw9-h14w 2025

  5. [5]

    , title =

    LeVeque, Randall J. , title =. 2007 , doi =

    2007

  6. [6]

    and Barends, Rami and Biswas, Rupak and Boixo, Sergio and Brandao, Fernando G

    Arute, Frank and Arya, Kunal and Babbush, Ryan and Bacon, Dave and Bardin, Joseph C. and Barends, Rami and Biswas, Rupak and Boixo, Sergio and Brandao, Fernando G. S. L. and Buell, David A. and Burkett, Brian and Chen, Yu and Chen, Zijun and Chiaro, Ben and Collins, Roberto and Courtney, William and Dunsworth, Andrew and Farhi, Edward and Foxen, Brooks an...

    2019

  7. [7]

    Quantum algorithm for the advection-diffusion equation by direct block encoding of the time-marching operator , volume=

    Over, Paul and Bengoechea, Sergio and Brearley, Peter and Laizet, Sylvain and Rung, Thomas , year=. Quantum algorithm for the advection-diffusion equation by direct block encoding of the time-marching operator , volume=. Physical Review A , publisher=. doi:10.1103/d8hb-fv93 , number=

    work page doi:10.1103/d8hb-fv93

  8. [8]

    2024 , eprint=

    Optimal high-precision shadow estimation , author=. 2024 , eprint=

    2024

  9. [9]

    2025 , eprint=

    Hamiltonian Simulation for Advection-Diffusion Equation with arbitrary transport field , author=. 2025 , eprint=

    2025

  10. [10]

    Error Correcting Codes in Quantum Theory , author =. Phys. Rev. Lett. , volume =. 1996 , month =. doi:10.1103/PhysRevLett.77.793 , url =

    work page doi:10.1103/physrevlett.77.793 1996

  11. [11]

    and Bluvstein, Dolev and Kalinowski, Marcin and Ebadi, Sepehr and Manovitz, Tom and Zhou, Hengyun and Li, Sophie H

    Evered, Simon J. and Bluvstein, Dolev and Kalinowski, Marcin and Ebadi, Sepehr and Manovitz, Tom and Zhou, Hengyun and Li, Sophie H. and et al. , title =. Nature , volume =. 2023 , doi =

    2023

  12. [12]

    Evered, Alexandra A

    Bluvstein, Dolev and Evered, Simon J. and Geim, Alexandra A. and others , title =. Nature , year =. doi:10.1038/s41586-023-06927-3 , url =

    work page doi:10.1038/s41586-023-06927-3

  13. [13]

    A tweezer array with 6100 highly coherent atomic qubits

    A tweezer array with 6100 highly coherent atomic qubits , author =. 2025 , month =. doi:10.48550/arXiv.2403.12021 , url =. 2403.12021 , archivePrefix =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2403.12021 2025

  14. [14]

    Quantum circuits for partial differential equations via Schr

    Hu, Junpeng and Jin, Shi and Liu, Nana and Zhang, Lei , journal=. Quantum circuits for partial differential equations via Schr. 2024 , publisher=

    2024

  15. [15]

    Nature , publisher=

    Acharya, Rajeev and Abanin, Dmitry A. and Google Quantum AI and Collaborators , title =. Nature , year =. doi:10.1038/s41586-024-08449-y , url =

    work page doi:10.1038/s41586-024-08449-y

  16. [16]

    and Ji, Zhengfeng and Wu, Xiaodi and Yu, Nengkun , journal=

    Haah, Jeongwan and Harrow, Aram W. and Ji, Zhengfeng and Wu, Xiaodi and Yu, Nengkun , journal=. Sample-Optimal Tomography of Quantum States , year=

  17. [17]

    Optimal Hamiltonian Simulation by Quantum Signal Processing , author =. Phys. Rev. Lett. , volume =. 2017 , month =. doi:10.1103/PhysRevLett.118.010501 , url =

    work page doi:10.1103/physrevlett.118.010501 2017

  18. [18]

    and Wiebe, Nathan , title =

    Childs, Andrew M. and Wiebe, Nathan , title =. Quantum Information & Computation , volume =. 2012 , eprint =

    2012

  19. [19]

    and Childs, Andrew M

    Berry, Dominic W. and Childs, Andrew M. and Kothari, Robin , booktitle=. Hamiltonian Simulation with Nearly Optimal Dependence on all Parameters , year=

  20. [20]

    Physical review letters , volume=

    Optimal Hamiltonian simulation by quantum signal processing , author=. Physical review letters , volume=. 2017 , publisher=

    2017

  21. [21]

    Hamiltonian Simulation Using Linear Combinations of Unitary Operations

    Hamiltonian simulation using linear combinations of unitary operations , author=. arXiv preprint arXiv:1202.5822 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  22. [22]

    Limitations on the simulation of non-sparse Hamiltonians

    Limitations on the simulation of non-sparse Hamiltonians , author=. arXiv preprint arXiv:0908.4398 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  23. [23]

    arXiv preprint arXiv:2308.00646 , year=

    Analog quantum simulation of partial differential equations , author=. arXiv preprint arXiv:2308.00646 , year=

    work page arXiv

  24. [24]

    Proceedings of the forty-sixth annual ACM symposium on Theory of computing , pages=

    Exponential improvement in precision for simulating sparse Hamiltonians , author=. Proceedings of the forty-sixth annual ACM symposium on Theory of computing , pages=

  25. [25]

    2015 IEEE 56th annual symposium on foundations of computer science , pages=

    Hamiltonian simulation with nearly optimal dependence on all parameters , author=. 2015 IEEE 56th annual symposium on foundations of computer science , pages=. 2015 , organization=

    2015

  26. [26]

    1968 , publisher=

    Handbook of mathematical functions with formulas, graphs, and mathematical tables , author=. 1968 , publisher=

    1968

  27. [27]

    Mathematical proceedings of the Cambridge philosophical society , volume=

    A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type , author=. Mathematical proceedings of the Cambridge philosophical society , volume=. 1947 , organization=

    1947

  28. [28]

    Communications on pure and applied mathematics , volume=

    On the solution of nonlinear hyperbolic differential equations by finite differences , author=. Communications on pure and applied mathematics , volume=. 1952 , publisher=

    1952

  29. [29]

    Proceedings of the national academy of sciences , volume=

    The theory of everything , author=. Proceedings of the national academy of sciences , volume=. 2000 , publisher=

    2000

  30. [30]

    Journal of Computational Physics , volume=

    Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations , author=. Journal of Computational Physics , volume=. 2023 , publisher=

    2023

  31. [31]

    classical algorithms for solving the heat equation , author=

    Quantum vs. classical algorithms for solving the heat equation , author=. Communications in Mathematical Physics , volume=. 2022 , publisher=

    2022

  32. [32]

    Physical Review A , volume=

    Quantum algorithm for simulating the wave equation , author=. Physical Review A , volume=. 2019 , publisher=

    2019

  33. [33]

    npj Quantum Information , volume=

    Finding flows of a Navier--Stokes fluid through quantum computing , author=. npj Quantum Information , volume=. 2020 , publisher=

    2020

  34. [34]

    Physical Review Research , volume=

    Efficient Hamiltonian simulation for solving option price dynamics , author=. Physical Review Research , volume=. 2023 , publisher=

    2023

  35. [35]

    2019 , school=

    Quantum singular value transformation & its algorithmic applications , author=. 2019 , school=

    2019

  36. [36]

    Quantum , volume=

    Option pricing using quantum computers , author=. Quantum , volume=. 2020 , publisher=

    2020

  37. [37]

    Physical review letters , volume=

    Quantum algorithm for linear systems of equations , author=. Physical review letters , volume=. 2009 , publisher=

    2009

  38. [38]

    45th Annual IEEE symposium on foundations of computer science , pages=

    Quantum speed-up of Markov chain based algorithms , author=. 45th Annual IEEE symposium on foundations of computer science , pages=. 2004 , organization=

    2004

  39. [39]

    Science , volume=

    Simulated quantum computation of molecular energies , author=. Science , volume=. 2005 , publisher=

    2005

  40. [40]

    The American Mathematical Monthly , volume=

    The story of the binomial theorem , author=. The American Mathematical Monthly , volume=. 1949 , publisher=

    1949

  41. [41]

    arXiv preprint arXiv:2107.10764 , year=

    Nonlinear transformation of complex amplitudes via quantum singular value transformation , author=. arXiv preprint arXiv:2107.10764 , year=

    work page arXiv

  42. [42]

    Rattew and Patrick Rebentrost.Non-Linear Transformations of Quantum Ampli- tudes: Exponential Improvement, Generalization, and Applications

    Non-Linear Transformations of Quantum Amplitudes: Exponential Improvement, Generalization, and Applications , author=. arXiv preprint arXiv:2309.09839 , year=

    work page arXiv

  43. [43]

    Physical Review A , volume=

    Minimal universal two-qubit controlled-NOT-based circuits , author=. Physical Review A , volume=. 2004 , publisher=

    2004

  44. [44]

    Physical Review A , volume=

    Quantum circuits with uniformly controlled one-qubit gates , author=. Physical Review A , volume=. 2005 , publisher=

    2005

  45. [45]

    A logarithmic-depth quantum carry-lookahead adder

    A logarithmic-depth quantum carry-lookahead adder , author=. arXiv preprint quant-ph/0406142 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  46. [46]

    Physical Review A , volume=

    Quantum-state preparation with universal gate decompositions , author=. Physical Review A , volume=. 2011 , publisher=

    2011

  47. [47]

    Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing , pages=

    Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics , author=. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing , pages=

  48. [48]

    American Journal of Mathematics , volume=

    A closed set of normal orthogonal functions , author=. American Journal of Mathematics , volume=. 1923 , publisher=

    1923

  49. [49]

    Physical review letters , volume=

    Quantum circuits for general multiqubit gates , author=. Physical review letters , volume=. 2004 , publisher=

    2004

  50. [50]

    arXiv preprint arXiv:2203.10236 , year=

    Explicit quantum circuits for block encodings of certain sparse matrices (2022) , author=. arXiv preprint arXiv:2203.10236 , year=

    work page arXiv 2022

  51. [51]

    2022 IEEE International Conference on Quantum Computing and Engineering (QCE) , pages=

    Fable: Fast approximate quantum circuits for block-encodings , author=. 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) , pages=. 2022 , organization=

    2022

  52. [52]

    Addition on a Quantum Computer

    Addition on a quantum computer , author=. arXiv preprint quant-ph/0008033 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  53. [53]

    arXiv preprint arXiv:2310.03011 , year=

    Quantum algorithms: A survey of applications and end-to-end complexities , author=. arXiv preprint arXiv:2310.03011 , year=

    work page arXiv

  54. [54]

    arXiv preprint arXiv:2312.02817 , year=

    Quantum simulation for time-dependent Hamiltonians--with applications to non-autonomous ordinary and partial differential equations , author=. arXiv preprint arXiv:2312.02817 , year=

    work page arXiv

  55. [55]

    Nature , volume=

    Evidence for the utility of quantum computing before fault tolerance , author=. Nature , volume=. 2023 , publisher=

    2023

  56. [56]

    IBM Research Blog (September 2020) , year=

    IBM’s roadmap for scaling quantum technology , author=. IBM Research Blog (September 2020) , year=

    2020

  57. [57]

    J Appl Phys , volume=

    The future of quantum computing with superconducting qubits , author=. J Appl Phys , volume=. 2022 , publisher=

    2022

  58. [58]

    Nature Reviews Physics , volume=

    Variational quantum algorithms , author=. Nature Reviews Physics , volume=. 2021 , publisher=

    2021

  59. [59]

    Nat Commun , volume=

    Efficient arbitrary simultaneously entangling gates on a trapped-ion quantum computer , author=. Nat Commun , volume=. 2020 , publisher=

    2020

  60. [60]

    Nature , volume=

    Demonstration of the trapped-ion quantum CCD computer architecture , author=. Nature , volume=. 2021 , publisher=

    2021

  61. [61]

    Surface codes: Towards practical large-scale quantum computation , author=. Phys. Rev. A , volume=. 2012 , publisher=

    2012

  62. [62]

    Quantum error correction for beginners , author=. Rep. Prog. Phys. , volume=. 2013 , publisher=

    2013

  63. [63]

    Preconditioned quantum linear system algorithm , author=. Phys. Rev. Lett. , volume=. 2013 , publisher=

    2013

  64. [64]

    SIAM Journal on Computing , volume=

    Quantum algorithm for systems of linear equations with exponentially improved dependence on precision , author=. SIAM Journal on Computing , volume=. 2017 , publisher=

    2017

  65. [65]

    A survey on HHL algorithm: From theory to application in quantum machine learning , author=. Phys. Lett. A , volume=. 2020 , publisher=

    2020

  66. [66]

    TPAMI , volume=

    Scale-space and edge detection using anisotropic diffusion , author=. TPAMI , volume=. 1990 , publisher=

    1990

  67. [67]

    1995 , publisher=

    The mathematics of financial derivatives: a student introduction , author=. 1995 , publisher=

    1995

  68. [68]

    New York , volume=

    Conduction of heat in solids: Oxford University Press , author=. New York , volume=

  69. [69]

    Hybrid classical-quantum approach to solve the heat equation using quantum annealers , author=. Phys. Rev. A , volume=. 2021 , publisher=

    2021

  70. [70]

    2020 , publisher=

    Forthcoming applications of quantum computing: peeking into the future , author=. 2020 , publisher=

    2020

  71. [71]

    ChemBioChem , volume=

    Quantum computing for molecular biology , author=. ChemBioChem , volume=. 2023 , publisher=

    2023

  72. [72]

    Nat Rev Phys , pages=

    Quantum computing for finance , author=. Nat Rev Phys , pages=. 2023 , publisher=

    2023

  73. [73]

    arXiv preprint arXiv:2304.02865 , year=

    Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra via schrodingerisation , author=. arXiv preprint arXiv:2304.02865 , year=

    work page arXiv

  74. [74]

    Quantum Algorithm for Linear Systems of Equations , author =. Phys. Rev. Lett. , volume =. 2009 , month =

    2009

  75. [75]

    Preskill, John , journal =. Quantum

  76. [76]

    arXiv preprint arXiv:2210.16668 , year=

    Advancing Algorithm to Scale and Accurately Solve Quantum Poisson Equation on Near-term Quantum Hardware , author=. arXiv preprint arXiv:2210.16668 , year=

    work page arXiv

  77. [77]

    Depth analysis of variational quantum algorithms for the heat equation , author=. Phys. Rev. A , volume=. 2023 , publisher=

    2023

  78. [78]

    New Journal of Physics , abstract =

    Hsin-Yuan Huang and Kishor Bharti and Patrick Rebentrost , title =. New Journal of Physics , abstract =. 2021 , month =. doi:10.1088/1367-2630/ac325f , url =

    work page doi:10.1088/1367-2630/ac325f 2021

  79. [79]

    Creating superpositions that correspond to efficiently integrable probability distributions

    Creating superpositions that correspond to efficiently integrable probability distributions , author=. arXiv preprint quant-ph/0208112 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  80. [80]

    arXiv preprint arXiv:2101.04023 , year=

    Simulating option price dynamics with exponential quantum speedup , author=. arXiv preprint arXiv:2101.04023 , year=

    work page arXiv

Showing first 80 references.