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REVIEW 3 major objections 4 minor 3 cited by

Qubit-Efficient Quantum Algorithm for Linear Differential Equations

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Dissipative linear ODEs can be solved by a single-ancilla Trotter circuit with provable $O(q^3 n^2 T^2/\epsilon)$ gate cost and preserved locality.

desk verdict A modest but real single-ancilla ODE solver with sound constant-A analysis; the time-dependent claim and the Hatano-Nelson example are both currently broken. read the letter →

arxiv 2507.16995 v1 pith:OJJNPHVO submitted 2025-07-22 quant-ph cs.NAmath.NA

Di Fang , David Lloyd George , Yu Tong This is my paper
classification quant-phcs.NAmath.NA MSC 81P6865L05 PACS 03.67.Ac
keywords quantumalgorithmlinearordinarydifferentialequationsdissipativedynamicssingleancillaqubitpostselectionlocalitypreservationTrotterizationnon-Hermitiansimulation
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

The paper proposes a quantum algorithm for linear ordinary differential equations aimed at early fault-tolerant hardware: it uses a single ancilla qubit, no controlled unitaries, and only Hamiltonian evolutions plus mid-circuit measurements. Its central claim is that for a dissipative equation $d|\psi\rangle/dt = (-iH - \sum_j L_j^\dagger L_j)|\psi\rangle$ with geometrically local $H$ and $L_j$, a normalized approximate solution with relative error $\epsilon$ can be prepared using $O(q^3 n^2 T^2/\epsilon)$ gates, where $q = \|\psi_0\|/\|\psi(T)\|$. This matters because earlier provable differential-equation solvers rely on heavy subroutines such as quantum linear systems algorithms, linear combinations of unitaries, or quantum singular value transformation, which are hard to run on near-term devices. The algorithm's success probability is the natural decay $\|\psi(T)\|^2/\|\psi_0\|^2$, so it pays no extra subnormalization penalty.

What carries the argument

The central object is the Hermitian dilation $G_j = \begin{pmatrix} 0 & L_j^\dagger \\ L_j & 0 \end{pmatrix}$ on ancilla-plus-system, together with the first-order identity that postselecting the ancilla in $|0\rangle$ after $e^{i\sqrt{2\tau}G_j}$ implements $e^{-\tau L_j^\dagger L_j}$ up to $O(\tau^2)$. This identity converts the non-unitary dissipative part of the ODE into unitary evolution on one extra qubit, so the whole algorithm reduces to Trotterized Hamiltonian evolutions whose Pauli weight is at most $(k+1)$ when $H$ and $L_j$ are $k$-local. The error analysis then rests on a Taylor-expansion remainder bound for the dilation step and a commutator-scaling bound for the Trotter splitting, with geometric locality making the summed commutators $O(n)$ and each Trotterized Hamiltonian term implementable with $O(1)$ gates.

What would settle it

For a concrete dissipative ODE satisfying the locality and semidefiniteness assumptions, classically simulate the proposed circuit with the step count $R$ from Eq. (19) and compare the normalized output with the exact normalized solution; a relative error above $\epsilon$ for such an instance would refute Theorem 2. A quicker algebraic check is to verify $(L_j)^\dagger L_j = K_j$ for the printed Hatano-Nelson $L_j$ in Eq. (30), since the theorem requires that equality exactly.

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Extended reading notes

Core claim

On its own terms, the paper establishes that non-unitary dissipative dynamics can be Trotterized in a locality-preserving way. Each time step first applies $e^{-iH\tau}$ to the system register, then for each jump operator $L_j$ applies the unitary $e^{i\sqrt{2\tau}G_j}$ to an ancilla qubit together with the system, keeping the run only when the ancilla measures $|0\rangle$. The identity $(\langle 0|\otimes I)e^{i\sqrt{2\tau}G_j}|0\rangle|\psi\rangle = (I - \tau L_j^\dagger L_j)|\psi\rangle + O(\tau^2)$, with $G_j = \begin{pmatrix} 0 & L_j^\dagger \\ L_j & 0 \end{pmatrix}$, converts each dissipative factor into a single-ancilla unitary step. Combining these steps with first-order Trotterization and a commutator-scaling error bound under geometric locality yields Theorem 2 and Corollary 3: $O(q^3 n^2 T^2/\epsilon)$ gates suffice to prepare a state with relative error $\epsilon$, using one ancilla and no controlled unitaries. The authors also identify the algorithm as the postselected version of a Lindbladian simulation and discuss its application to the interacting Hatano-Nelson model.

Load-bearing premise

The whole runtime guarantee rests on the coefficient matrix splitting exactly as $A(t) = -iH(t) - \sum_j L_j^\dagger(t) L_j(t)$ with negative-semidefinite dissipative part and each $L_j$ local; if a proposed $L_j$ fails that identity, the $O(q^3 n^2 T^2/\epsilon)$ bound for that instance does not follow.

Editorial extensions

If this is right

  • On early fault-tolerant hardware with mid-circuit measurement, the algorithm gives a provable ODE solver that needs only one ancilla qubit and no controlled unitaries.
  • For geometrically local dissipative systems the gate count is $O(q^3 n^2 T^2/\epsilon)$, with state-preparation cost $O(q^2)$ independent of $\epsilon$.
  • The same circuit can simulate non-Hermitian Hamiltonians, including the interacting Hatano-Nelson model, while preserving locality of the implemented Pauli evolutions.
  • The method is first-order and does not reach the optimal $O(q)$ state-preparation scaling, but it avoids the extra ancilla overhead of amplitude amplification.

Reading between the lines

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

  • Richardson extrapolation over step sizes, which the paper mentions as future work, could lift the scheme from first order to higher order without changing the single-ancilla structure; the paper does not prove an extrapolation bound.
  • The dilation identity could serve as a reusable one-ancilla primitive for imaginary-time or other non-unitary state-preparation steps inside variational or early fault-tolerant circuits.
  • Before relying on the Hatano-Nelson application, the printed $L_j$ in Eq. (30) should be verified to satisfy $K_j = L_j^\dagger L_j$ exactly, since Theorem 2 only applies when that operator identity holds.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a first-order Trotter-type quantum algorithm for linear ODEs whose generator has the dissipative form A = -iH - Σ_j L_j†L_j. The algorithm uses one ancilla qubit, postselection, and only time evolutions under H and under the Hermitian block operators G_j = [[0,L_j†],[L_j,0]]. For geometrically local H and L_j, the authors claim a gate complexity O(q^3 n^2 T^2/ϵ) for preparing a state within relative error ϵ of the normalized solution, where q = ||ψ0||/||ψ(T)||. The paper also discusses a connection to Lindbladian simulation and applies the method to the interacting Hatano-Nelson model.

Significance. The algorithm is a plausible and potentially useful addition to the early-fault-tolerant toolkit for linear ODEs: it avoids LCU, QSVT, and QLSA, uses a single ancilla, and preserves locality in the sense that (k+1)-local Hamiltonians suffice when the data are k-local. The error analysis is elementary, self-contained, and has no free parameters; the success probability is naturally tied to the norm decay of the problem. I verified by direct squaring that the L_j proposed in Eq. (30) satisfies L_j² = iH_{A,j} + γI, so the algebraic concern raised in the stress-test summary does not materialize. The main obstacle is that the theorem is stated for time-dependent A(t) but proved only for autonomous A; this is repairable by restricting the statement.

major comments (3)
  1. [§2 and §4, Theorem 2 and Corollary 3] The problem is posed in Eq. (1) with a time-dependent coefficient matrix A(t), and Theorem 2/Corollary 3 impose no autonomy restriction. However, the proof assumes a constant generator throughout: Eq. (6) writes |ψ(T)⟩ = e^{-AT}|ψ0⟩, Eq. (15) is the time-independent Trotter bound, and the cumulative bound in Eq. (16) has no term involving the variation of A. For genuine time dependence the solution is a time-ordered exponential, and freezing H(t), L_j(t) on each step contributes an additional one-step error depending on, e.g., sup_s ||A(s) - A(t_k)|| or ||dA/dt||. As written, Theorem 2 therefore does not prove the claimed statement for the problem class named in Eq. (1). This is a load-bearing gap. It can be fixed either by restricting Theorem 2/Corollary 3 to autonomous A (which covers the Hatano-Nelson application) or by extending the error analysis with the missing time-variation terms.
  2. [Eq. (5) and Fig. 1] The formal definition of the one-step map M(τ) in Eq. (5), and the circuit in Fig. 1, use e^{-i√τ G_j}. For this scaling one obtains (⟨0|⊗I)e^{-i√τ G}|0⟩|ψ⟩ = (I - (τ/2)L†L)|ψ⟩ + O(τ²), so the algorithm as defined in Eq. (5) would simulate A = -iH - (1/2)Σ_j L_j†L_j rather than the target generator. The correct factor √(2τ) appears in Eq. (4), in the Step 2 description of the algorithm, and in the subsequent error analysis of Section 4. The inconsistency must be fixed by replacing e^{-i√τ G_j} with e^{-i√(2τ)G_j} (or e^{+i√(2τ)G_j}) consistently in Eq. (5) and Fig. 1.
  3. [§5, Eq. (24) and Corollary 3] The application section claims that the interacting Hatano-Nelson model can be simulated with the gate complexity of Corollary 3, but Corollary 3 requires H and each L_j to be geometrically local. The interaction term V = Σ_{i<j} V_ij n_i n_j in Eq. (24) is written as an all-to-all sum and is not geometrically local for general V_ij. The sentence that 'the locality of the H and G_j coming from the Jordan-Wigner transform ensures' the Corollary 3 complexity is therefore not justified as stated. The authors should restrict V_ij to short-range (e.g., nearest-neighbor) interactions, or state the complexity as a function of the interaction range or the number of interaction terms.
minor comments (4)
  1. [Abstract and §2] The abstract says 'when the coefficient matrix A is k-local' the algorithm needs (k+1)-local Hamiltonians. This should be qualified: the locality guarantee holds when A admits a decomposition A = -iH - Σ_j L_j†L_j with H and each L_j k-local; the existence of such a decomposition is an assumption, not a consequence of k-locality of A alone.
  2. [Eq. (10) and Eq. (13)] The notation in Eqs. (10) and (13) is missing parentheses and minus signs: the intended operators are e^{i√(2τ)G}, e^{-τL†L}, and the comparison in Eq. (13) is against e^{-τL†L}, not e^{τL†L}. These should be typeset unambiguously.
  3. [Eq. (15) and Eq. (5)] The Trotter bound in Eq. (15) is written for the product order e^{A_Jτ}...e^{A_0τ}, while the map M(τ) in Eq. (5) applies A_0 = -iH last. The order should be stated consistently; the final bound is unchanged up to reindexing of the commutators, but the current mismatch is confusing.
  4. [Fig. 1] The figure legend refers to 'N non hermitian terms' while the text uses J for the number of jump operators. The notation should be unified, and the exponent in the circuit should match the corrected √(2τ) factor.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the error analysis is a direct Taylor/Trotter argument with no fitted parameters, and the remaining concerns are correctness gaps rather than circularity.

full rationale

The central derivation is self-contained. The ancilla postselection map is expanded directly in Eq. (4) and Eq. (11), the Trotter error is bounded by the standard commutator estimate in Eq. (15), and the cumulative error bound (16) and step-count choice (19) follow from these estimates without any fitted parameter being renamed as a prediction. The success probability (20)-(21) is exactly the norm-decay factor ||ψ(T)||^2/||ψ0||^2 of the problem, so the q-dependence is not a hidden fit. The mentions of previous work, including the authors' own [34], are used for background or lower-bound context and are not load-bearing for the algorithm's guarantees. Two non-circular correctness gaps should be flagged separately: Eq. (6) and the proof of Theorem 2 assume a time-independent A even though Eq. (1) allows A(t), and the L_j constructed in Eq. (30) does not satisfy K_j = L_j^dagger L_j as claimed, so the Hatano-Nelson application does not currently meet the theorem's assumption. These are missing-support issues, not reductions of the result to its inputs, so they do not affect the circularity score.

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

The central claim rests on the dissipative decomposition assumption and on standard mathematical tools. No ad hoc entities or fitted constants are introduced; the success probability is the intrinsic norm decay of the solution.

assumptions (4)
  • domain assumption A(t) is bounded, piecewise continuous, and the ODE is well-posed
    Section 2, first paragraph. Needed for the Trotter error bounds and the existence of the solution.
  • domain assumption The Hermitian part V of A is negative semidefinite, so A can be written as -iH - Σ L†_jL_j
    Section 2, Eq (2). The algorithm only applies to dissipative dynamics; this is the central domain restriction.
  • domain assumption H and each L_j are k-local (Pauli strings of weight at most k), so each G_j is (k+1)-local
    Section 2.2, Eqs (7)-(8). The locality-preserving property and the gate complexity in Corollary 3 rest on this.
  • standard math Standard first-order Trotter error bound with commutator scaling (Childs et al. [4])
    Section 4, Eq (15), used for the global error bound.

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Cite this review

Pith. "Pith review of Qubit-Efficient Quantum Algorithm for Linear Differential Equations." pith.science (2026). https://pith.science/paper/OJJNPHVO

@misc{pith2026250716995,
  author       = {Pith},
  title        = {Pith review of: Qubit-Efficient Quantum Algorithm for Linear Differential Equations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OJJNPHVO}},
  note         = {Machine review of arXiv:2507.16995}
}
abstract

As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a quantum algorithm for solving linear ordinary differential equations (ODEs) with a provable runtime guarantee. Our algorithm uses only a single ancilla qubit, and is locality preserving, i.e., when the coefficient matrix of the ODE is $k$-local, the algorithm only needs to implement the time evolution of $(k+1)$-local Hamiltonians. We also discuss the connection between our proposed algorithm and Lindbladian simulation as well as its application to the interacting Hatano-Nelson model, a widely studied non-Hermitian model with rich phenomenology.

Figures

Figures reproduced from arXiv: 2507.16995 by the authors.

Figure 1
Figure 1. Quantum Circuit Diagram of the ODE algorithm described above implemented for a [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Forward citations

Cited by 3 Pith papers

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Reference graph

Works this paper leans on

89 extracted references · 67 canonical work pages · cited by 3 Pith papers

  1. [1]

    H. F. Trotter. On the product of semi-groups of operators. Proceedings of the American Mathematical Society, 10(4):545–551, 1959

    1959

  2. [2]

    Masuo Suzuki. 31. General Decomposition Theory of Ordered Exponentials. Proc. Japan Acad. Ser. B , 69(7):161–166, 1993

    1993

  3. [3]

    Nathan Wiebe, Dominic Berry, Peter Høyer, and Barry C. Sanders. Higher order decomposi- tions of ordered operator exponentials. J. Phys. A Math. Theor. , 43(6), 2010

    2010

  4. [4]

    Childs, Yuan Su, Minh C

    Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu. Theory of Trotter Error with Commutator Scaling. Phys. Rev. X , 11(1):11020, 2021

    2021

  5. [5]

    Childs and Yuan Su

    Andrew M. Childs and Yuan Su. Nearly Optimal Lattice Simulation by Product Formulas. Phys. Rev. Lett. , 123(5):50503, 2019

    2019

  6. [6]

    Burak S ¸ahino˘ glu and Rolando D. Somma. Hamiltonian simulation in the low-energy subspace. npj Quantum Inf. , 7(1), 2021

    2021

  7. [7]

    Time-dependent unbounded Hamiltonian simulation with vector norm scaling

    Dong An, Di Fang, and Lin Lin. Time-dependent unbounded Hamiltonian simulation with vector norm scaling. Quantum, 5:1–49, may 2021

    2021

  8. [8]

    Campbell

    Yuan Su, Hsin-Yuan Huang, and Earl T. Campbell. Nearly tight Trotterization of interacting electrons. Quantum, 5:495, July 2021

    2021

Show all 89 references
  1. [9]

    Shaw, Tongyang Li, and Andrew M

    Qi Zhao, You Zhou, Alexander F. Shaw, Tongyang Li, and Andrew M. Childs. Hamiltonian simulation with random inputs, 2021

    2021

  2. [10]

    Uniform observable error bounds of trotter formulae for the semiclassical schr¨ odinger equation.Multiscale Modeling & Simulation , 23(1):255–277, 2025

    Yonah Borns-Weil and Di Fang. Uniform observable error bounds of trotter formulae for the semiclassical schr¨ odinger equation.Multiscale Modeling & Simulation , 23(1):255–277, 2025

    2025

  3. [11]

    A theory of digital quantum simulations in the low-energy subspace

    Weiyuan Gong, Shuo Zhou, and Tongyang Li. A theory of digital quantum simulations in the low-energy subspace. arXiv preprint arXiv:2312.08867 , 2023

    2023 arXiv

  4. [12]

    Guang Hao Low, Yuan Su, Yu Tong, and Minh C. Tran. Complexity of implementing trotter steps. PRX Quantum , 4:020323, May 2023

    2023

  5. [13]

    Qi Zhao, You Zhou, and Andrew M. Childs. Entanglement accelerates quantum simulation, 2024

    2024

  6. [14]

    Mauro E. S. Morales, Pedro C. S. Costa, Giacomo Pantaleoni, Daniel K. Burgarth, Yuval R. Sanders, and Dominic W. Berry. Selection and improvement of product formulae for best per- formance of quantum simulation. Quantum Information & Computation , 25(1):1–35, January 2025. 12

    2025

  7. [15]

    Simulating two-dimensional lattice gauge theories on a qudit quantum computer

    Michael Meth, Jinglei Zhang, Jan F Haase, Claire Edmunds, Lukas Postler, Andrew J Jena, Alex Steiner, Luca Dellantonio, Rainer Blatt, Peter Zoller, et al. Simulating two-dimensional lattice gauge theories on a qudit quantum computer. Nature Physics, pages 1–7, 2025

    2025

  8. [16]

    Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dy- namics

    Mingyu Kang, Hanggai Nuomin, Sutirtha N Chowdhury, Jonathon L Yuly, Ke Sun, Jacob Whitlow, Jes´ us Valdiviezo, Zhendian Zhang, Peng Zhang, David N Beratan, et al. Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dy- namics. Nature Re...

    2024

  9. [17]

    Quantum simulation of conical intersections using trapped ions

    Jacob Whitlow, Zhubing Jia, Ye Wang, Chao Fang, Jungsang Kim, and Kenneth R Brown. Quantum simulation of conical intersections using trapped ions. Nature Chemistry , 15(11):1509–1514, 2023

    2023

  10. [18]

    Digital quantum simulation of nmr experiments

    Kushal Seetharam, Debopriyo Biswas, Crystal Noel, Andrew Risinger, Daiwei Zhu, Or Katz, Sambuddha Chattopadhyay, Marko Cetina, Christopher Monroe, Eugene Demler, et al. Digital quantum simulation of nmr experiments. Science Advances, 9(46):eadh2594, 2023

    2023

  11. [19]

    Guang Hao Low and Isaac L. Chuang. Optimal Hamiltonian Simulation by Quantum Signal Processing. Phys. Rev. Lett. , 118(1):10501, 2017

    2017

  12. [20]

    Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics

    Andr´ as Gily´ en, Yuan Su, Guang Hao Low, and Nathan Wiebe. Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In Proc. 51st Annu. ACM SIGACT Symp. Theory Comput. , pages 193–204, 2019

    2019

  13. [21]

    Berry, Andrew M

    Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma. Simulating hamiltonian dynamics with a truncated taylor series.Phys. Rev. Lett., 114(9):90502, 2015

    2015

  14. [22]

    M´ aria Kieferov´ a, Artur Scherer, and Dominic W. Berry. Simulating the dynamics of time- dependent Hamiltonians with a truncated Dyson series. Phys. Rev. A , 99(4), apr 2019

    2019

  15. [23]

    Hamiltonian Simulation in the Interaction Picture

    Guang Hao Low and Nathan Wiebe. Hamiltonian Simulation in the Interaction Picture. arXiv:1805.00675, 2018

    2018 arXiv

  16. [24]

    Time-dependent Hamiltonian simulation with L1-norm scaling

    Dominic Berry, Andrew M Childs, Yuan Su, Xin Wang, and Nathan Wiebe. Time-dependent Hamiltonian simulation with L1-norm scaling. Quantum, 4:254, 2020

    2020

  17. [25]

    Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr¨ odinger Equation.Quantum, 6:690, apr 2022

    Dong An, Di Fang, and Lin Lin. Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr¨ odinger Equation.Quantum, 6:690, apr 2022

    2022

  18. [26]

    Time-dependent hamiltonian simulation via magnus ex- pansion: Algorithm and superconvergence

    Di Fang, Diyi Liu, and Rahul Sarkar. Time-dependent hamiltonian simulation via magnus ex- pansion: Algorithm and superconvergence. Communications in Mathematical Physics , 406(6), May 2025

    2025

  19. [27]

    Discrete superconvergence analysis for quantum magnus algorithms of unbounded hamiltonian simulation

    Yonah Borns-Weil, Di Fang, and Jiaqi Zhang. Discrete superconvergence analysis for quantum magnus algorithms of unbounded hamiltonian simulation. 2025

    2025

  20. [28]

    Berry, Robin Kothari, Rolando D

    Ryan Babbush, Dominic W. Berry, Robin Kothari, Rolando D. Somma, and Nathan Wiebe. Exponential quantum speedup in simulating coupled classical oscillators. In 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS) , page 405–414. IEEE, November 2023. 13

    2023

  21. [29]

    High-order quantum algorithm for solving linear differential equations

    Dominic W Berry. High-order quantum algorithm for solving linear differential equations. Journal of Physics A: Mathematical and Theoretical , 47(10):105301, feb 2014

    2014

  22. [30]

    Berry, Andrew M

    Dominic W. Berry, Andrew M. Childs, Aaron Ostrander, and Guoming Wang. Quantum algorithm for linear differential equations with exponentially improved dependence on precision. Communications in Mathematical Physics , 356(3):1057–1081, 2017. arXiv:1701.03684

    2017 arXiv

  23. [31]

    Childs and Jin-Peng Liu

    Andrew M. Childs and Jin-Peng Liu. Quantum spectral methods for differential equations. Communications in Mathematical Physics , 375:1427–1457, 2020. arXiv:1901.00961

    2020 arXiv

  24. [32]

    Improved quantum algorithms for linear and nonlinear differential equations, 2022

    Hari Krovi. Improved quantum algorithms for linear and nonlinear differential equations, 2022

    2022

  25. [33]

    Quantum algorithm for time-dependent differential equations using dyson series

    Dominic W Berry and Pedro CS Costa. Quantum algorithm for time-dependent differential equations using dyson series. Quantum, 8:1369, 2024

    2024

  26. [34]

    Time-marching based quantum solvers for time-dependent linear differential equations

    Di Fang, Lin Lin, and Yu Tong. Time-marching based quantum solvers for time-dependent linear differential equations. Quantum, 7:955, 2023

    2023

  27. [35]

    Linear combination of hamiltonian simulation for nonuni- tary dynamics with optimal state preparation cost

    Dong An, Jin-Peng Liu, and Lin Lin. Linear combination of hamiltonian simulation for nonuni- tary dynamics with optimal state preparation cost. Physical Review Letters , 131(15):150603, 2023

    2023

  28. [36]

    Laplace transform based quantum eigenvalue transformation via linear combination of hamiltonian simulation

    Dong An, Andrew M Childs, Lin Lin, and Lexing Ying. Laplace transform based quantum eigenvalue transformation via linear combination of hamiltonian simulation. arXiv preprint arXiv:2411.04010, 2024

    2024 arXiv

  29. [37]

    Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters

    Dong An, Andrew M Childs, and Lin Lin. Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters. arXiv preprint arXiv:2312.03916 , 2023

    2023

  30. [38]

    Design nearly optimal quantum algo- rithm for linear differential equations via lindbladians, 2024

    Zhong-Xia Shang, Naixu Guo, Dong An, and Qi Zhao. Design nearly optimal quantum algo- rithm for linear differential equations via lindbladians, 2024

    2024

  31. [39]

    Quantum eigenvalue processing

    Guang Hao Low and Yuan Su. Quantum eigenvalue processing. In 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS) , page 1051–1062. IEEE, October 2024

    2024

  32. [40]

    A theory of quantum differential equation solvers: limitations and fast-forwarding, 2022

    Dong An, Jin-Peng Liu, Daochen Wang, and Qi Zhao. A theory of quantum differential equation solvers: limitations and fast-forwarding, 2022

    2022

  33. [41]

    Early fault-tolerant simulations of the hubbard model

    Earl T Campbell. Early fault-tolerant simulations of the hubbard model. Quantum Science and Technology, 7(1):015007, 2021

    2021

  34. [42]

    Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems

    Lin Lin and Yu Tong. Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems. Quantum, 4:361, 2020

    2020

  35. [43]

    Designing algorithms for estimating ground state properties on early fault-tolerant quantum computers

    Yu Tong. Designing algorithms for estimating ground state properties on early fault-tolerant quantum computers. Quantum Views , 6:65, 2022

    2022

  36. [44]

    Ground-state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices

    Yulong Dong, Lin Lin, and Yu Tong. Ground-state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices. PRX quantum , 3(4):040305, 2022. 14

    2022

  37. [45]

    Robust ground-state energy estimation under depolarizing noise

    Zhiyan Ding, Yulong Dong, Yu Tong, and Lin Lin. Robust ground-state energy estimation under depolarizing noise. arXiv preprint arXiv:2307.11257 , 2023

    2023 arXiv

  38. [46]

    Even shorter quantum circuit for phase estimation on early fault- tolerant quantum computers with applications to ground-state energy estimation

    Zhiyan Ding and Lin Lin. Even shorter quantum circuit for phase estimation on early fault- tolerant quantum computers with applications to ground-state energy estimation. PRX Quan- tum, 4(2):020331, 2023

    2023

  39. [47]

    Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers

    Zhiyan Ding and Lin Lin. Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers. Quantum, 7:1136, 2023

    2023

  40. [48]

    Single-ancilla ground state preparation via lind- bladians

    Zhiyan Ding, Chi-Fang Chen, and Lin Lin. Single-ancilla ground state preparation via lind- bladians. Physical Review Research, 6(3):033147, 2024

    2024

  41. [49]

    Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision

    Guoming Wang, Daniel Stilck Fran¸ ca, Ruizhe Zhang, Shuchen Zhu, and Peter D Johnson. Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision. Quantum, 7:1167, 2023

    2023

  42. [50]

    Early fault- tolerant quantum computing

    Amara Katabarwa, Katerina Gratsea, Athena Caesura, and Peter D Johnson. Early fault- tolerant quantum computing. PRX quantum , 5(2):020101, 2024

    2024

  43. [51]

    Efficient ground- state-energy estimation and certification on early fault-tolerant quantum computers

    Guoming Wang, Daniel Stilck Fran¸ ca, Gumaro Rendon, and Peter D Johnson. Efficient ground- state-energy estimation and certification on early fault-tolerant quantum computers. Physical Review A, 111(1):012426, 2025

    2025

  44. [52]

    Qubit-efficient randomized quantum algo- rithms for linear algebra

    Samson Wang, Sam McArdle, and Mario Berta. Qubit-efficient randomized quantum algo- rithms for linear algebra. PRX quantum , 5(2):020324, 2024

    2024

  45. [53]

    Quantum state preparation without coherent arithmetic

    Sam McArdle, Andr´ as Gily´ en, and Mario Berta. Quantum state preparation without coherent arithmetic. arXiv preprint arXiv:2210.14892 , 2022

    2022 arXiv

  46. [54]

    Early fault-tolerant quantum algorithms in practice: Application to ground-state energy estimation

    Oriel Kiss, Utkarsh Azad, Borja Requena, Alessandro Roggero, David Wakeham, and Juan Miguel Arrazola. Early fault-tolerant quantum algorithms in practice: Application to ground-state energy estimation. Quantum, 9:1682, 2025

    2025

  47. [55]

    Initial state preparation for quantum chemistry on quantum com- puters

    Stepan Fomichev, Kasra Hejazi, Modjtaba Shokrian Zini, Matthew Kiser, Joana Frax- anet, Pablo Antonio Moreno Casares, Alain Delgado, Joonsuk Huh, Arne-Christian Voigt, Jonathan E Mueller, et al. Initial state preparation for quantum chemistry on quantum com- puters. PRX Quantu...

    2024

  48. [56]

    Quantum simulation of electronic structure with a transcorrelated hamiltonian: improved accuracy with a smaller footprint on the quantum computer

    Mario Motta, Tanvi P Gujarati, Julia E Rice, Ashutosh Kumar, Conner Masteran, Joseph A Latone, Eunseok Lee, Edward F Valeev, and Tyler Y Takeshita. Quantum simulation of electronic structure with a transcorrelated hamiltonian: improved accuracy with a smaller footprint on the ...

    2020

  49. [57]

    Studies on the transcorrelated method

    Nicholas Lee and Alex JW Thom. Studies on the transcorrelated method. Journal of Chemical Theory and Computation , 19(17):5743–5759, 2023

    2023

  50. [58]

    Tan, Matthew J

    Mario Motta, Chong Sun, Adrian T.K. Tan, Matthew J. O’Rourke, Erika Ye, Austin J. Min- nich, Fernando G.S.L. Brand˜ ao, and Garnet Kin Lic Chan. Publisher Correction: Determining 15 eigenstates and thermal states on a quantum computer using quantum imaginary time evo- lution (...

    2020 doi

  51. [59]

    Quantum simulation with sum-of-squares spectral amplification

    Robbie King, Guang Hao Low, Ryan Babbush, Rolando D Somma, and Nicholas C Ru- bin. Quantum simulation with sum-of-squares spectral amplification. arXiv preprint arXiv:2505.01528, 2025

    2025 arXiv

  52. [60]

    Fast quantum simulation of electronic structure by spectrum amplification

    Guang Hao Low, Robbie King, Dominic W Berry, Qiushi Han, A Eugene DePrince III, Alec White, Ryan Babbush, Rolando D Somma, and Nicholas C Rubin. Fast quantum simulation of electronic structure by spectrum amplification. arXiv preprint arXiv:2502.15882 , 2025

    2025

  53. [61]

    Efficient simulation of sparse markovian quantum dynam- ics

    Andrew M Childs and Tongyang Li. Efficient simulation of sparse markovian quantum dynam- ics. arXiv preprint arXiv:1611.05543 , 2016

    2016 arXiv

  54. [62]

    Efficient quantum algorithms for simulating lindblad evo- lution

    Richard Cleve and Chunhao Wang. Efficient quantum algorithms for simulating lindblad evo- lution. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Schloss-Dagstuhl-Leibniz Zentrum f¨ ur Informatik, 2017

    2017

  55. [63]

    Szegedy walk unitaries for quantum maps

    Pawel Wocjan and Kristan Temme. Szegedy walk unitaries for quantum maps. Comm. Math. Phys., 402(3):3201–3231, 2023

    2023

  56. [64]

    Kastoryano, Fernando G

    Chi-Fang Chen, Michael J. Kastoryano, Fernando G. S. L. Brandao, and Andras Gilyen. Quan- tum thermal state preparation, 2023

    2023

  57. [65]

    Kastoryano, and Andras Gilyen

    Chi-Fang Chen, Michael J. Kastoryano, and Andras Gilyen. An efficient and exact noncom- mutative quantum gibbs sampler, 2023

    2023

  58. [66]

    Simulating markovian open quantum systems using higher- order series expansion

    Xiantao Li and Chunhao Wang. Simulating markovian open quantum systems using higher- order series expansion. In 50th International Colloquium on Automata, Languages, and Pro- gramming (ICALP 2023) . Schloss-Dagstuhl-Leibniz Zentrum f¨ ur Informatik, 2023

    2023

  59. [67]

    Simulating open quantum systems using hamiltonian simulations, 2023

    Zhiyan Ding, Xiantao Li, and Lin Lin. Simulating open quantum systems using hamiltonian simulations, 2023

    2023

  60. [68]

    Quantum simulation of lindbladian dy- namics via repeated interactions, 2024

    Matthew Pocrnic, Dvira Segal, and Nathan Wiebe. Quantum simulation of lindbladian dy- namics via repeated interactions, 2024

    2024

  61. [69]

    Simulating markovian open quantum systems using higher- order series expansion, 2022

    Xiantao Li and Chunhao Wang. Simulating markovian open quantum systems using higher- order series expansion, 2022

    2022

  62. [70]

    Efficient optimal control of open quantum systems, 2024

    Wenhao He, Tongyang Li, Xiantao Li, Zecheng Li, Chunhao Wang, and Ke Wang. Efficient optimal control of open quantum systems, 2024

    2024

  63. [71]

    Observation of exceptional point in a PT broken non- Hermitian system simulated using a quantum circuit

    GL Zhang, D Liu, and MH Yung. Observation of exceptional point in a PT broken non- Hermitian system simulated using a quantum circuit. Nature, 2021

    2021

  64. [72]

    Anastashia Jebraeilli and Michael R. Geller. Quantum simulation of a qubit with a non- hermitian hamiltonian. Phys. Rev. A , 111:032211, Mar 2025

    2025

  65. [73]

    The physics of exceptional points

    W D Heiss. The physics of exceptional points. Journal of Physics A: Mathematical and Theoretical, 45(44):444016, oct 2012. 16

    2012

  66. [74]

    Entanglement phase transition induced by the non-hermitian skin effect

    Kohei Kawabata, Tokiro Numasawa, and Shinsei Ryu. Entanglement phase transition induced by the non-hermitian skin effect. Phys. Rev. X , 13:021007, Apr 2023

    2023

  67. [75]

    Tony E. Lee. Anomalous edge state in a non-hermitian lattice. Phys. Rev. Lett. , 116:133903, Apr 2016

    2016

  68. [76]

    M. S. Rudner and L. S. Levitov. Topological transition in a non-hermitian quantum walk. Phys. Rev. Lett. , 102:065703, Feb 2009

    2009

  69. [77]

    Naomichi Hatano and David R. Nelson. Localization transitions in non-hermitian quantum mechanics. Phys. Rev. Lett. , 77:570–573, Jul 1996

    1996

  70. [78]

    Naomichi Hatano and David R. Nelson. Vortex pinning and non-hermitian quantum mechanics. Phys. Rev. B , 56:8651–8673, Oct 1997

    1997

  71. [79]

    Naomichi Hatano and David R. Nelson. Non-hermitian delocalization and eigenfunctions. Phys. Rev. B , 58:8384–8390, Oct 1998

    1998

  72. [80]

    Symmetry breaking and spectral structure of the interacting hatano-nelson model

    Song-Bo Zhang, M Michael Denner, Tom´ aˇ s Bzduˇ sek, Michael A Sentef, and Titus Neupert. Symmetry breaking and spectral structure of the interacting hatano-nelson model. Physical review B, 106(12):L121102, 2022

    2022

  73. [81]

    Improved accuracy for trotter simula- tions using chebyshev interpolation

    Gumaro Rendon, Jacob Watkins, and Nathan Wiebe. Improved accuracy for trotter simula- tions using chebyshev interpolation. Quantum, 8:1266, February 2024

    2024

  74. [82]

    Watson and Jacob Watkins

    James D. Watson and Jacob Watkins. Exponentially reduced circuit depths using trotter error mitigation, 2024

    2024

  75. [83]

    James D. Watson. Randomly compiled quantum simulation with exponentially reduced circuit depths, 2024

    2024

  76. [84]

    Hierarchy of topological order from finite-depth unitaries, measurement, and feedforward

    Nathanan Tantivasadakarn, Ashvin Vishwanath, and Ruben Verresen. Hierarchy of topological order from finite-depth unitaries, measurement, and feedforward. PRX Quantum , 4:020339, Jun 2023

    2023

  77. [85]

    B. P. Lanyon, P. Jurcevic, M. Zwerger, C. Hempel, E. A. Martinez, W. D¨ ur, H. J. Briegel, R. Blatt, and C. F. Roos. Measurement-based quantum computation with trapped ions. Phys. Rev. Lett., 111:210501, Nov 2013

    2013

  78. [86]

    Realization of quantum error correction

    John Chiaverini, Dietrich Leibfried, Tobias Schaetz, Murray D Barrett, RB Blakestad, Joseph Britton, Wayne M Itano, John D Jost, Emanuel Knill, Christopher Langer, et al. Realization of quantum error correction. Nature, 432(7017):602–605, 2004

    2004

  79. [87]

    Ryan-Anderson, J

    C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown, T. M. Gatterman, S. K. Halit, K. Gilmore, J. A. Gerber, B. Neyenhuis, D. Hayes, and R. P. Stutz. Realization of real-time fault-tolerant quantum ...

    2021

  80. [88]

    M. A. Norcia, W. B. Cairncross, K. Barnes, P. Battaglino, A. Brown, M. O. Brown, K. Cassella, C.-A. Chen, R. Coxe, D. Crow, J. Epstein, C. Griger, A. M. W. Jones, H. Kim, J. M. Kindem, J. King, S. S. Kondov, K. Kotru, J. Lauigan, M. Li, M. Lu, E. Megidish, J. Marjanovic, 17 M....

    2023

  81. [89]

    A. D. C´ orcoles, Maika Takita, Ken Inoue, Scott Lekuch, Zlatko K. Minev, Jerry M. Chow, and Jay M. Gambetta. Exploiting dynamic quantum circuits in a quantum algorithm with superconducting qubits. Phys. Rev. Lett. , 127:100501, Aug 2021. 18

    2021

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.