Pith. sign in

REVIEW 2 major objections 6 minor 88 references

Simulation of Lindbladian dynamics via adaptive variational quantum trajectory compression

T0 review · 2 major / 6 minor · reviewed 2026-07-13 · grok-4.5

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

Pith's one-line read A compact mixed-unitary channel plus variational compression lets NISQ devices simulate Pauli-dissipative Lindblad dynamics without ancillas and with substantially shallower circuits.

desk verdict Cleaner Pauli adjoint channel plus honest depth compression; solid methods paper inside a stated regime, not a foundational breakthrough. read the letter →

arxiv 2607.09051 v1 pith:44DVVS76 submitted 2026-07-10 quant-ph

Huan-Yu Liu , Cheng Xue , Yun-Jie Wang , Xi-Ning Zhuang , Chao Wang , Yu-Chun Wu , Zhao-Yun Chen , Guo-Ping Guo This is my paper
classification quant-ph
keywords LindbladdynamicsopenquantumsystemsNISQsimulationmixed-unitarychanneltrajectorysamplingvariationalcompressionPaulidissipationancilla-free
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

Simulating open quantum systems on near-term hardware is hard because dissipation is non-unitary and circuits quickly become too deep. This paper shows that when the jumps are Pauli operators, each short-time Lindblad step can be replaced by a mixed-unitary adjoint channel whose only non-trivial unitary is ordinary Hamiltonian evolution. The channel is sampled by classical Monte-Carlo trajectories that need no extra qubits. Because the no-jump probability is usually large, those trajectories contain long runs of the same Hamiltonian block; the authors train shallow, depth-adaptive parameterized circuits to replace those runs, cutting gate count while leaving the sampling structure intact. Numerical tests on a dissipative XY chain recover the correct domain-wall melting and cut single- and two-qubit gates by roughly forty percent. The result is a concrete, ancilla-free route to open-system simulation on the processors that exist today.

What carries the argument

The mixed-unitary adjoint channel together with adaptive variational trajectory compression: a depth-adaptive PQC is trained (optionally on finite basis batches, without ancillas) to replace consecutive no-jump Hamiltonian blocks inside the sampled trajectories.

What would settle it

On the same dissipative XY instance, replace the trained PQCs by the original Trotter blocks (or force strong dissipation so that no-jump runs become short) and check whether the reported ~43 percent gate reduction and sub-0.05 imbalance error both disappear.

Watch

Extended reading notes

Core claim

For open systems with Pauli dissipations the short-time Lindblad map admits a compact mixed-unitary adjoint channel A(ρ)=∑ p_k U_k ρ U_k† (U_0 = e^{-i H Δt}, U_{k>0}=P_k) whose local error is O(δt²). The channel can be Monte-Carlo sampled without ancillas; inserting depth-adaptive PQCs trained to approximate the powers (U_0)^s then compresses the resulting trajectories, reducing average gate counts by about 43 percent on the dissipative XY model while preserving the physical dynamics.

Load-bearing premise

The whole construction needs the jump operators to be Pauli strings and the no-jump probability to dominate, so that trajectories are mostly long products of one unitary that a shallow circuit can replace.

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

2 major / 6 minor

Summary. The manuscript proposes an ancilla-free NISQ algorithm for Lindbladian dynamics with Pauli jump operators. It first derives a mixed-unitary adjoint channel A(ρ)=∑_k p_k U_k ρ U_k† (Eqs. 5–7) that approximates one Lindblad step with local error O(δt²), with U_0 a rescaled Hamiltonian evolution and U_{k>0}=P_k, so that multi-step evolution can be Monte-Carlo sampled without auxiliary qubits. It then introduces adaptive variational trajectory compression: depth-adaptive Hamiltonian-variational PQCs are trained (with a basis-sampled, ancilla-free loss) to approximate consecutive no-jump blocks (U_0)^s and are inserted into sampled trajectories. Numerical tests on a dissipative XY domain-wall problem (n=10) show agreement with the exact master equation and deterministic Kraus sum, small replacement error, and roughly 43% average single- and two-qubit gate reduction for the direct library.

Significance. If the claims hold within the stated Pauli/weak-dissipation regime, the work gives a concrete, implementable route that jointly removes ancillas (via a compact mixed-unitary channel) and reduces trajectory depth (via variational compression of repeated U_0 segments). Strengths include an explicit O(δt²) channel derivation that eliminates the classical post-processing of the authors’ prior adjoint-channel construction, an ancilla-free training surrogate, controlled sampling diagnostics (Fig. 2, 100 repetitions), and a full-space Hilbert–Schmidt appendix that corroborates the B=32 batch results. The contribution is incremental relative to existing trajectory and VQC literature, but the combination is practically motivated for NISQ open-system simulation and is supported by reproducible-style numerics (gate counts, direct vs iterative libraries, error bars).

major comments (2)
  1. §I–II and abstract: the channel is repeatedly called “stable” relative to Ref. [62] because post-processing is removed, yet the manuscript never quantifies stability under finite sampling or hardware noise. A short comparison (e.g., imbalance variance or bias under depolarizing noise / finite M for the old post-processed channel vs Eqs. 6–7) is needed to substantiate that claim, or the wording should be softened to “post-processing-free.”
  2. §III–IV and Fig. 4: the reported ~43% gate reduction counts only the compressed simulation trajectories. Direct training of (U_0)^s still requires deep target circuits during optimization (acknowledged in §III), and training cost is not folded into the resource analysis. For the central “resource-efficient / depth-reduced” claim, please state how training overhead is amortized (one-shot vs many-query use) and under what s_max / iterative-vs-direct regime the net cost is favorable.
minor comments (6)
  1. §V: the suggestion to sample basis states only in the half-filling sector for the XY model is important for trainability; consider elevating a brief numerical check (or a sentence that B=32 already used unrestricted sampling) into the main text.
  2. Fig. 1(d) trajectory sketches use labels such as “¯3”, “¯4”; a one-line legend tying ¯s to U(θ_s) would help readers who skip the caption body.
  3. Eq. (5) and the definition of Δt=2δt/(2−Γδt): a short remark that Δt=δt+O(δt²) and that the global phase/rescaling is absorbed into the probabilities would make the O(δt²) bookkeeping easier to verify.
  4. Related-work placement: Refs. [60,61] on mixed-unitary / unitary-dissipation sampling are cited; a one-sentence contrast of Kraus-block structure (simple U_0 and P_k only) versus those works would clarify the compression premise.
  5. Appendix B layer-merging (Eq. B8): state explicitly that the merged circuit remains first-order Trotter-accurate so that depth comparisons with the HVA ansatz remain fair.
  6. Minor notation: Γ is introduced after Eq. (4) as ∑γ_k; defining it at first use would avoid a brief forward reference.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: adjoint channel is derived from the Lindblad generator, and numerics are validated against independent exact/Kraus benchmarks.

full rationale

The load-bearing construction is the mixed-unitary adjoint channel (Eqs. 3–7): starting from the standard first-order Kraus form of a Lindblad step with Pauli jumps, M_0 is rewritten as a rescaled unitary e^{-iH Δt} plus O(δt²), yielding probabilities p_k and unitaries U_k that are fixed by the Hamiltonian and rates, not fitted to the XY imbalance or any other target observable. Trajectory sampling is ordinary Monte Carlo of that channel. Variational compression trains PQCs to approximate (U_0)^s via Hilbert–Schmidt / basis-sampled fidelity; that is an approximation step, not a prediction forced by a fitted free constant. Validation compares sampled and compressed trajectories to the exact Lindblad solution and a deterministic Kraus sum (Figs. 2–4, App. C), which are independent of the variational loss. Self-citations ([62] prior adjoint channel; [78] transfer-learning init) supply background methods and motivation; the improved channel is re-derived in-place and is not justified by an imported uniqueness theorem. No step reduces a claimed prediction to its own inputs by construction. Scope limitations (Pauli jumps, weak dissipation so p_0 dominates) are stated explicitly and are not circularity.

Assumptions & free parameters 5 free parameters · 5 assumptions · 2 invented entities

The central claim rests on standard open-system and Monte-Carlo mathematics plus the domain restriction to Pauli jumps and the modeling choice that shallow Hamiltonian-variational ansätze can approximate powers of the Trotterized U_0. Simulation hyperparameters (δt, γ, s_max, B, M) control numerics but are not fitted to invent the channel. No new physical entity is postulated.

free parameters (5)
  • time step δt = 0.1
    Chosen as 0.1 for T=10 numerics; sets both channel accuracy O(δt²) and the rescaled Δt. Not fitted to data but load-bearing for reported accuracy.
  • maximum compression length s_max = 10–20
    Hand-chosen (tested 10, 15, 20); trades training cost and accumulated iterative error against depth reduction.
  • basis batch size B = 32
    B=32 random computational-basis states per optimization step; surrogate for full Hilbert–Schmidt fidelity.
  • trajectory sample size M = 128
    M=128 used for main compressed runs; statistical error scales as 1/√M.
  • adaptive ansatz depth L = up to 9 at s=20
    Depth increased only until target fidelity; reaches L=9 at s=20 in reported runs—chosen by optimization success, not a physical constant.
assumptions (5)
  • domain assumption Open-system dynamics are described by the Lindblad master equation with time-independent H and Pauli jump operators.
    Stated in §II, Eqs. (1)–(2); restricts the algorithm’s scope.
  • standard math The first-order Kraus map with M_0 ≈ (1−½Γδt) exp(−iH Δt) has local error O(δt²) and yields a valid mixed-unitary channel after normalization.
    Derived in Eqs. (3)–(7); standard expansion, not machine-checked.
  • standard math Monte Carlo sampling of trajectories with probabilities p_k converges to the channel expectation at rate O(1/√M).
    Invoked via the central limit theorem in §II, Eq. (10).
  • ad hoc to paper A shallow Hamiltonian variational ansatz can approximate (U_0)^s well enough that replacement error stays small relative to sampling error.
    Empirical premise of §III–IV; supported numerically for this model but not proved in general.
  • ad hoc to paper Finite basis-state fidelity F_B is a sufficient training surrogate for phase-insensitive unitary fidelity on the relevant subspace.
    §III and App. C; full-space HS training gives similar depths, but equivalence is not guaranteed for all models.
invented entities (2)
  • compact stable mixed-unitary adjoint channel A for Pauli Lindbladians independent evidence
    purpose: Approximate dissipative dynamics as a sampleable mixture of unitaries without classical post-processing or ancillas.
    Mathematical channel construction derived from Kraus operators; not a new physical particle or force. Independent evidence is the match to exact Lindblad numerics in Fig. 2.
  • adaptive variational quantum trajectory compression framework independent evidence
    purpose: Replace consecutive no-jump U_0 segments in sampled trajectories by depth-adaptive trained PQCs.
    Algorithmic framework, not a physical entity; evidence is numerical gate reduction and imbalance error in Figs. 3–4.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Simulation of Lindbladian dynamics via adaptive variational quantum trajectory compression." pith.science (2026). https://pith.science/paper/44DVVS76

@misc{pith2026260709051,
  author       = {Pith},
  title        = {Pith review of: Simulation of Lindbladian dynamics via adaptive variational quantum trajectory compression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/44DVVS76}},
  note         = {Machine review of arXiv:2607.09051}
}
abstract

Quantum simulation of open quantum systems in the noisy intermediate-scale quantum (NISQ) era is hindered by the non-unitary nature of dissipative dynamics and the limited quantum resources available on near-term quantum processors. In this work, we propose a resource-efficient algorithm for simulating Lindbladian dynamics on NISQ devices. For open quantum systems with Pauli dissipations, we first derive a compact and stable mixed-unitary adjoint channel that approximates the target dissipative dynamics and enables ancilla-free implementation through trajectory sampling. To further reduce the circuit depth required for implementing the sampled trajectories, we introduce an adaptive variational quantum trajectory compression framework. In this framework, a depth-adaptive parameterized quantum circuit is trained to approximate repeated Trotterized Hamiltonian simulation operators, which are then used to replace repeated unitary segments appearing in the sampled trajectories. Importantly, the training procedure can also be performed without auxiliary qubits. Numerical simulations of the dissipative quantum $XY$ model demonstrate the accuracy and resource efficiency of the proposed algorithm. Our results provide a practical route toward ancilla-free and depth-reduced simulation of open quantum systems on near-term quantum hardware.

Figures

Figures reproduced from arXiv: 2607.09051 by the authors.

Figure 1
Figure 1. (c). Then the basis-sampled fidelity becomes 𝐹B (𝑈(𝜽), (𝑈0) 𝑠 ) = 1 𝐵 ∑︁ 𝐵 𝑖=1 𝑃𝑥𝑖 . (15) The corresponding loss function is 𝐿B (𝜽) = 1 − 𝐹B (𝑈(𝜽), (𝑈0) 𝑠 ) . (16) This basis-sampled loss provides a hardware-friendly sur￾rogate for training the compressed Hamiltonian-evolution blocks. Besides the choice of the loss function, the construction of the target circuit for (𝑈0) 𝑠 is also important. Here we consider two tr… view at source ↗
Figure 3
Figure 3. (a), we first plot the signed error of the mean value over the above 100 independent sampling repetitions, which remains close to zero throughout the dynamics. We then show another independently sampled trajectory ensemble, which fluctuates around the mean curve with a maximum error of about 0.03. We also evaluate the same sampled trajectory ensemble after transforming each trajectory into a quantum circuit, where a… view at source ↗
Figure 4
Figure 4. FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Therefore, the optimized ansatz depth can be directly compared with the number of layers in the original uncom￾pressed circuit. Appendix C: Additional simulation results using the full-space objective In this section, we present the corresponding results ob￾tained with…
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

88 extracted references · 2 linked inside Pith

  1. [62]

    Liu, T.-P

    H.-Y. Liu, T.-P. Sun, Z.-Y. Chen, C. Xue, C. Wang, X.-N. Zhuang, J.-P. Liu, W. Yi, Y.-C. Wu, and G.-P. Guo, Variational quantum simulation of many-body dissipative dynamics on a superconducting quantum processor (2025), arXiv:2510.20118 [quant-ph]

    arXiv 2025

  2. [1]

    In iterative training, the target at step𝑠is constructed from the previously trained circuit as𝑈(𝜽 𝑠−1 )𝑈0. Direct training is therefore benchmarked against the exact coherent evolution over𝑠repetitions, while iterative training mimics a procedure in which longer coherent blocks are built progressively from shorter trained blocks. Figure 3(b) shows the se...

  3. [2]

    Figure 8 shows the full-space training and replacement results

    For iterative training, the teacher target is con- structed as𝑈(𝜽 𝑠−1 )𝑈0, as in the finite-batch calculation. Figure 8 shows the full-space training and replacement results. Panel (a) repeats the same error-source diagnostic used in the main text. The 100-run sampling mean remains close to the deterministic Kraus curve, whereas a single same- seed𝑀=128 t...

  4. [3]

    All replacement simulations use𝑀=128 trajectories

    (d) Signed replacement errors for the direct library and the iterative libraries with𝑠 max =10,15, and 20. All replacement simulations use𝑀=128 trajectories. The full-space optimization selects essentially the same compact PQC depths as the finite-batch optimization. As shown in Fig. 8(b), both direct and iterative training require only slowly increasing ...

  5. [4]

    The direct full-space training remains highly accurate throughout the tested range and preserves the coherent block𝑈 𝑠 0 well. The iterative training is optimized to match its teacher target at each step, but its fidelity to the exact power𝑈 𝑠 0 decreases gradually with𝑠, reflecting the accumulation of teacher errors. This behavior is consistent with the ...

  6. [5]

    McArdle, S

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Quantum computational chemistry, Rev. Mod. Phys. 92, 015003 (2020)

    2020

  7. [6]

    Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferov´a, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. D. Sawaya, S. Sim, L. Veis, and A. Aspuru-Guzik, Quantum chem- istry in the age of quantum computing, Chemical Reviews119, 10856 (2019)

    2019

  8. [7]

    Bauer, S

    B. Bauer, S. Bravyi, M. Motta, and G. K.-L. Chan, Quantum al- gorithms for quantum chemistry and quantum materials science, Chemical Reviews120, 12685 (2020)

    2020

Show all 88 references
  1. [8]

    Herman, C

    D. Herman, C. Googin, X. Liu, Y. Sun, A. Galda, I. Safro, M. Pistoia, and Y. Alexeev, Quantum computing for finance, Nature Reviews Physics5, 450 (2023)

    2023

  2. [9]

    D. J. Egger, C. Gambella, J. Marecek, S. McFaddin, M. Mevis- sen, R. Raymond, A. Simonetto, S. Woerner, and E. Yndurain, Quantum computing for finance: State-of-the-art and future prospects, IEEE Transactions on Quantum Engineering1, 1 12 (2020)

    2020

  3. [10]

    Liu, X.-N

    H.-Y. Liu, X.-N. Zhuang, C. Wang, Q.-S. Li, M.-H. Dou, Z.-Y. Chen, C. Xue, Y.-C. Wu, G.-P. Guo, and G.-C. Guo, Quantum computational insurance and actuarial science, Science China Information Sciences68, 202501 (2025)

    2025

  4. [11]

    Biamonte, P

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Nature549, 195 (2017)

    2017

  5. [12]

    Schuld and N

    M. Schuld and N. Killoran, Quantum machine learning in feature hilbert spaces, Phys. Rev. Lett.122, 040504 (2019)

    2019

  6. [13]

    Jerbi, C

    S. Jerbi, C. Gyurik, S. C. Marshall, R. Molteni, and V. Dunjko, Shadows of quantum machine learning, Nature Communica- tions15, 5676 (2024)

    2024

  7. [14]

    Jerbi, L

    S. Jerbi, L. J. Fiderer, H. Poulsen Nautrup, J. M. K¨ ubler, H. J. Briegel, and V. Dunjko, Quantum machine learning beyond ker- nel methods, Nature Communications14, 517 (2023)

    2023

  8. [15]

    A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pearson, M. Troyer, and P. Zoller, Practical quantum advantage in quan- tum simulation, Nature607, 667 (2022)

    2022

  9. [16]

    C. W. Bauer, Z. Davoudi, A. B. Balantekin, T. Bhattacharya, M. Carena, W. A. de Jong, P. Draper, A. El-Khadra, N. Gemelke, M. Hanada, D. Kharzeev, H. Lamm, Y.-Y. Li, J. Liu, M. Lukin, Y. Meurice, C. Monroe, B. Nachman, G. Pagano, J. Preskill, E. Rinaldi, A. Roggero, D. I. Sant...

    2023

  10. [17]

    I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys.86, 153 (2014)

    2014

  11. [18]

    Wu, W.-S

    Y. Wu, W.-S. Bao, S. Cao, F. Chen, M.-C. Chen, X. Chen, T.-H. Chung, H. Deng, Y. Du, D. Fan, M. Gong, C. Guo, C. Guo, S. Guo, L. Han, L. Hong, H.-L. Huang, Y.-H. Huo, L. Li, N. Li, S. Li, Y. Li, F. Liang, C. Lin, J. Lin, H. Qian, D. Qiao, H. Rong, H. Su, L. Sun, L. Wang, S. Wa...

    2021

  12. [19]

    Huang, D

    H.-L. Huang, D. Wu, D. Fan, and X. Zhu, Superconducting quantum computing: a review, Science China Information Sci- ences63, 180501 (2020)

    2020

  13. [20]

    Manovitz, Y

    T. Manovitz, Y. Shapira, L. Gazit, N. Akerman, and R. Ozeri, Trapped-ion quantum computer with robust entangling gates and quantum coherent feedback, PRX Quantum3, 010347 (2022)

    2022

  14. [21]

    Grzesiak, R

    N. Grzesiak, R. Bl¨ umel, K. Wright, K. M. Beck, N. C. Pisenti, M. Li, V. Chaplin, J. M. Amini, S. Debnath, J.-S. Chen, and Y. Nam, Efficient arbitrary simultaneously entangling gates on a trapped-ion quantum computer, Nature Communications11, 2963 (2020)

    2020

  15. [22]

    Ransford, M

    A. Ransford, M. S. Allman, J. Arkinstall, J. P. Campora, S. F. Cooper, R. D. Delaney, J. M. Dreiling, B. Estey, C. Figgatt, A. Hall, A. A. Husain, A. Isanaka, C. J. Kennedy, N. Kotib- haskar, I. S. Madjarov, K. Mayer, A. R. Milne, A. J. Park, A. P. Reed, R. Ancona, M. P. Ander...

    2026

  16. [23]

    Acharya, D

    R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Black- well, S. Boixo, G. Bortoli, A. Bourass...

    2025

  17. [24]

    T. He, W. Lin, R. Wang, Y. Li, J. Bei, J. Cai, S. Cao, D. Chen, K. Chen, X. Chen, Z. Chen, Z. Chen, Z. Chen, W. Chu, H. Deng, X. Ding, Z. Ding, B. Fan, D. Fan, Y. Fu, D. Gao, M. Gong, J. Gui, C. Guo, S. Guo, L. Han, L. Hong, Y. Hu, H.-L. Huang, Y.-H. Huo, C. Jiang, L. Jiang, T...

    2025

  18. [25]

    Huang, X.-Y

    H.-L. Huang, X.-Y. Xu, C. Guo, G. Tian, S.-J. Wei, X. Sun, W.-S. Bao, and G.-L. Long, Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation, Science China Physics, Mechanics & Astron...

    2023

  19. [26]

    Bharti, A

    K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin- Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.-C. Kwek, and A. Aspuru- Guzik, Noisy intermediate-scale quantum algorithms, Rev. Mod. Phys.94, 015004 (2022)

    2022

  20. [27]

    Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    2018

  21. [28]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, 13 K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Variational quantum algorithms, Nature Reviews Physics 3, 625 (2021)

    2021

  22. [29]

    Liu, Z.-Y

    H.-Y. Liu, Z.-Y. Chen, T.-P. Sun, C. Xue, Y.-C. Wu, and G.-P. Guo, Can variational quantum algorithms demonstrate quan- tum advantages? time really matters (2023), arXiv:2307.04089 [quant-ph]

    2023 arXiv

  23. [30]

    De Palma, M

    G. De Palma, M. Marvian, C. Rouz ´e, and D. S. Franc ¸a, Limi- tations of variational quantum algorithms: A quantum optimal transport approach, PRX Quantum4, 010309 (2023)

    2023

  24. [31]

    Bittel and M

    L. Bittel and M. Kliesch, Training variational quantum algo- rithms is np-hard, Phys. Rev. Lett.127, 120502 (2021)

    2021

  25. [32]

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature Communications9, 4812 (2018)

    2018

  26. [33]

    Akshay, H

    V. Akshay, H. Philathong, M. E. S. Morales, and J. D. Bia- monte, Reachability deficits in quantum approximate optimiza- tion, Phys. Rev. Lett.124, 090504 (2020)

    2020

  27. [34]

    Z. He, L. Li, S. Zheng, Y. Li, and H. Situ, Variational quantum compiling with double q-learning, New Journal of Physics23, 033002 (2021)

    2021

  28. [35]

    Mizuta, Y

    K. Mizuta, Y. O. Nakagawa, K. Mitarai, and K. Fujii, Local variational quantum compilation of large-scale hamiltonian dy- namics, PRX Quantum3, 040302 (2022)

    2022

  29. [36]

    X. Yuan, S. Endo, Q. Zhao, Y. Li, and S. C. Benjamin, Theory of variational quantum simulation, Quantum3, 191 (2019)

    2019

  30. [37]

    Y.-X. Yao, N. Gomes, F. Zhang, C.-Z. Wang, K.-M. Ho, T. Iadecola, and P. P. Orth, Adaptive variational quantum dy- namics simulations, PRX Quantum2, 030307 (2021)

    2021

  31. [38]

    C ˆırstoiu, Z

    C. C ˆırstoiu, Z. Holmes, J. Iosue, L. Cincio, P. J. Coles, and A. Sornborger, Variational fast forwarding for quantum simula- tion beyond the coherence time, npj Quantum Information6, 82 (2020)

    2020

  32. [39]

    Dborin, V

    J. Dborin, V. Wimalaweera, F. Barratt, E. Ostby, T. E. O’Brien, and A. G. Green, Simulating groundstate and dynamical quan- tum phase transitions on a superconducting quantum computer, Nature Communications13, 5977 (2022)

    2022

  33. [40]

    Rotter and J

    I. Rotter and J. P. Bird, A review of progress in the physics of open quantum systems: theory and experiment, Reports on Progress in Physics78, 114001 (2015)

    2015

  34. [41]

    de Vega and D

    I. de Vega and D. Alonso, Dynamics of non-markovian open quantum systems, Rev. Mod. Phys.89, 015001 (2017)

    2017

  35. [42]

    Christopoulos, P

    A. Christopoulos, P. Le Doussal, D. Bernard, and A. De Luca, Universal out-of-equilibrium dynamics of 1d critical quantum systems perturbed by noise coupled to energy, Phys. Rev. X13, 011043 (2023)

    2023

  36. [43]

    Purkayastha, A

    A. Purkayastha, A. Dhar, and M. Kulkarni, Out-of-equilibrium open quantum systems: A comparison of approximate quantum master equation approaches with exact results, Phys. Rev. A93, 062114 (2016)

    2016

  37. [44]

    Rakovszky, S

    T. Rakovszky, S. Gopalakrishnan, and C. von Keyserlingk, Defining stable phases of open quantum systems, Phys. Rev. X14, 041031 (2024)

    2024

  38. [45]

    C. Jung, M. M¨ uller, and I. Rotter, Phase transitions in open quantum systems, Phys. Rev. E60, 114 (1999)

    1999

  39. [46]

    Nakanishi and T

    Y. Nakanishi and T. Sasamoto,PTphase transition in open quantum systems with lindblad dynamics, Phys. Rev. A105, 022219 (2022)

    2022

  40. [47]

    L. H. Delgado-Granados, T. J. Krogmeier, L. M. Sager- Smith, I. Avdic, Z. Hu, M. Sajjan, M. Abbasi, S. E. Smart, P. Narang, S. Kais, A. W. Schlimgen, K. Head-Marsden, and D. A. Mazziotti, Quantum algorithms and applications for open quantum systems, Chemical Reviews125, 1823 (...

    2025 doi

  41. [48]

    Weimer, A

    H. Weimer, A. Kshetrimayum, and R. Or´ us, Simulation methods for open quantum many-body systems, Rev. Mod. Phys.93, 015008 (2021)

    2021

  42. [49]

    Cleve and C

    R. Cleve and C. Wang, Efficient quantum algorithms for simu- lating lindblad evolution (2019), arXiv:1612.09512 [quant-ph]

    2019 arXiv

  43. [50]

    H. Wang, S. Ashhab, and F. Nori, Quantum algorithm for sim- ulating the dynamics of an open quantum system, Phys. Rev. A 83, 062317 (2011)

    2011

  44. [51]

    Gaikwad, Arvind, and K

    A. Gaikwad, Arvind, and K. Dorai, Simulating open quantum dynamics on an nmr quantum processor using the sz.-nagy di- lation algorithm, Phys. Rev. A106, 022424 (2022)

    2022

  45. [52]

    Z. Ding, X. Li, and L. Lin, Simulating open quantum systems using hamiltonian simulations, PRX Quantum5, 020332 (2024)

    2024

  46. [53]

    J. Han, W. Cai, L. Hu, X. Mu, Y. Ma, Y. Xu, W. Wang, H. Wang, Y. P. Song, C.-L. Zou, and L. Sun, Experimental simulation of open quantum system dynamics via trotterization, Phys. Rev. Lett.127, 020504 (2021)

    2021

  47. [54]

    Zhang, X

    W. Zhang, X. Ouyang, X. Huang, X. Wang, H. Zhang, Y. Yu, X. Chang, Y. Liu, D.-L. Deng, and L.-M. Duan, Observation of non-hermitian topology with nonunitary dynamics of solid-state spins, Phys. Rev. Lett.127, 090501 (2021)

    2021

  48. [55]

    S. Jin, N. Liu, and Y. Yu, Quantum simulation of partial dif- ferential equations via schr¨odingerization, Phys. Rev. Lett.133, 230602 (2024)

    2024

  49. [56]

    R. Shen, T. Chen, B. Yang, and C. H. Lee, Observation of the non-hermitian skin effect and fermi skin on a digital quantum computer, Nature Communications16, 1340 (2025)

    2025

  50. [57]

    Bacon, A

    D. Bacon, A. M. Childs, I. L. Chuang, J. Kempe, D. W. Le- ung, and X. Zhou, Universal simulation of markovian quantum dynamics, Phys. Rev. A64, 062302 (2001)

    2001

  51. [58]

    J. D. Guimar ˜aes, J. Lim, M. I. Vasilevskiy, S. F. Huelga, and M. B. Plenio, Noise-assisted digital quantum simulation of open systems using partial probabilistic error cancellation, PRX Quantum4, 040329 (2023)

    2023

  52. [59]

    A. W. Schlimgen, K. Head-Marsden, L. M. Sager, P. Narang, and D. A. Mazziotti, Quantum simulation of open quantum systems using a unitary decomposition of operators, Phys. Rev. Lett.127, 270503 (2021)

    2021

  53. [60]

    An, J.-P

    D. An, J.-P. Liu, and L. Lin, Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state prepara- tion cost, Phys. Rev. Lett.131, 150603 (2023)

    2023

  54. [61]

    Wang, H.-Y

    C. Wang, H.-Y. Liu, C. Xue, X.-N. Zhuang, M. Dou, Z.-Y. Chen, and G.-P. Guo, Quantum simulation of non-hermitian special functions and dynamics via contour-based matrix decomposi- tion, Quantum Science and Technology11, 035027 (2026)

    2026

  55. [63]

    A. M. Childs and N. Wiebe, Hamiltonian simulation using linear combinations of unitary operations, Quantum Information and Computation 10.26421/qic12.11-12 (2012)

    2012 doi

  56. [64]

    Peetz, S

    J. Peetz, S. E. Smart, S. Tserkis, and P. Narang, Simulation of open quantum systems via low-depth convex unitary evolutions, Phys. Rev. Res.6, 023263 (2024)

    2024

  57. [65]

    Borras and M

    E. Borras and M. Marvian, Quantum algorithm to simulate lind- blad master equations, Phys. Rev. Res.7, 023076 (2025)

    2025

  58. [66]

    H.-Y. Liu, X. Lin, Z.-Y. Chen, C. Xue, T.-P. Sun, Q.-S. Li, X.-N. Zhuang, Y.-J. Wang, Y.-C. Wu, M. Gong, and G.-P. Guo, Simu- lation of open quantum systems on universal quantum comput- ers, Quantum9, 1765 (2025)

    2025

  59. [67]

    S. Endo, J. Sun, Y. Li, S. C. Benjamin, and X. Yuan, Variational quantum simulation of general processes, Phys. Rev. Lett.125, 14 010501 (2020)

    2020

  60. [68]

    Huang, H.-E

    J.-C. Huang, H.-E. Li, Y.-C. Wang, G.-Z. Zhang, J. Li, and H.-S. Hu, Towards robust variational quantum simulation of lindblad dynamics via stochastic magnus expansion, PRX Quantum6, 040312 (2025)

    2025

  61. [69]

    Lindblad, On the generators of quantum dynamical semi- groups, Communications in Mathematical Physics48, 119 (1976)

    G. Lindblad, On the generators of quantum dynamical semi- groups, Communications in Mathematical Physics48, 119 (1976)

    1976

  62. [70]

    Manzano, A short introduction to the lindblad master equa- tion, AIP Advances10, 025106 (2020)

    D. Manzano, A short introduction to the lindblad master equa- tion, AIP Advances10, 025106 (2020)

    2020

  63. [71]

    H.-B. Chen, C. Gneiting, P.-Y. Lo, Y.-N. Chen, and F. Nori, Simulating open quantum systems with hamiltonian ensembles and the nonclassicality of the dynamics, Phys. Rev. Lett.120, 030403 (2018)

    2018

  64. [72]

    Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Huggins, Y. Li, J. R. McClean, and T. E. O’Brien, Quantum error mitiga- tion, Rev. Mod. Phys.95, 045005 (2023)

    2023

  65. [73]

    van den Berg, Z

    E. van den Berg, Z. K. Minev, A. Kandala, and K. Temme, Prob- abilistic error cancellation with sparse pauli–lindblad models on noisy quantum processors, Nature Physics19, 1116 (2023)

    2023

  66. [74]

    T. E. O’Brienet al., Purification-based quantum error mitigation of pair-correlated electron simulations, Nature Physics19, 1787 (2023)

    2023

  67. [75]

    Y. Kim, C. J. Wood, T. J. Yoder, S. T. Merkel, J. M. Gambetta, K. Temme, and A. Kandala, Scalable error mitigation for noisy quantum circuits produces competitive expectation values, Na- ture Physics19, 752 (2023)

    2023

  68. [76]

    E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature549, 172 (2017)

    2017

  69. [77]

    A. P. Babu, T. Orell, V. Vadimov, W. Teixeira, M. M ¨ott¨onen, and M. Silveri, Quantum error correction under numerically ex- act open-quantum-system dynamics, Phys. Rev. Res.5, 043161 (2023)

    2023

  70. [78]

    V. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsioutsios, S. Ganjam, A. Miano, B. L. Brock, A. Z. Ding, L. Frunzio, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret, Real-time quantum error correction beyond break-even, Nature616, 50 (2023)

    2023

  71. [79]

    K. C. Miaoet al., Overcoming leakage in quantum error correc- tion, Nature Physics19, 1780 (2023)

    2023

  72. [80]

    Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. van den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme, and A. Kandala, Evidence for the utility of quantum computing be- fore fault tolerance, Nature618, 500 (2023)

    2023

  73. [81]

    F. Alam, J. L. Bosse, I. ˇCepait˙e, A. Chapman, L. Clinton, M. Crichigno, E. Crosson, T. Cubitt, C. Derby, O. Dowin- ton, P. K. Faehrmann, S. Flammia, B. Flynn, F. M. Gambetta, R. Garc´ıa-Patr´on, M. Hunter-Gordon, G. Jones, A. Khedkar, J. Klassen, M. Kreshchuk, E. H. McMullan...

    2025

  74. [82]

    Liu, T.-P

    H.-Y. Liu, T.-P. Sun, Y.-C. Wu, Y.-J. Han, and G.-P. Guo, Miti- gating barren plateaus with transfer-learning-inspired parameter initializations, New Journal of Physics25, 013039 (2023)

    2023

  75. [83]

    Wiersema, C

    R. Wiersema, C. Zhou, Y. de Sereville, J. F. Carrasquilla, Y. B. Kim, and H. Yuen, Exploring entanglement and optimization within the hamiltonian variational ansatz, PRX Quantum1, 020319 (2020)

    2020

  76. [84]

    Park and N

    C.-Y. Park and N. Killoran, Hamiltonian variational ansatz with- out barren plateaus, Quantum8, 1239 (2024)

    2024

  77. [85]

    J. Hu, D. Appelo, and Y. Cheng, Arbitrary high order low- rank completely positive and trace preserving (cptp) schemes for lindblad equations with time-dependent hamiltonian (2025), arXiv:2511.12012 [math.NA]

    2025

  78. [86]

    Appel ¨o and Y

    D. Appel ¨o and Y. Cheng, Kraus is king: High-order completely positive and trace preserving (cptp) low rank method for the lindblad master equation, Journal of Computational Physics534, 114036 (2025)

    2025

  79. [87]

    Steinbach, B

    J. Steinbach, B. M. Garraway, and P. L. Knight, High-order unraveling of master equations for dissipative evolution, Phys. Rev. A51, 3302 (1995)

    1995

  80. [88]

    V. V. Shende, I. L. Markov, and S. S. Bullock, Minimal universal two-qubit controlled-not-based circuits, Phys. Rev. A69, 062321 (2004)

    2004

Pith tools

Reviewed July 13, 2026 · model on record in the stance chip above.