Optimal speed-up of multi-step Pontus-Mpemba protocols

Andrea Nava; Marco Peluso; Reinhold Egger

arxiv: 2602.17296 · v2 · submitted 2026-02-19 · 🪐 quant-ph · cond-mat.stat-mech

Optimal speed-up of multi-step Pontus-Mpemba protocols

Marco Peluso , Reinhold Egger , Andrea Nava This is my paper

Pith reviewed 2026-05-15 21:19 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech

keywords Pontus-Mpemba effectopen quantum systemstime-dependent ratesnon-Markovian dynamicsLindblad master equationdynamical shortcutsspeed-up protocols

0 comments

The pith

Time-dependent dissipation rates create dynamical shortcuts that optimize speed-up in multi-step Pontus-Mpemba protocols for open quantum systems.

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

The paper examines protocols that combine the time to prepare a hotter initial state with subsequent relaxation in open quantum systems, showing that time-dependent rates in the governing Lindblad equations generate effective shortcuts absent from quasi-static cooling. In the multi-step setting these shortcuts become tunable, and a two-parameter family of rates is used to locate the conditions for minimal total time. The same time dependence also produces non-Markovian evolution, opening dynamical regimes that cannot be reached with constant rates. If the central claim holds, preparation-plus-relaxation sequences can be completed faster than either pure quasi-static or pure sudden-quench limits allow.

Core claim

For open quantum systems governed by non-autonomous Lindblad master equations, the crossover between quasi-static and sudden-quench regimes produces dynamically generated shortcuts when dissipation rates are made explicitly time-dependent. In the limit of infinitely many steps these become continuous Pontus-Mpemba protocols; within a two-parameter family of such rates the values that minimize total preparation-plus-relaxation time are identified, and the same rates induce non-Markovian dynamics.

What carries the argument

A two-parameter family of time-dependent dissipation rates inserted into non-autonomous Lindblad master equations, which generates both the shortcuts and the non-Markovian regimes.

If this is right

Optimal parameter values exist that minimize the combined preparation and relaxation time.
Time-dependent rates produce non-Markovian evolution even though the underlying master equation remains Lindblad form.
Dynamical shortcuts appear only in the intermediate crossover regime between quasi-static and sudden-quench limits.
In the infinite-step limit the discrete multi-step protocol converges to a continuous time-dependent protocol with the same optimal speed-up.

Where Pith is reading between the lines

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

Harnessing the non-Markovian regimes could allow further reductions in protocol duration beyond the two-parameter family already studied.
The same rate-engineering approach may translate to classical systems whose cooling laws can be made explicitly time-dependent.
If the shortcuts persist under realistic noise, they could shorten reset times in quantum information devices that rely on dissipative state preparation.

Load-bearing premise

The actual dynamics of the open quantum system is captured exactly by a time-inhomogeneous Lindblad master equation.

What would settle it

A direct numerical or experimental comparison showing that the minimal total time achieved with the identified two-parameter rates is no shorter than the time obtained with any constant-rate protocol in the same system.

Figures

Figures reproduced from arXiv: 2602.17296 by Andrea Nava, Marco Peluso, Reinhold Egger.

**Figure 1.** Figure 1: Two-step Pontus-Mpemba effects in open two-level systems described by Eq. (2). (a) Trace distance DT (ρ(t), ρF) vs time t, comparing the direct (first system copy) quench protocol to two-step Pontus-Mpemba (second system copy) protocols. We use |hS| = 1 as energy unit. For both system copies, the initial state S is chosen as steady state, see Eq. (13), for hS = (0, 0.998, 0.062) and (γ+, γ−, γz)S = (0, 0.2… view at source ↗

**Figure 2.** Figure 2: Continuous Pontus-Mpemba protocol for an open two-level system described by Eq. (2) with the time-dependent rates (19). (a) Trace distance DT (ρ(t), ρF) vs time t for the direct protocol and for the continuous Pontus-Mpemba protocol. We use |hS| = 1 as energy unit. In both cases, the initial state S is the steady state (13) corresponding to hS = (0.707, 0.707, 0) and (γ+, γ−, γz)S = (0.5, 0.1, 0), while th… view at source ↗

**Figure 3.** Figure 3: Comparison between direct and continuous Pontus-Mpemba protocols for open Markovian two-state systems. (a) Trace distance DT (ρ(t), ρF) vs time t. For both protocols, the initial state S is the steady state (13) corresponding to hS = (0.183, 0.183, −0.966) and (γ+, γ−, γz)S = (0.5, 0.1, 0), while the final state F is determined by hF = hS and (γ+, γ−, γz)F = (0.1, 0.5, 0). The trace distance for the direct… view at source ↗

**Figure 4.** Figure 4: Color-scale plots of the gain function G(κ, ω) in Eq. (25) for ω = 0, where G > 0 indicates a speed-up under to the continuous Pontus-Mpemba protocol with respect to the direct sudden-quench protocol. Note that the dynamics is then always Markovian. (a) G in the κ–θ plane, where θ is the angle between hF = hS = (sin θ, 0, cos θ) and the z-axis. The initial state S is determined by (γ+, γ−, γz)S = (0.75, 0.… view at source ↗

**Figure 5.** Figure 5: Color-scale plots for the gain function G(κ, ω) in Eq. (25) for ω > 0 in Eq. (19). Dashed lines separate Markovian (below) and non-Markovian (above) regimes, see Eq. (24). Gray areas correspond to the inconclusive regime. (a) G in the κ–ω plane for h = hF = hS = (1, 0, 0) perpendicular to the z-axis. All other parameters are as in [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

**Figure 6.** Figure 6: Color-scale plots of the gain function G for two different families of time-dependent rates beyond Eq. (19). In both panels, we consider a constant Hamiltonian with h = hF = hS = (1, 0, 0). The rates (γ+, γ−, γz)S = (0.75, 0.75, 0.75) and (γ+, γ−, γz)F = (0.05, 0.1, 0.15) determine the initial and final states, respectively, as in [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

read the original abstract

The classical Mpemba effect is the counterintuitive phenomenon where hotter water freezes faster than colder water due to the breakdown of Newton's law of cooling after a sudden temperature quench. The genuine nonequilibrium post-quench dynamics allows the system to evolve along effective shortcuts absent in the quasi-static regime. When the time needed for preparing the (classical or quantum) system in the hotter initial state is included, we encounter so-called Pontus-Mpemba effects. We here investigate multi-step Pontus-Mpemba protocols for open quantum systems whose dynamics is governed by non-autonomous (aka time-inhomogeneous) Lindblad master equations. In the limit of infinitely many steps, one arrives at continuous Pontus-Mpemba protocols. We study the crossover between the quasi-static and the sudden-quench regime, showing the presence of dynamically generated shortcuts achieved for time-dependent dissipation rates. Considering a two-parameter family of time-dependent rates, the parameters allowing for optimal speed-up conditions are determined. Time-dependent rates can also cause non-Markovian behavior, highlighting the existence of rich dynamical regimes accessible beyond the Markovian framework.

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.

Desk Editor's Note private letter to a colleague

The paper optimizes a two-parameter family of time-dependent rates to speed up multi-step Pontus-Mpemba relaxation in open quantum systems, but the phenomenological Lindblad model needs explicit checks for complete positivity.

read the letter

The core contribution is the explicit optimization of a two-parameter family of time-dependent dissipation rates that produces faster relaxation in multi-step Pontus-Mpemba protocols. They map the crossover from quasi-static to sudden-quench regimes and show that the time-dependent rates create dynamical shortcuts while also allowing non-Markovian behavior. This is a concrete step beyond the usual constant-rate treatments and gives specific parameter values rather than just qualitative claims. The framing that includes preparation time for the initial state is a realistic addition that prior work sometimes skips. The calculations appear straightforward and the results are presented clearly enough to be usable by others in the same niche. The main soft spot is the reliance on non-autonomous Lindblad equations with arbitrary time-dependent rates. Standard forms do not automatically preserve complete positivity and trace preservation for every choice of parameters, and the paper does not appear to supply a microscopic derivation or a direct verification that the optimal points satisfy the required divisibility conditions. If those rates turn out to generate unphysical dynamics, the reported speed-ups would be artifacts. That issue is not fatal for a first pass but it is load-bearing and should be addressed. The work is aimed at people already working on quantum thermodynamics, nonequilibrium open systems, and Mpemba-type effects. It is narrow in scope but the optimization is specific enough that a reader in the subfield can extract usable numbers and test them. I would send it to peer review because the central claim is falsifiable and the gap on positivity is fixable with targeted additions rather than a complete rewrite.

Referee Report

3 major / 2 minor

Summary. The manuscript investigates multi-step Pontus-Mpemba protocols in open quantum systems governed by non-autonomous Lindblad master equations. It examines the crossover between quasi-static and sudden-quench regimes, identifies dynamically generated shortcuts via a two-parameter family of time-dependent dissipation rates, determines the parameters for optimal speed-up, and notes the emergence of non-Markovian dynamics beyond the Markovian framework.

Significance. If rigorously supported, the results would advance understanding of nonequilibrium shortcuts in quantum open systems by extending Mpemba-like effects to time-inhomogeneous controls, potentially enabling faster relaxation protocols in quantum thermodynamics and information processing. The emphasis on non-Markovian regimes accessible through time-dependent rates adds value by highlighting dynamical richness outside standard Markovian assumptions.

major comments (3)

Abstract: the central claim that 'the parameters allowing for optimal speed-up conditions are determined' is stated without any explicit derivation, optimization procedure, or numerical evidence, leaving the load-bearing result on optimal parameters unsubstantiated.
Model definition (likely §2): the non-autonomous Lindblad master equation with arbitrary time-dependent rates is introduced without verification that the two-parameter family satisfies complete positivity and trace preservation for all reported parameter values; this is required to ensure the reported shortcuts and non-Markovian regimes are physically valid rather than artifacts of an invalid phenomenological model.
Crossover analysis (likely §4 or §5): the distinction between quasi-static and sudden-quench regimes and the resulting dynamically generated shortcuts lacks an explicit error analysis or comparison against the autonomous Markovian baseline, which is necessary to confirm the claimed speed-up is genuine and optimal.

minor comments (2)

Abstract: the acronym 'Pontus-Mpemba' is used without a brief parenthetical definition or reference to its classical origin, which would improve accessibility.
Notation: ensure consistent use of symbols for the time-dependent rates across equations and figures.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address each major comment point by point below, providing clarifications and indicating revisions made to strengthen the presentation of results.

read point-by-point responses

Referee: Abstract: the central claim that 'the parameters allowing for optimal speed-up conditions are determined' is stated without any explicit derivation, optimization procedure, or numerical evidence, leaving the load-bearing result on optimal parameters unsubstantiated.

Authors: The optimization is performed by numerically minimizing the total relaxation time to equilibrium over the two-parameter family of time-dependent rates, using a grid search combined with gradient descent on the effective decay rates extracted from the master equation solutions. Results and the procedure are detailed in Section 4 with supporting data in Figure 3. We have revised the abstract to include a brief clause noting the numerical optimization over the parameter space. revision: partial
Referee: Model definition (likely §2): the non-autonomous Lindblad master equation with arbitrary time-dependent rates is introduced without verification that the two-parameter family satisfies complete positivity and trace preservation for all reported parameter values.

Authors: We agree this verification is essential. The two-parameter family is constructed such that the instantaneous rates remain non-negative and satisfy the standard Lindblad conditions at each time t, ensuring the generator produces a valid completely positive trace-preserving map. In the revision we add an explicit check in Section 2, including a short proof that trace preservation holds by construction and complete positivity is preserved for the reported parameter ranges (verified numerically across the domain). revision: yes
Referee: Crossover analysis (likely §4 or §5): the distinction between quasi-static and sudden-quench regimes and the resulting dynamically generated shortcuts lacks an explicit error analysis or comparison against the autonomous Markovian baseline.

Authors: We have added a direct comparison subsection showing the relaxation time for the optimized multi-step protocol versus the autonomous Markovian baseline (constant rates), with the speed-up quantified as the ratio of times. Convergence with respect to step number and time-step size is demonstrated via error plots in a new figure, confirming the shortcuts are genuine and not discretization artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: optimization parameters derived from explicit dynamics analysis

full rationale

The paper examines multi-step Pontus-Mpemba protocols governed by non-autonomous Lindblad master equations, analyzing the quasi-static to sudden-quench crossover to identify dynamically generated shortcuts via a two-parameter family of time-dependent dissipation rates. Optimal speed-up parameters are determined through direct study of the time-inhomogeneous dynamics rather than by fitting to the target outcome or self-definition. No load-bearing step reduces to a prior self-citation chain, ansatz smuggling, or renaming of known results; the central claims rest on the stated model equations and regime crossover without presupposing the reported speed-up. The derivation remains self-contained against the explicit assumptions of the phenomenological framework.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard framework of open quantum systems and introduces time-dependent rates whose two free parameters are adjusted to achieve the reported speed-up; no new particles or forces are postulated.

free parameters (1)

two parameters of the time-dependent dissipation rate family
These parameters are varied to locate the optimal speed-up conditions in the multi-step protocols.

axioms (1)

domain assumption Dynamics of the open quantum system is governed by non-autonomous Lindblad master equations
This is the governing equation class stated in the abstract for all protocols considered.

pith-pipeline@v0.9.0 · 5493 in / 1342 out tokens · 31110 ms · 2026-05-15T21:19:02.391005+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Considering a two-parameter family of time-dependent rates, the parameters allowing for optimal speed-up conditions are determined.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

non-autonomous (aka time-inhomogeneous) Lindblad master equations

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

[1]

Clemens Gneiting, Akshay Koottandavida, A. V. Rozhkov, and Franco Nori. Unraveling the topology of dissipative quantum systems.Phys. Rev. Res.,4:023036, 2022.doi:10.1103/ PhysRevResearch.4.023036

work page 2022
[2]

Cinnirella, Andrea Nava, Gabriele Campagnano, and Domenico Giuliano

Emmanuele G. Cinnirella, Andrea Nava, Gabriele Campagnano, and Domenico Giuliano. Fate of high winding number topological phases in the disordered extended Su-Schrieffer-Heeger model.Phys. Rev. B,109:035114, 2024.doi:10.1103/PhysRevB.109.035114

work page doi:10.1103/physrevb.109.035114 2024
[3]

Phase diagram of the disordered Kitaev chain with long-range pairing connected to external baths

EmmanueleG.Cinnirella, AndreaNava, GabrieleCampagnano, andDomenicoGiuliano. Phase diagram of the disordered Kitaev chain with long-range pairing connected to external baths. Phys. Rev. B,111:155149, 2025.doi:10.1103/PhysRevB.111.155149

work page doi:10.1103/physrevb.111.155149 2025
[4]

Cinnirella, Andrea Nava, and Domenico Giuliano

Emmanuele G. Cinnirella, Andrea Nava, and Domenico Giuliano. Charge current and phase diagram of the disordered open longer-range Kitaev chain.Phys. Rev. B,113:045152, 2026. doi:10.1103/mvcm-fbjl

work page doi:10.1103/mvcm-fbjl 2026
[5]

Dissipative diffusion in quantum state preparation: from passive cooling to system-bath engineering, 2026.arXiv: 2601.18894

Tim Pokart, Lukas König, Sebastian Diehl, and Jan Carl Budich. Dissipative diffusion in quantum state preparation: from passive cooling to system-bath engineering, 2026.arXiv: 2601.18894

work page arXiv 2026
[6]

Physical Review Letters 110(17) (2013) https://doi.org/10.1103/physrevlett.110

Alexey V. Gorshkov, Rejish Nath, and Thomas Pohl. Dissipative Many-Body Quantum Optics in Rydberg Media.Phys. Rev. Lett.,110:153601, 2013.doi:10.1103/PhysRevLett.110. 153601

work page doi:10.1103/physrevlett.110 2013
[7]

Dissipative cooling induced by pulse perturbations.SciPost Phys.,12:014, 2022.doi:10.21468/SciPostPhys.12.1.014

Andrea Nava and Michele Fabrizio. Dissipative cooling induced by pulse perturbations.SciPost Phys.,12:014, 2022.doi:10.21468/SciPostPhys.12.1.014

work page doi:10.21468/scipostphys.12.1.014 2022
[8]

Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks.New Journal of Physics,25(9):093020, 2023.doi:10.1088/1367-2630/aceff4

Mario Boneberg, Federico Carollo, and Igor Lesanovsky. Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks.New Journal of Physics,25(9):093020, 2023.doi:10.1088/1367-2630/aceff4

work page doi:10.1088/1367-2630/aceff4 2023
[9]

Numerical study ofdisorderednoninteractingchainscoupledtoalocalLindbladbath.SciPost Phys

Viktor Berger, Andrea Nava, Jens Hjorleifur Bardarson, and Claudia Artiaco. Numerical study ofdisorderednoninteractingchainscoupledtoalocalLindbladbath.SciPost Phys. Core,8:080, 2025.doi:10.21468/SciPostPhysCore.8.4.080

work page doi:10.21468/scipostphyscore.8.4.080 2025
[10]

Electro nic transport in two-dimensional graphene

Lukas M. Sieberer, Michael Buchhold, Jamir Marino, and Sebastian Diehl. Universality in driven open quantum matter.Rev. Mod. Phys.,97:025004, 2025.doi:10.1103/RevModPhys. 97.025004

work page doi:10.1103/revmodphys 2025
[11]

Wauters, Emanuele Panizon, Glen B

Matteo M. Wauters, Emanuele Panizon, Glen B. Mbeng, and Giuseppe E. Santoro. Reinforcement-learning-assisted quantum optimization.Phys. Rev. Res., 2:033446, Sep

work page
[12]

1103/PhysRevResearch.2.033446

URL:https://link.aps.org/doi/10.1103/PhysRevResearch.2.033446,doi:10. 1103/PhysRevResearch.2.033446

work page doi:10.1103/physrevresearch.2.033446
[13]

Self-correcting quantum many-body control using rein- forcement learning with tensor networks.Nature Machine Intelligence, 5(7):780–791, Jul 2023

Friederike Metz and Marin Bukov. Self-correcting quantum many-body control using rein- forcement learning with tensor networks.Nature Machine Intelligence, 5(7):780–791, Jul 2023. doi:10.1038/s42256-023-00687-5

work page doi:10.1038/s42256-023-00687-5 2023
[14]

Robust quantum control using reinforcement learn- ing from demonstration.npj Quantum Information, 11(1):124, Jul 2025.doi:10.1038/ s41534-025-01065-2

Shengyong Li, Yidian Fan, Xiang Li, Xinhui Ruan, Qianchuan Zhao, Zhihui Peng, Re-Bing Wu, Jing Zhang, and Pengtao Song. Robust quantum control using reinforcement learn- ing from demonstration.npj Quantum Information, 11(1):124, Jul 2025.doi:10.1038/ s41534-025-01065-2

work page 2025
[15]

Optimal speed-up of multi-step Pontus- Mpemba protocols, 2026.doi:10.5281/zenodo.18671474

Marco Peluso, Reinhold Egger, and Andrea Nava. Optimal speed-up of multi-step Pontus- Mpemba protocols, 2026.doi:10.5281/zenodo.18671474. 23

work page doi:10.5281/zenodo.18671474 2026

[1] [1]

Clemens Gneiting, Akshay Koottandavida, A. V. Rozhkov, and Franco Nori. Unraveling the topology of dissipative quantum systems.Phys. Rev. Res.,4:023036, 2022.doi:10.1103/ PhysRevResearch.4.023036

work page 2022

[2] [2]

Cinnirella, Andrea Nava, Gabriele Campagnano, and Domenico Giuliano

Emmanuele G. Cinnirella, Andrea Nava, Gabriele Campagnano, and Domenico Giuliano. Fate of high winding number topological phases in the disordered extended Su-Schrieffer-Heeger model.Phys. Rev. B,109:035114, 2024.doi:10.1103/PhysRevB.109.035114

work page doi:10.1103/physrevb.109.035114 2024

[3] [3]

Phase diagram of the disordered Kitaev chain with long-range pairing connected to external baths

EmmanueleG.Cinnirella, AndreaNava, GabrieleCampagnano, andDomenicoGiuliano. Phase diagram of the disordered Kitaev chain with long-range pairing connected to external baths. Phys. Rev. B,111:155149, 2025.doi:10.1103/PhysRevB.111.155149

work page doi:10.1103/physrevb.111.155149 2025

[4] [4]

Cinnirella, Andrea Nava, and Domenico Giuliano

Emmanuele G. Cinnirella, Andrea Nava, and Domenico Giuliano. Charge current and phase diagram of the disordered open longer-range Kitaev chain.Phys. Rev. B,113:045152, 2026. doi:10.1103/mvcm-fbjl

work page doi:10.1103/mvcm-fbjl 2026

[5] [5]

Dissipative diffusion in quantum state preparation: from passive cooling to system-bath engineering, 2026.arXiv: 2601.18894

Tim Pokart, Lukas König, Sebastian Diehl, and Jan Carl Budich. Dissipative diffusion in quantum state preparation: from passive cooling to system-bath engineering, 2026.arXiv: 2601.18894

work page arXiv 2026

[6] [6]

Physical Review Letters 110(17) (2013) https://doi.org/10.1103/physrevlett.110

Alexey V. Gorshkov, Rejish Nath, and Thomas Pohl. Dissipative Many-Body Quantum Optics in Rydberg Media.Phys. Rev. Lett.,110:153601, 2013.doi:10.1103/PhysRevLett.110. 153601

work page doi:10.1103/physrevlett.110 2013

[7] [7]

Dissipative cooling induced by pulse perturbations.SciPost Phys.,12:014, 2022.doi:10.21468/SciPostPhys.12.1.014

Andrea Nava and Michele Fabrizio. Dissipative cooling induced by pulse perturbations.SciPost Phys.,12:014, 2022.doi:10.21468/SciPostPhys.12.1.014

work page doi:10.21468/scipostphys.12.1.014 2022

[8] [8]

Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks.New Journal of Physics,25(9):093020, 2023.doi:10.1088/1367-2630/aceff4

Mario Boneberg, Federico Carollo, and Igor Lesanovsky. Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks.New Journal of Physics,25(9):093020, 2023.doi:10.1088/1367-2630/aceff4

work page doi:10.1088/1367-2630/aceff4 2023

[9] [9]

Numerical study ofdisorderednoninteractingchainscoupledtoalocalLindbladbath.SciPost Phys

Viktor Berger, Andrea Nava, Jens Hjorleifur Bardarson, and Claudia Artiaco. Numerical study ofdisorderednoninteractingchainscoupledtoalocalLindbladbath.SciPost Phys. Core,8:080, 2025.doi:10.21468/SciPostPhysCore.8.4.080

work page doi:10.21468/scipostphyscore.8.4.080 2025

[10] [10]

Electro nic transport in two-dimensional graphene

Lukas M. Sieberer, Michael Buchhold, Jamir Marino, and Sebastian Diehl. Universality in driven open quantum matter.Rev. Mod. Phys.,97:025004, 2025.doi:10.1103/RevModPhys. 97.025004

work page doi:10.1103/revmodphys 2025

[11] [11]

Wauters, Emanuele Panizon, Glen B

Matteo M. Wauters, Emanuele Panizon, Glen B. Mbeng, and Giuseppe E. Santoro. Reinforcement-learning-assisted quantum optimization.Phys. Rev. Res., 2:033446, Sep

work page

[12] [12]

1103/PhysRevResearch.2.033446

URL:https://link.aps.org/doi/10.1103/PhysRevResearch.2.033446,doi:10. 1103/PhysRevResearch.2.033446

work page doi:10.1103/physrevresearch.2.033446

[13] [13]

Self-correcting quantum many-body control using rein- forcement learning with tensor networks.Nature Machine Intelligence, 5(7):780–791, Jul 2023

Friederike Metz and Marin Bukov. Self-correcting quantum many-body control using rein- forcement learning with tensor networks.Nature Machine Intelligence, 5(7):780–791, Jul 2023. doi:10.1038/s42256-023-00687-5

work page doi:10.1038/s42256-023-00687-5 2023

[14] [14]

Robust quantum control using reinforcement learn- ing from demonstration.npj Quantum Information, 11(1):124, Jul 2025.doi:10.1038/ s41534-025-01065-2

Shengyong Li, Yidian Fan, Xiang Li, Xinhui Ruan, Qianchuan Zhao, Zhihui Peng, Re-Bing Wu, Jing Zhang, and Pengtao Song. Robust quantum control using reinforcement learn- ing from demonstration.npj Quantum Information, 11(1):124, Jul 2025.doi:10.1038/ s41534-025-01065-2

work page 2025

[15] [15]

Optimal speed-up of multi-step Pontus- Mpemba protocols, 2026.doi:10.5281/zenodo.18671474

Marco Peluso, Reinhold Egger, and Andrea Nava. Optimal speed-up of multi-step Pontus- Mpemba protocols, 2026.doi:10.5281/zenodo.18671474. 23

work page doi:10.5281/zenodo.18671474 2026