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arxiv: 2601.07522 · v2 · submitted 2026-01-12 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

Thermodynamic Recycling of Algorithmic Failure Branches: Quantum-Computer Demonstration with Quantum Error Correction

Nobumasa Ishida , Yoshihiko Hasegawa
Authors on Pith no claims yet

Pith reviewed 2026-05-16 15:08 UTC · model grok-4.3

classification 🪐 quant-ph
keywords thermodynamic recyclingquantum error correctionLandauer limitinformation erasureHarrow-Hassidim-Lloyd algorithmquantum thermodynamicssuperconducting qubitsfailure branch reset
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The pith

Quantum algorithm failure branches can be recycled as athermal baths to erase information with heat below the Landauer limit.

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

The paper proposes thermodynamic recycling, a method that treats the non-equilibrium states created when resetting discarded failure branches in quantum algorithms as usable resources rather than waste. By coupling the athermal bath from such a reset to a target system before relaxation occurs, the framework performs tasks like information erasure while dissipating less heat than standard thermodynamic bounds allow. An analytic derivation shows how the recycled bath reduces the heat cost of erasure, and the approach is tested on IBM superconducting hardware by running the Harrow-Hassidim-Lloyd algorithm together with three-qubit quantum error correction to erase syndrome bits. The experiment reports erasure heat below the Landauer limit of kT ln 2 per bit even under realistic device noise. The result links routine quantum-computing operations to thermodynamic efficiency by turning algorithmic waste into a thermodynamic asset.

Core claim

Thermodynamic recycling exploits the athermal bath naturally generated when a failure branch is reset. Coupling this bath to the target system before relaxation enables information erasure with heat dissipation reduced below the conventional Landauer bound, as derived analytically and shown experimentally on a superconducting processor using the HHL algorithm plus three-qubit error correction.

What carries the argument

The athermal bath generated during reset of an algorithmic failure branch, which is coupled to the target system prior to relaxation to reduce dissipation in erasure.

If this is right

  • Heat dissipated while erasing syndrome information can be lowered analytically by recycling the bath from discarded branches.
  • Three-qubit quantum error correction can be combined with the recycling step to make the method viable on noisy hardware.
  • The operational link between algorithmic failure branches and thermodynamic tasks extends resource accounting in quantum processors.
  • Erasure of any information tied to error-correction outcomes can achieve sub-Landauer heat costs when the recycled bath is used.

Where Pith is reading between the lines

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

  • The same recycling step could be applied to other quantum algorithms that generate measurable failure branches, potentially lowering total energy cost per useful output.
  • If the athermal bath can be harvested repeatedly, quantum processors might treat error events as an internal energy source rather than pure overhead.
  • The framework suggests a general route to close the loop between computation and thermodynamics by converting non-equilibrium states produced inside the algorithm into work or reduced dissipation.

Load-bearing premise

The athermal bath created by resetting a failure branch can be coupled to the target system before it relaxes, without hidden thermodynamic costs or law violations.

What would settle it

A direct calorimetric or energy-balance measurement on the same HHL-plus-QEC circuit that shows the total heat released during syndrome erasure is not lower than kT ln 2 per bit.

Figures

Figures reproduced from arXiv: 2601.07522 by Nobumasa Ishida, Yoshihiko Hasegawa.

Figure 1
Figure 1. Figure 1: FIG. 1. Illustration of thermodynamic recycling. During the reset of a failure branch state after running an algorithm, the bath [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Circuit sketch of the demonstration protocol. The [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Information-erasure results on ibm [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Dependence of heat dissipation ∆ [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Execution time of the circuits composed of (a) X [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

Thermodynamic trade-off relations dictate fundamental limits on the performance of thermodynamic tasks through costs such as heat dissipation. Here, we propose a framework called thermodynamic recycling to circumvent these limits in quantum processors by exploiting failure branches of quantum algorithms, which are usually discarded. The key component is an athermal bath naturally generated during the resetting of a failure branch. By coupling this bath to a target system prior to relaxation, thermodynamic tasks can be performed beyond conventional thermodynamic limits. We apply this framework to information erasure and derive the reduction in heat dissipation analytically. As a demonstration, we implement our framework on IBM's superconducting quantum processor by combining the Harrow--Hassidim--Lloyd algorithm with three-qubit quantum error correction, thereby reducing the heat dissipated in erasing syndrome information. Despite substantial noise and errors in current hardware, our method achieves erasure with heat dissipation below the Landauer limit. This work establishes an operational connection between quantum computing and quantum thermodynamics for resource-efficient quantum computation.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper proposes a 'thermodynamic recycling' framework that exploits athermal baths generated during the reset of failure branches in quantum algorithms to perform tasks such as information erasure with reduced heat dissipation. It derives an analytical reduction in heat below the Landauer limit and demonstrates the approach experimentally on IBM superconducting hardware by combining the HHL algorithm with three-qubit quantum error correction, claiming sub-Landauer erasure despite hardware noise.

Significance. If the analytical derivation is independent of heat-measurement conventions and the experimental heat accounting isolates the recycled-bath contribution without hidden offsets from QEC or reset operations, the work would establish a concrete operational link between algorithmic failure modes and thermodynamic resource savings, enabling quantum computation beyond conventional limits. The parameter-free character of the derivation (if confirmed) and the use of existing hardware for the demonstration would be notable strengths.

major comments (2)
  1. [Experimental demonstration] Abstract and experimental demonstration section: the claim that erasure is achieved with heat dissipation below the Landauer limit on noisy hardware requires explicit reporting of how total dissipated heat is measured, how contributions from syndrome extraction, correction gates, and reset operations are bounded or subtracted, and what baseline (standard erasure without recycling) is used. Without this accounting, the below-Landauer result cannot be attributed to the athermal-bath coupling mechanism rather than unaccounted noise or protocol costs.
  2. [Analytical framework] Analytical derivation: the reduction in heat dissipation is stated as derived from coupling the athermal bath prior to relaxation, but the manuscript must show that this reduction is independent of the precise definition and measurement protocol for heat (including any work costs of the coupling step itself). If the derivation relies on the ad-hoc assumption that the failure-branch reset produces a usable athermal bath with no offsetting dissipation, this must be stated as an axiom and tested against the experimental noise model.
minor comments (2)
  1. Clarify the precise definition of 'heat dissipation' used in both the derivation and the experiment, including units and any assumptions about the bath temperature.
  2. Add a short discussion of how the three-qubit QEC code interacts with the thermodynamic recycling protocol, particularly whether syndrome measurements introduce additional entropy that must be accounted for.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and will revise the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Experimental demonstration] Abstract and experimental demonstration section: the claim that erasure is achieved with heat dissipation below the Landauer limit on noisy hardware requires explicit reporting of how total dissipated heat is measured, how contributions from syndrome extraction, correction gates, and reset operations are bounded or subtracted, and what baseline (standard erasure without recycling) is used. Without this accounting, the below-Landauer result cannot be attributed to the athermal-bath coupling mechanism rather than unaccounted noise or protocol costs.

    Authors: We agree that explicit heat accounting is required to substantiate the claim. In the revised manuscript we will add a dedicated subsection in the experimental demonstration that reports: (i) the precise protocol used to extract total dissipated heat from the IBM hardware (including calibration of qubit energies and readout), (ii) quantitative bounds on the heat contributions from syndrome extraction, correction gates, and reset operations obtained from separate calibration runs and the device noise model, and (iii) a direct side-by-side comparison with the baseline protocol of standard erasure performed without coupling to the recycled athermal bath. These additions will isolate the contribution of the recycling mechanism. revision: yes

  2. Referee: [Analytical framework] Analytical derivation: the reduction in heat dissipation is stated as derived from coupling the athermal bath prior to relaxation, but the manuscript must show that this reduction is independent of the precise definition and measurement protocol for heat (including any work costs of the coupling step itself). If the derivation relies on the ad-hoc assumption that the failure-branch reset produces a usable athermal bath with no offsetting dissipation, this must be stated as an axiom and tested against the experimental noise model.

    Authors: The derivation employs the standard quantum-thermodynamic definitions of heat (energy exchange with the bath) and work. We will revise the analytical section to prove explicitly that the reported reduction holds under both the Clausius and stochastic-thermodynamic conventions, including the work cost of the coupling operation. We will also state the assumption that the failure-branch reset generates a usable athermal bath as an explicit axiom and compare its validity against the measured noise model of the IBM superconducting processor used in the experiment. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper proposes thermodynamic recycling by using failure-branch resets to generate an athermal bath, then analytically derives a reduction in heat dissipation for erasure and demonstrates it experimentally via HHL plus three-qubit QEC on superconducting hardware. The central analytical step is presented as a first-principles consequence of coupling the athermal bath prior to relaxation, without reducing to a fitted parameter, self-citation chain, or redefinition of the target quantity. No load-bearing step equates the claimed sub-Landauer savings to the input definitions or to costs internal to the recycling protocol itself; the experimental claim is framed as an observed outcome amid noise rather than a forced identity. The derivation therefore remains self-contained against external thermodynamic benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The framework rests on the existence of an athermal bath generated by failure-branch resetting and on standard thermodynamic trade-off relations; no free parameters or invented entities with independent evidence are detailed in the abstract.

axioms (2)
  • domain assumption Thermodynamic trade-off relations dictate fundamental limits on performance through costs such as heat dissipation
    Invoked in the opening sentence as the limits to be circumvented.
  • ad hoc to paper An athermal bath is naturally generated during the resetting of a failure branch
    Presented as the key component enabling the recycling.
invented entities (1)
  • athermal bath from failure-branch resetting no independent evidence
    purpose: To serve as a resource for performing thermodynamic tasks beyond conventional limits when coupled to a target system
    Introduced as the central new resource; no independent falsifiable prediction outside the framework is given in the abstract

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Reference graph

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