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Thermodynamic coprocessor for linear operations with input-size-independent calculation time based on open quantum system
by I. V. Vovchenko, A. A. Zyablovsky, A. A. Pukhov, E. S. Andrianov
Submission summary
| Authors (as registered SciPost users): | Ivan Vovchenko |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2509.09382v1 (pdf) |
| Date submitted: | Oct. 13, 2025, 1:22 p.m. |
| Submitted by: | Ivan Vovchenko |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Linear operations, e.g., vector-matrix or vector-vector multiplications, are core operations of modern neural networks. To diminish computational time, these operations are implemented by parallel computations using different coprocessors. In this work we show that open quantum system consisting of bosonic modes and interacting with bosonic reservoirs can be used as analog coprocessor implementing multiple vector-matrix multiplications with stochastic matrices in parallel. Input vectors are encoded in occupancies of reservoirs, and output result is presented by stationary energy flows. The operation takes time needed for the system's transition to non-equilibrium stationary state independently on number of the reservoirs, i.e., on the input vector dimension. The computations are accompanied by entropy growth. We construct a direct mapping between open quantum systems and electrical crossbar structures, showing that dissipation rates multiplied by open quantum system's modes frequencies can be seen as conductivities, reservoirs' occupancies can be seen as potentials, and stationary energy flows can be seen as electric currents.
Current status:
Reports on this Submission
Strengths
- The authors show that open quantum system consisting of bosonic modes interacting with bosonic reservoirs can be used as analog coprocessor implementing multiple vector matrix multiplications with stochastic matrices in parallel.
Weaknesses
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There are a number of assumptions made in the construction, without proper justifications.
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In establishing an electrical analogy for open quantum systems, Ohm's Law is taken for granted.... which need not be the case.
Report
While the problem studied is interesting and is of relevance, there are some issues that could be sorted out.
- There are a number of assumptions made in the construction. Thus, for e.g.,
a. An assumption is made about being able to sort out the dissipation rates of open quantum systems at different frequencies independently. This needs to be justified concretely.
b. For establishing an electrical analogy for open quantum systems, the central assumption that is made is the Ohm's Law. However, as has been shown in recent literature, Ohm's law may have only limited validity in the parameter regimes where open system effects are being considered. Under such scenarios, how is the present analogy still holding?
- I also feel that the standard of English, in the paper, could be improved.
Recommendation
Ask for major revision
Strengths
1- The paper is well organized and, consequently, easy to follow 2- Provides an alternative method for implementing fundamental computations by exploiting non-unitary processes
Weaknesses
1- Missing definition of quantities at the core of the discussion obscure results 2- No comparison of the proposed scheme with previous/traditional ones 3- No clear motivation for the "Electrical analogy" section
Report
It would also be useful to improve some features of the presentation. Neither $\lambda$ nor the Q-factor are defined in the text. Also, figures 3 and 4 are hard to understand at first sight. Finally, while the article is generally well written, there are several expressions which are grammatically incorrect, as all those starting with “Let” (“Let consider an OQS …”, “Let OQS interacts with …”).
Therefore, I believe the article needs modifications before being considered for publishing in SciPost Core.
Recommendation
Ask for major revision
Strengths
Weaknesses
1) absence of comparison of the suggested scheme of operations with the conventional ones; 2) absence of analysis of the effects related with possible realization of the set-up in real systems (interactions, non-Markovianity, nonlinearity)
Report
Recommendation
Reject