Thermodynamic Signature of Logical Depth in Quantum Circuits

IF 1 3区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

Foundations of Physics Pub Date : 2025-09-05 DOI:10.1007/s10701-025-00883-w

Issam Ibnouhsein

引用次数: 0

Abstract

We demonstrate that the internal logical structure of a quantum circuit can leave a distinct thermodynamic signature under progressive decoherence. By comparing deep, conditionally branching circuits with shallow, uniform counterparts—while controlling for overall halting probability and physical resources—we show that branching architectures induce greater entropy flow into the environment. This effect is captured by a logical depth factor \(L_d\), which quantifies entropy accumulation during environmental interactions. We validate our framework through detailed analysis of two 4-branch quantum circuits, demonstrating greater entropy production with \(L_d \approx 1.615\) for conditional versus uniform architectures. An ancilla-based experimental protocol using controlled-phase gates provides a concrete pathway for detecting these thermodynamic signatures on current quantum platforms. Our results establish logical depth as a physically measurable quantity with implications for circuit design, compilation strategies, and verification protocols.

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量子电路中逻辑深度的热力学特征

我们证明了量子电路的内部逻辑结构可以在渐进退相干下留下明显的热力学特征。通过比较深层的、有条件的分支电路与浅层的、均匀的分支电路，同时控制总体停止概率和物理资源，我们发现分支架构会诱导更大的熵流进入环境。这种效应由逻辑深度因子\(L_d\)捕获，该因子量化了环境相互作用期间的熵积累。我们通过对两个4分支量子电路的详细分析验证了我们的框架，证明了在条件架构与统一架构中使用\(L_d \approx 1.615\)产生更大的熵。一种基于辅助装置的实验方案使用控制相门，为在当前量子平台上检测这些热力学特征提供了具体途径。我们的研究结果将逻辑深度作为一个物理上可测量的量，对电路设计、编译策略和验证协议具有指导意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Foundations of Physics 物理-物理：综合

CiteScore

2.70

自引率

6.70%

发文量

104

审稿时长

6-12 weeks

期刊介绍： The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.