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arXiv · 2508.03203

Thermodynamic Signature of Logical Depth in Quantum Circuits

Issam Ibnouhsein
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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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Issam Ibnouhsein. 2025-08-05. Thermodynamic Signature of Logical Depth in Quantum Circuits. https://doi.org/10.1007/s10701-025-00883-w

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