Thermodynamic Signature of Logical Depth in Quantum Circuits
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918137175212032 |
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| author | Ibnouhsein, Issam |
| author_facet | Ibnouhsein, Issam |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_03203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermodynamic Signature of Logical Depth in Quantum Circuits Ibnouhsein, Issam Quantum Physics Computational Complexity 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. |
| title | Thermodynamic Signature of Logical Depth in Quantum Circuits |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2508.03203 |