Thermodynamic Proof of Quantumness without Structure
Abstract
Demonstrating that a machine performs genuinely quantum operations is a central challenge in quantum information processing. Existing proofs of quantumness typically rely on computational tasks that are infeasible for classical machines under assumptions such as computational hardness, or explicit bounds on classical runtime, memory, or oracle queries. Here we introduce an alternative paradigm: a thermodynamic proof of quantumness based on energy consumption. Using the search problem of Yamakawa and Zhandry with a structureless uniformly random oracle, we show that any classical machine solving the task with constant success probability must generate entropy that grows exponentially with the security parameter. By Landauer's principle, this implies an exponential lower bound on heat dissipation and hence on the energy consumption of any cyclic classical implementation. In contrast, the corresponding quantum prover solves the task with polynomial query and gate complexity, giving polynomial energy consumption under standard assumptions for quantum implementations. Thus, in the random-oracle setting, sufficiently low energy consumption in a successful implementation certifies quantumness through a macroscopic thermodynamic observation of energy consumption.
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BibTeX
@misc{meier2026thermodynamic,
title = {{Thermodynamic Proof of Quantumness without Structure}},
author = {Florian Meier and Hayata Yamasaki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25211},
eprint = {2609.25211},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25211},
}
RIS
TY - UNPB
TI - Thermodynamic Proof of Quantumness without Structure
AU - Florian Meier
AU - Hayata Yamasaki
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25211
UR - https://arxiv.org/abs/2609.25211
AB - Demonstrating that a machine performs genuinely quantum operations is a central challenge in quantum information processing. Existing proofs of quantumness typically rely on computational tasks that are infeasible for classical machines under assumptions such as computational hardness, or explicit bounds on classical runtime, memory, or oracle queries. Here we introduce an alternative paradigm: a thermodynamic proof of quantumness based on energy consumption. Using the search problem of Yamakawa and Zhandry with a structureless uniformly random oracle, we show that any classical machine solving the task with constant success probability must generate entropy that grows exponentially with the security parameter. By Landauer's principle, this implies an exponential lower bound on heat dissipation and hence on the energy consumption of any cyclic classical implementation. In contrast, the corresponding quantum prover solves the task with polynomial query and gate complexity, giving polynomial energy consumption under standard assumptions for quantum implementations. Thus, in the random-oracle setting, sufficiently low energy consumption in a successful implementation certifies quantumness through a macroscopic thermodynamic observation of energy consumption.
ER -