Quantum Computer-Based Verification of Quantum Thermodynamic Uncertainty Relation

• URL: http://arxiv.org/abs/2402.19293v2
• Date: Sun, 21 Jul 2024 06:13:52 GMT
• Title: Quantum Computer-Based Verification of Quantum Thermodynamic Uncertainty Relation
• Authors: Nobumasa Ishida, Yoshihiko Hasegawa,
• Abstract summary: Quantum thermodynamic uncertainty relations establish the fundamental trade-off between precision and thermodynamic costs. We present an approach that utilizes a noisy quantum computer for verifying a general quantum thermodynamic uncertainty relation. This study highlights the potential and limitations of noisy quantum computers for demonstrating quantum thermodynamic trade-offs.
• Score: 1.6574413179773757
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum thermodynamic uncertainty relations establish the fundamental trade-off between precision and thermodynamic costs, yet their empirical verification is scarce. To extend the range of real-world tests, we present an approach that utilizes a noisy quantum computer for verifying a general quantum thermodynamic uncertainty relation. We employ a three-fold methodology to tackle the limitations of current quantum processors: generalizing a thermodynamic uncertainty relation to arbitrary observables under completely positive trace-preserving maps, proposing a method to measure the thermodynamic cost (survival activity) in the weak coupling regime, and reducing the required circuit depth by exploiting the properties of our thermodynamic uncertainty relation. We apply our bound to a quantum time correlator measurement protocol on IBM's cloud-based quantum processor. The empirical results show that our bound tightly constrains precision, with the relative variance approaching the theoretical limit within a single order of magnitude. Furthermore, our approach enables the saturation of our thermodynamic uncertainty relation by constructing the optimal observable that requires entangled measurements. This study highlights the potential and limitations of noisy quantum computers for demonstrating quantum thermodynamic trade-offs.

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