Quantum-Computer-Based Verification of Quantum Thermodynamic Uncertainty Relation
arXiv:2402.19293 · doi:10.1103/9xpz-62cw
Abstract
Quantum thermodynamic uncertainty relations establish fundamental trade-offs between the precision achievable in quantum systems and associated thermodynamic quantities such as entropy production or dynamical activity. While foundational, empirical demonstrations have thus far been confined to specific cases, either assuming time-reversal symmetry or involving particular measurement types, leaving the verification of their universal validity unrealized. This work leverages a quantum computer to report the first empirical verification of a general quantum thermodynamic uncertainty relation, valid for arbitrary dynamics and observables. We theoretically derive the relation, revealing survival activity as the pivotal thermodynamic quantity governing the precision bound. The verification is demonstrated on IBM's cloud-based quantum processor, which is treated as a real thermodynamic system. To achieve accurate results despite substantial device errors, we introduce a generic protocol for measuring survival activity and employ circuit reduction techniques based on the relation's properties. This strategy allows us to empirically identify survival activity for the first time and confirm the derived relation. Furthermore, the quantum computer's versatility enables the implementation of optimal observables, leading to the saturation of the relation and demonstrating the sharpness of our bound on a physical device. The method's broad applicability is further illustrated by verifying the trade-off for quantum time correlators. Our findings establish quantum computers as effective platforms for investigating fundamental thermodynamic trade-off relations.
Published version. Main text: 11 pages with 6 figures. Appendix: 16 pages with 19 figures
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