Quantum Computer-Based Verification of Quantum Thermodynamic Uncertainty Relation (2402.19293v3)
Abstract: Quantum thermodynamic uncertainty relations reveal fundamental trade-offs between precision and thermodynamic quantities, yet their empirical verification remains limited. We present an approach using quantum computers to verify a general quantum thermodynamic uncertainty relation. Our method, which implements quantum dynamics on physical qubits, enables us to investigate the measurability of relevant quantities, the relation's validity under physical noise, and its empirical tightness. Specifically, quantum computers' versatility allows for the examination of arbitrary observables. We address current quantum processor limitations through a three-fold strategy: generalizing the relation to generic observables under arbitrary quantum channels, proposing a method to measure the target thermodynamic quantity (survival activity) in the weak coupling regime, and reducing circuit depth by leveraging relation properties. Demonstrations on IBM's cloud-based quantum processor validate our relation in open qubit systems and achieve saturation with an optimal observable requiring entangled measurements. The relation is further verified in a quantum time correlator measurement protocol, confirming the broad applicability of our method. This study highlights the potential of noisy quantum computers for demonstrating quantum thermodynamic trade-offs.
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