Thermodynamic uncertainty relations (TURs) are a set of inequalities expressing a fundamental trade-off between precision and dissipation in nonequilibrium classical and quantum thermodynamic processes. TURs show that achieving low fluctuations in a thermodynamic quantity (e.g., heat or work) requires a minimum entropy production, with profound implications for the efficiency of biological and artificial thermodynamic processes. The accurate evaluation of TURs is a necessary requirement to quantify the fluctuation and dissipation entailed by a thermodynamic process, and ultimately to optimize the performance of quantum devices, whose operation is fundamentally a quantum thermodynamic process. Here, we simulate TURs in a transverse-field Ising model subjected to a time-dependent driving protocol, using quantum and classical computers in concert. Varying the duration and strength of the drive as well as the system size, we verify the validity of TURs, identify quantum signatures in the work statistics within the linear response regime, and observe TUR saturation in the high-temperature limit.

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• Quantum algorithms & computation
• Quantum simulation
• Quantum thermodynamics
• Uncertainty relation