Irreversible quantum computation requires thermodynamic work. In principle, one can often evade work costs by implementing reversible transformations. In practice, complexity---the difficulty of realizing a quantum process---poses an obstacle: a realistic agent can perform only a limited number of gates and so not every reversible transformation. Hence an agent, if unable to complete a task unitarily, may expend work on an irreversible process, such as erasure, to finish the job. We pinpoint a work--complexity trade-off, quantifying how protocols that involve higher-complexity unitaries require less work and vice versa. We illustrate with the task of resetting qubits to the all-zero state using a limited number of gates and work-costing erasure. To quantify the resetting’s optimal efficiency, we introduce the complexity entropy, which quantifies a state's apparent randomness to an agent who can implement only limited-complexity measurement effects. The complexity entropy emerges as a general tool for quantifying the optimal efficiencies with which complexity-restricted agents can perform tasks in quantum thermodynamics and information.

A. Munson, N. B. T. Kothakonda, J. Haferkamp, N. Yunger Halpern, J. Eisert, and P. Faist, Complexity-Constrained Quantum Thermodynamics, PRX Quantum 6, 010346 (2025), arXiv:2403.04828

Pizza and drinks will be served after the seminar in ATL 2117.