The Impact of Imperfect Timekeeping on Quantum Control

Abstract

In order to unitarily evolve a quantum system, an agent requires knowledge of time, a parameter which no physical clock can ever perfectly characterise. In this letter, we study how limitations on acquiring knowledge of time impact controlled quantum operations in different paradigms. We show that the quality of timekeeping an agent has access to limits the circuit complexity they are able to achieve within circuit-based quantum computation. We do this by deriving an upper bound on the average gate fidelity achievable under imperfect timekeeping for a general class of random circuits. Another area where quantum control is relevant is quantum thermodynamics. In that context, we show that cooling a qubit can be achieved using a timer of arbitrary quality for control: timekeeping error only impacts the rate of cooling and not the achievable temperature. Our analysis combines techniques from the study of autonomous quantum clocks and the theory of quantum channels to understand the effect of imperfect timekeeping on controlled quantum dynamics.

V3 5 + 8 pages, Published version

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• Mitigating controller noise in quantum gates using optimal control theory
• Fidelity-dissipation relations in quantum gates
• Powering an autonomous clock with quantum electromechanics
• Autonomous Quantum Processing Unit: An Autonomous Thermal Computing Machine & its Physical Limitations
• Quantum Coding with Finite Thermodynamic Resources
• Recovering optimal precision in quantum sensing with time domain imperfections
• Thermodynamic Constraints on Information Transmission in Quantum Ensembles
• Active Quantum Distillation
• Memory effects in repeated uses of quantum channels
• Resilience-Runtime Tradeoff Relations for Quantum Algorithms