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.

arXiv commentV3 5 + 8 pages, Published version

References in corpus (40)

• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Thermodynamic uncertainty relation for biomolecular processes
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• Robust randomized benchmarking of quantum processes
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Dissipation bounds all steady-state current fluctuations
• Scalable Noise Estimation with Random Unitary Operators
• Resilient Quantum Computation: Error Models and Thresholds
• Minimal Universal Two-qubit Quantum Circuits
• Fast quantum logic gates with trapped-ion qubits
• Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
• Estimating the Coherence of Noise
• Cost and Precision of Brownian Clocks
• Introduction to Quantum Optimal Control for Quantum Sensing with Nitrogen-Vacancy Centers in Diamond
• High precision differential clock comparisons with a multiplexed optical lattice clock
• Autonomous quantum clocks: does thermodynamics limit our ability to measure time?
• Native qudit entanglement in a trapped ion quantum processor
• Landauer vs. Nernst: What is the True Cost of Cooling a Quantum System?
• Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamic resource
• Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling
• On the CNOT-complexity of CNOT-PHASE circuits
• Energetic cost of Hamiltonian quantum gates
• Clock-Driven Quantum Thermal Engines
• Measuring the thermodynamic cost of timekeeping
• Classical pendulum clocks break the thermodynamic uncertainty relation
• Energetics of a Single Qubit Gate
• Sensitivity of quantum gate fidelity to laser phase and intensity noise
• Approaching the theoretical limit in quantum gate decomposition
• Bounding the average gate fidelity of composite channels using the unitarity
• Fundamental energy requirement of reversible quantum operations
• From randomized benchmarking experiments to gateset circuit fidelity: how to interpret randomized benchmarking decay parameters
• Unifying paradigms of quantum refrigeration: fundamental limits of cooling and associated work costs
• Reducing the CNOT count for Clifford+T circuits on NISQ architectures
• Autonomous Temporal Probability Concentration: Clockworks and the Second Law of Thermodynamics
• The nonequilibrium cost of accurate information processing
• Imperfect Thermalizations Allow for Optimal Thermodynamic Processes
• Autonomous Ticking Clocks from Axiomatic Principles
• Autonomous Quantum Devices: When Are They Realizable without Additional Thermodynamic Costs?
• A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits)

Cited by in corpus (15)

• Key Issues Review: Useful autonomous quantum machines
• Quantum Control of Radical Pair Dynamics beyond Time-Local Optimization
• Optimal time estimation and the clock uncertainty relation for stochastic processes
• Precision is not limited by the second law of thermodynamics
• Efficiently Cooling Quantum Systems with Finite Resources: Insights from Thermodynamic Geometry
• 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