Noise and Controllability: suppression of controllability in large quantum systems

Abstract

A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise. Can one design control fields such that the effect of noise is negligible on the time-scale of the transformation? Complete controllability in practice requires that the effect of noise can be suppressed for an arbitrary transformation. The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system increases, determined by the dimension of the Hilbert space representation of the algebra. We show that for large quantum systems, generic noise in the controls dominates for a typical class of target transformations i.e., complete controllability is destroyed by the noise.

4 pages, no figures

References in corpus (7)

• Fault-Tolerant Quantum Dynamical Decoupling
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences
• Quantum Control of the Hyperfine Spin of a Cs Atom Ensemble
• Universal dynamical decoherence control of noisy single-and multi-qubit systems
• A smoothing monotonic convergent optimal control algorithm for NMR pulse sequence design
• Generalized Coherent States as Preferred States of Open Quantum Systems

Cited by in corpus (6)

• Noise Resistant Quantum Control Using Dynamical Invariants
• Characterization of control noise effects in optimal quantum unitary dynamics
• Incoherent Control of the Retinal Isomerization in Rhodopsin
• Quantum control with noisy fields: computational complexity vs. sensitivity to noise
• Action-Noise-Assisted Quantum Control
• Mitigating controller noise in quantum gates using optimal control theory