Quantum control with noisy fields: computational complexity versus sensitivity to noise

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, which has to be suppressed to retain controllability. Can one design control fields such that the effect of noise is negligible on the time-scale of the transformation? This question is intimately related to the fundamental problem of a connection between the computational complexity of the control problem and the sensitivity of the controlled system to noise. 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 with the dimension of the Hilbert space representation of the algebra. We find two types of control tasks, easy and hard. Easy tasks are characterized by a small variance of the evolving state with respect to the operators of the control operators. They are relatively immune to noise and the control field is easy to find. Hard tasks have a large variance, are sensitive to noise and the control field is hard to find. The influence of noise increases with the size of the system, which

The roles of drift and control field constraints upon quantum control speed limits

“…There can exist multiple different pulse shapes driving the system to the same target evolution for a given final time T. Roughly speaking, equation (4), instantiated with the above choice for U 1 and U 2 , yields a description of how much the drift Hamiltonian is 'needed' in order to reach a gate. We note that a similar separation has been suggested in [21] by constructing an observable that commutes with H 0 . However, the speed limit in [21] applies only to state-to-state transfer and it captures only the effect of constrained control fields and fails to characterize the role of the strength of the drift Hamiltonian.…”

Noise resistant quantum control using dynamical invariants

“…The sum over k includes the possibility of independent types of noise simultaneously affecting the dynamics. This equation was derived in different contexts, including the singular coupling limit [54], phase noise [55], action noise [8], amplitude noise [56], quantum noise from monitoring weakly the quadrature of the system [3,57], Gaussian noise and Poisson noise for SU(2) algebra [58,59], and more [60][61][62].…”

Focus on coherent control of complex quantum systems

“…Control of decoherence and dissipation continues to be a major motivating goal for both theory and experiment. In Reflecting an increasing focus in the community on analysis of resources as qubit architectures are scaled to larger sizes and greater complexity, Kallush et al explore the tradeoff between complexity of the control Hamiltonians and sensitivity of the system to noise in the controls in 'Quantum control with noisy fields: computational complexity versus sensitivity to noise' [10]. The complexity of control procedures is an emerging theme that is significant for analysis of scaleup of qubit architectures for quantum information.…”