Provably Optimal Control for Multiplicative Amplitude Control Noise

Abstract

We provide a technique to obtain provably optimal control sequences for quantum systems under the influence of time-correlated multiplicative control noise. Utilizing the circuit-level noise model introduced in [Phys. Rev. Research 3, 033229(2021)], we show that we can map the problem of finding such a sequence to a convex optimization problem with guaranteed optimality that follows from the convexity. We also show that this technique is compatible with more general off-axis timecorrelated dephasing noise. In spite of losing provable optimality, numerically optimized control sequences under this scenario can still achieve nearly optimal performance when the control noise is strong relative to the dephasing contribution. This approach will enable the development of optimal quantum logic gates in systems where noise due to amplitude drifts in the control is strong relative to dephasing such as in ion-trap based quantum computers or in the limit of fast control.I.

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…GRAPE can be modified to include binary control pulse optimization [221]. Time-correlated multiplicative control noise can be mitigated based on a circuit-level representation of the control dynamics [572]. Also, gradient-free optimal control can be formulated such as to yield phase modulated-only driving fields which are more robust than pulses which are both amplitude and phase modulated [563].…”

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…GRAPE can be modified to include binary control pulse optimization [218]. Time-correlated multiplicative control noise can be mitigated based on a circuit-level representation of the control dynamics [566]. Also, gradient-free optimal control can be formulated such as to yield phase modulated-only driving fields which are more robust than pulses which are both amplitude and phase modulated [557].…”