Optimal Control Theory for Continuous Variable Quantum Gates

TL;DR

This paper applies optimal control theory to continuous variable quantum systems, demonstrating trap-free fidelity measures and analyzing the complexity and controllability of CV quantum gates compared to discrete systems.

Contribution

It introduces a trap-free fidelity measure for CV quantum gate optimization and compares the complexity and control mechanisms of CV and discrete quantum systems.

Findings

CV gate optimization is more computationally expensive than discrete gates

Exact-time controllability influences maximum achievable fidelity

Optimal control fields have complex Fourier spectra

Abstract

We apply the methodology of optimal control theory to the problem of implementing quantum gates in continuous variable systems with quadratic Hamiltonians. We demonstrate that it is possible to define a fidelity measure for continuous variable (CV) gate optimization that is devoid of traps, such that the search for optimal control fields using local algorithms will not be hindered. The optimal control of several quantum computing gates, as well as that of algorithms composed of these primitives, is investigated using several typical physical models and compared for discrete and continuous quantum systems. Numerical simulations indicate that the optimization of generic CV quantum gates is inherently more expensive than that of generic discrete variable quantum gates, and that the exact-time controllability of CV systems plays an important role in determining the maximum achievable gate fidelity. The resulting optimal control fields typically display more complicated Fourier spectra that suggest a richer variety of possible control mechanisms. Moreover, the ability to control interactions between qunits is important for delimiting the total control fluence. The comparative ability of current experimental protocols to implement such time-dependent controls may help determine which physical incarnations of CV quantum information processing will be the easiest to implement with optimal fidelity.