Qudit Quantum Computation in the Jaynes-Cummings Model

TL;DR

This paper introduces three methods for implementing qudit quantum computation within the Jaynes-Cummings model, including analytical, numerically optimized, and direct evolution optimization techniques, with the latter being faster for small qudits.

Contribution

It presents novel control strategies for qudit gates in the Jaynes-Cummings model, combining analytical and numerical optimization approaches for efficient quantum computation.

Findings

The direct optimization approach achieves faster gate implementation for small qudits.

Analytical control sequences are derived for universal qudit gates.

Numerical optimization improves speed over analytical methods.

Abstract

We have developed methods for performing qudit quantum computation in the Jaynes-Cummings model with the qudits residing in a finite subspace of individual harmonic oscillator modes, resonantly coupled to a spin-1/2 system. The first method determines analytical control sequences for the one- and two-qudit gates necessary for universal quantum computation by breaking down the desired unitary transformations into a series of state preparations implemented with the Law-Eberly scheme. The second method replaces some of the analytical pulse sequences with more rapid numerically optimized sequences. In our third approach, we directly optimize the evolution of the system, without making use of any analytic techniques. While limited to smaller dimensional qudits, the third approach finds pulse sequences which carry out the desired gates in a time which is much shorter than either of the other two approaches.