Holonomic quantum control with continuous variable systems

TL;DR

This paper proposes a method for universal quantum computation using adiabatic holonomic gates on continuous variable systems, enabling complex quantum operations through phase space manipulations.

Contribution

It introduces three families of adiabatic holonomic gates for continuous variable systems, expanding quantum control techniques with potential implementations in trapped ions and circuit QED.

Findings

Demonstrates how to implement holonomic gates via phase space paths

Shows potential for reservoir engineering in physical systems

Provides a framework for universal quantum computation

Abstract

Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems which support tunable nonlinearities, such as trapped ions and circuit QED.