# Implementation of holonomic quantum computation through engineering and manipulating environment

## TL;DR

This paper proposes a method for implementing holonomic quantum computation by engineering an environment that enables a geometric CPHASE gate between distant atoms, combining reservoir engineering, decoherence-free space, and geometric phases.

## Contribution

It introduces a novel scheme to realize a two-qubit geometric CPHASE gate via environment engineering and adiabatic manipulation in a cavity-QED system.

## Key findings

- Effective squeezing reservoir can be engineered.
- A CPHASE gate with arbitrary phase shift can be implemented.
- The scheme integrates environment engineering with geometric quantum computation.

## Abstract

We consider an atom-field coupled system, in which two pairs of four-level atoms are respectively driven by laser fields and trapped in two distant cavities that are connected by an optical fiber. First, we show that an effective squeezing reservoir can be engineered under appropriate conditions. Then, we show that a two-qubit geometric CPHASE gate between the atoms in the two cavities can be implemented through adiabatically manipulating the engineered reservoir along a closed loop. This scheme that combines engineering environment with decoherence-free space and geometric phase quantum computation together has the remarkable feature: a CPHASE gate with arbitrary phase shift is implemented by simply changing the strength and relative phase of the driving fields.