Compatible Transformations for a Qudit Decoherence-free/Noiseless Encoding

TL;DR

This paper explores transformations compatible with decoherence-free subsystems in qudit systems, enabling universal quantum computation while preserving the encoded states against collective noise.

Contribution

It introduces methods for compatible transformations in d-state systems that protect against collective noise and demonstrate universal quantum computation on a three-qudit DFS/NS.

Findings

Transformations preserve the DFS/NS during evolution.

Hamiltonian evolutions enable universal quantum computation.

Methods applicable to various DFS/NSs.

Abstract

The interest in decoherence-free, or noiseless subsystems (DFS/NSs) of quantum systems is both of fundamental and practical interest. Understanding the invariance of a set of states under certain transformations is mutually associated with a better understanding of some fundamental aspects of quantum mechanics as well as the practical utility of invariant subsystems. For example, DFS/NSs are potentially useful for protecting quantum information in quantum cryptography and quantum computing as well as enabling universal computation. Here we discuss transformations which are compatible with a DFS/NS that is composed of d-state systems which protect against collective noise. They are compatible in the sense that they do not take the logical (encoded) states outside of the DFS/NS during the transformation. Furthermore, it is shown that the Hamiltonian evolutions derived here can be used to perform universal quantum computation on a three qudit DFS/NS. Many of the methods used in our derivations are directly applicable to a large variety of DFS/NSs. More generally, we may also state that these transformations are compatible with collective motions.