Quantum circuit optimization for arbitrary high-dimensional bipartite quantum computation

TL;DR

This paper presents a universal quantum circuit synthesis scheme for high-dimensional bipartite systems, optimizing gate count and demonstrating efficiency improvements over previous methods.

Contribution

It introduces a new synthesis scheme using controlled increment gates and local gates, achieving the best known upper bound for arbitrary quNit-quMit gates.

Findings

Achieves an $O(n^2)$ upper bound of CINC gates for general quNit-quMit gates.

Requires only 2 CINC gates for controlled quNit-quMit gates, improving over previous $2n$ gates.

Proves that CINC gates combined with local gates form a universal gate set for high-dimensional quantum computation.

Abstract

Implementation of high-dimensional (HD) quantum gates shows very promising perspectives for HD quantum computation. A bipartite quantum system with arbitrary dimensions $n$ and $m$ is termed a quNit-quMit. Here we propose a synthesis scheme to construct the quantum circuit for general quNit-quMit gates with controlled increment (CINC) gates and local gates. This shows that CINC gates combined with local gates form a universal gate set for HD quantum computation. An upper bound of $O(n^2)$ CINC gates is achieved for arbitrary quNit-quMit gate implementation in the proposed scheme, which is the best known result. Especially for the controlled quNit-quMit gates, our scheme requires only 2 CINC gates, whereas the previous scheme required $2n$.