# Separation and approximate separation of multipartite quantum gates

## TL;DR

This paper investigates the theoretical conditions for separating multipartite quantum gates and explores approximate separation methods, supported by experiments on IBM quantum computers, to facilitate quantum parallel programming.

## Contribution

It provides a theoretical analysis of separability conditions for multipartite quantum gates and introduces approximate separation techniques with experimental validation.

## Key findings

- Few multipartite quantum gates are exactly separable.
- Approximate separation can bring multipartite gates close to separable ones.
- Experimental results demonstrate the feasibility of approximate separation on IBM quantum computers.

## Abstract

The number of qubits of current quantum computers is one of the most dominating restrictions for applications. So it is naturally conceived to use two or more small capacity quantum computers to form a larger capacity quantum computing system by quantum parallel programming. To design the parallel program for quantum computers, the primary obstacle is to decompose quantum gates in the whole circuit to the tensor product of local gates. In the paper, we first devote to analyzing theoretically separability conditions of multipartite quantum gates on finite or infinite dimensional systems. Furthermore, we perform the separation experiments for $n$-qubit quantum gates on the IBM's quantum computers by the software Q$|SI\rangle$. Not surprisedly, it is showed that there exist few separable ones among multipartite quantum gates. Therefore, we pay our attention to the approximate separation problems of multipartite gates, i.e., how a multipartite gate can be closed to separable ones.