Exact and approximate continuous-variable gate decompositions

TL;DR

This paper reviews and introduces techniques for decomposing gates in continuous-variable quantum computing, comparing exact and approximate methods in terms of gate count and circuit depth.

Contribution

It provides a detailed analysis of existing decomposition techniques and introduces new methods to improve efficiency in continuous-variable quantum gates.

Findings

Exact decompositions have lower gate counts.

Approximate methods can cover all operations but need deeper circuits.

Trade-offs exist between precision and circuit complexity.

Abstract

We gather and examine in detail gate decomposition techniques for continuous-variable quantum computers and also introduce some new techniques which expand on these methods. Both exact and approximate decomposition methods are studied and gate counts are compared for some common operations. While each having distinct advantages, we find that exact decompositions have lower gate counts whereas approximate techniques can cover decompositions for all continuous-variable operations but require significant circuit depth for a modest precision.