Combinatorial structure of a holonomic controlled phase gate

TL;DR

This paper explores the combinatorial and geometric structures underlying a holonomic controlled phase gate in quantum computing, revealing relations with toric varieties across multiple qubit systems.

Contribution

It provides a detailed analysis of the combinatorial structures of holonomic controlled gates on multi-qubit states using toric varieties, a novel geometric approach.

Findings

Identifies relations between toric varieties and multi-qubit holonomic gates

Analyzes combinatorial structures for two, three, and four-qubit systems

Highlights geometric insights into quantum gate actions

Abstract

We investigate the combinatorial structures of a holonomic controlled quantum gate based on toric varieties. In particular, we in detail discuss the combinatorial structures of a two-qubit holonomic controlled quantum gate on a two-qubit, a three-qubit, and a four-qubit quantum states. Our results show interesting relations between toric varieties of qubit systems and action of a two-qubit holonomic quantum gate on multi-qubit states.