Journal Article

CS-count-optimal quantum circuits for arbitrary multi-qubit unitaries

Mukhopadhyay, Priyanka

2024

Overview

In quantum computing there are quite a few universal gate sets, each having their own characteristics. In this paper we study the Clifford+CS universal fault-tolerant gate set. The CS gate is used is many applications and this gate set is an important alternative to Clifford+T. We introduce a generating set in order to represent any unitary implementable by this gate set and with this we derive a bound on the CS-count of arbitrary multi-qubit unitaries. Analysing the channel representation of the generating set elements, we infer J n CS ⊂ J n T , where J n CS and J n T are the set of unitaries exactly implementable by the Clifford+CS and Clifford+T gate sets, respectively. We develop CS-count optimal synthesis algorithms for both approximately and exactly implementable multi-qubit unitaries. With the help of these we derive a CS-count-optimal circuit for Toffoli, implying J n Tof = J n CS , where J n Tof is the set of unitaries exactly implementable by the Clifford+Toffoli gate set. Such conclusions can have an important impact on resource estimates of quantum algorithms.

• Publisher: Nature Publishing Group UK,Nature Publishing Group,Nature Portfolio
• Subject: 639/705/117 / 639/766/483/481 / Algorithms / Humanities and Social Sciences / multidisciplinary / Science / Science (multidisciplinary)