New techniques for fault-tolerant decomposition of Multi-Controlled Toffoli gate

TL;DR

This paper introduces new fault-tolerant decomposition techniques for Multi-Controlled Toffoli gates using a Clifford+$Z_N$ gate library, reducing phase depth and count, crucial for scalable quantum computing.

Contribution

It presents an ancilla-free decomposition with linear phase depth and a method for unit phase depth decomposition, addressing key challenges in fault-tolerant quantum gate implementation.

Findings

Ancilla-free decomposition achieves linear phase depth.

Unit phase depth decomposition with ancillary lines.

Quadratic phase count in both methods.

Abstract

Physical implementation of scalable quantum architectures faces an immense challenge in form of fragile quantum states. To overcome it, quantum architectures with fault tolerance is desirable. This is achieved currently by using surface code along with a transversal gate set. This dictates the need for decomposition of universal Multi Control Toffoli~(MCT) gates using a transversal gate set. Additionally, the transversal non-Clifford phase gate incurs high latency which makes it an important factor to consider during decomposition.Besides, the decomposition of large Multi-control Toffoli~(MCT) gate without ancilla presents an additional hurdle. In this manuscript, we address both of these issues by introducing Clifford+$Z_N$ gate library. We present an ancilla free decomposition of MCT gates with linear phase depth and quadratic phase count. Furthermore, we provide a technique for decomposition of MCT gates in unit phase depth using the Clifford+$Z_N$ library, albeit at the cost of ancillary lines and quadratic phase count.