Fault-tolerant gates via homological product codes

TL;DR

This paper introduces a method using homological product codes to implement universal fault-tolerant logical gates, enabling transversal gate application and overcoming no-go theorems while maintaining sparse stabilizer generators.

Contribution

It presents a novel scheme for fault-tolerant quantum computation using homological product codes that allows fault-tolerant gate mapping between different encoded states.

Findings

Fault-tolerant gate mapping between encoded states demonstrated

Circumvents no-go theorems for transversal gates

Maintains sparsity of stabilizer generators

Abstract

A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a given logical state, enabling the application of different classes of transversal gates belonging to the underlying quantum codes. This allows for the circumvention of no-go results pertaining to universal sets of transversal gates and provides a general scheme for fault-tolerant computation while keeping the stabilizer generators of the code sparse.