Fault-Tolerant Quantum Computation with Constant Overhead

TL;DR

This paper demonstrates that in large-scale fault-tolerant quantum computing, the ratio of physical to logical qubits can remain constant, using quantum low-density parity check codes, thus achieving constant overhead.

Contribution

It introduces a fault-tolerance scheme with constant overhead based on quantum low-density parity check codes, improving scalability in quantum computing.

Findings

Physical-to-logical qubit ratio can be constant asymptotically

Uses quantum low-density parity check codes for fault-tolerance

Overhead matches that of underlying quantum error-correcting codes

Abstract

What is the minimum number of extra qubits needed to perform a large fault-tolerant quantum circuit? Working in a common model of fault-tolerance, I show that in the asymptotic limit of large circuits, the ratio of physical qubits to logical qubits can be a constant. The construction makes use of quantum low-density parity check codes, and the asymptotic overhead of the protocol is equal to that of the family of quantum error-correcting codes underlying the fault-tolerant protocol.