Low-overhead fault-tolerant quantum computing using long-range connectivity

TL;DR

This paper proposes a low-overhead fault-tolerant quantum computing scheme using LDPC codes and long-range interactions, potentially reducing physical qubit requirements significantly compared to surface codes.

Contribution

It introduces a novel approach combining LDPC codes with long-range connectivity to lower overheads in fault-tolerant quantum computing.

Findings

Order-of-magnitude reduction in overheads compared to surface codes.

Potential for scalable quantum computing with a few thousand physical qubits.

High thresholds of LDPC codes make this approach feasible at practical error rates.

Abstract

Vast numbers of qubits will be needed for large-scale quantum computing due to the overheads associated with error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density parity-check (LDPC) codes, where long-range interactions enable many logical qubits to be encoded with a modest number of physical qubits. In our approach, logic gates operate via logical Pauli measurements that preserve both the protection of the LDPC codes as well as the low overheads in terms of the required number of additional qubits. Compared with surface codes with the same code distance, we estimate order-of-magnitude improvements in the overheads for processing around one hundred logical qubits using this approach. Given the high thresholds demonstrated by LDPC codes, our estimates suggest that fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at comparable error rates to what is needed for current approaches.