Low overhead quantum computation using lattice surgery

TL;DR

This paper demonstrates that lattice surgery significantly reduces the overhead of fault-tolerant quantum computation with surface codes, enabling large algorithms with fewer physical qubits compared to defect-based methods.

Contribution

It shows that lattice surgery decreases storage and distillation overheads by over 4 and 5 times respectively, advocating for its adoption over defects and braids.

Findings

Lattice surgery reduces storage overhead by over 4 times.

Lattice surgery reduces distillation overhead by nearly 5 times.

Enables running $10^8$ T gates with only $3.7 imes 10^5$ physical qubits.

Abstract

When calculating the overhead of a quantum algorithm made fault-tolerant using the surface code, many previous works have used defects and braids for logical qubit storage and state distillation. In this work, we show that lattice surgery reduces the storage overhead by over a factor of 4, and the distillation overhead by nearly a factor of 5, making it possible to run algorithms with $10^8$ T gates using only $3.7\times 10^5$ physical qubits capable of executing gates with error $p\sim 10^{-3}$. These numbers strongly suggest that defects and braids in the surface code should be deprecated in favor of lattice surgery.