Surface code quantum computing by lattice surgery

TL;DR

This paper introduces a lattice surgery technique for surface code quantum computing that enables coupling of planar codes without transversal operations, maintaining 2D nearest-neighbor interactions and reducing qubit resources for universal quantum computation.

Contribution

It presents a novel lattice surgery method for coupling planar surface codes, eliminating the need for braiding, and demonstrating resource-efficient quantum logic operations in 2D.

Findings

Enables universal quantum computation with planar codes via lattice surgery.

Reduces qubit overhead for logical operations compared to previous methods.

Demonstrates a logical CNOT operation with only 53 physical qubits.

Abstract

In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance 3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.