Quantum computing by color-code lattice surgery

TL;DR

This paper introduces a novel method called color-code lattice surgery for fault-tolerant quantum computing, which is more qubit-efficient and faster for certain operations compared to traditional surface-code methods.

Contribution

It develops a new color-code lattice-surgery technique that improves efficiency and speed of fault-tolerant quantum operations, including implementing gates in fewer steps.

Findings

Uses fewer qubits than surface-code lattice surgery at the same code distance.

Enables faster implementation of Hadamard and phase gates in a single transversal step.

Achieves comparable fault-tolerance with fewer resources at low noise rates.

Abstract

We demonstrate how to use lattice surgery to enact a universal set of fault-tolerant quantum operations with color codes. Along the way, we also improve existing surface-code lattice-surgery methods. Lattice-surgery methods use fewer qubits and the same time or less than associated defect-braiding methods. Furthermore, per code distance, color-code lattice surgery uses approximately half the qubits and the same time or less than surface-code lattice surgery. Color-code lattice surgery can also implement the Hadamard and phase gates in a single transversal step---much faster than surface-code lattice surgery can. Against uncorrelated circuit-level depolarizing noise, color-code lattice surgery uses fewer qubits to achieve the same degree of fault-tolerant error suppression as surface-code lattice surgery when the noise rate is low enough and the error suppression demand is high enough.