A circuit-level protocol and analysis for twist-based lattice surgery

TL;DR

This paper introduces a detailed twist-based lattice surgery protocol for fault-tolerant quantum computing, including new stabilizer measurement circuits and error correction simulations, showing mild performance trade-offs compared to twist-free methods.

Contribution

It provides the first explicit circuit-level protocol for twist-based lattice surgery with compatible measurement circuits and analyzes its error threshold through simulations.

Findings

Slight decrease in logical failure threshold with twist defects

Performance remains robust below $5 imes 10^{-3}$ CNOT infidelity

Efficient boundary measurement scheme for Y operators

Abstract

Lattice surgery is a measurement-based technique for performing fault-tolerant quantum computation in two dimensions. When using the surface code, the most general lattice surgery operations require lattice irregularities called twist defects. However, implementing twist-based lattice surgery may require additional resources, such as extra device connectivity, and could lower the threshold and overall performance for the surface code. Here we provide an explicit twist-based lattice surgery protocol and its requisite connectivity layout. We also provide new stabilizer measurement circuits for measuring twist defects which are compatible with our chosen gate scheduling. We undertake the first circuit-level error correction simulations during twist-based lattice surgery using a biased depolarizing noise model. Our results indicate a slight decrease in the threshold for timelike logical failures compared to lattice surgery protocols with no twist defects in the bulk. However, comfortably below threshold (i.e. with CNOT infidelities below $5 \times 10^{-3}$), the performance degradation is mild and in fact preferable over proposed alternative twist-free schemes. Lastly, we provide an efficient scheme for measuring $Y$ operators along boundaries of surface codes which bypasses certain steps that were required in previous schemes.