Tailored quantum error correction for large-scale quantum computing under structured noise*

Large-scaling quantum computers will require error correction in order to reliably perform computations. However, the hardware overhead for error correction remains dauntingly large, with each logical qubit potentially requiring thousands of physical qubits for reliable operation. One promising approach to reducing the overheads of error correction is to tailor quantum error correcting codes to the dominant noise in the qubit hardware.

In this talk, I’ll present two examples of recent work in tailoring quantum error correction, both based on the recently introduced XZZX surface code. In the first part of the talk, I’ll present a blueprint for building the XZZX surface code out of Kerr cat qubits, which predominantly suffer from dephasing errors. I’ll explain how to efficiently implement gates and distill magic states in the presence of dephasing noise, and derive estimates for the improved overhead offered by the XZZX surface code. In the second part, I’ll show how a cluster state derived from the XZZX surface code, the so-called XZZX cluster state, can be tailored to correct probabilistic gate failures in dual-rail linear optics. Notably, our tailored error correction allows for a threshold of over 25% using simple resource states, overcoming a key barrier for photonic quantum computing.