Ultrahigh threshold nonstabilizer nonlinear quantum error correcting code

TL;DR

This paper introduces the spinor code, a nonlinear, nonstabilizer quantum error correcting code based on total spin spaces, capable of protecting against single qubit errors with high thresholds, especially for Gaussian states.

Contribution

The paper presents a novel nonlinear quantum error correcting code called the spinor code, based on total spin spaces, expanding the types of codes beyond stabilizer frameworks.

Findings

Capable of protecting against any single qubit Pauli error for Gaussian states.

Estimated code-capacity threshold between 32-75%.

Phenomenological threshold ranges from 9-75%.

Abstract

We introduce a novel type of quantum error correcting code, called the spinor code, based on spaces defined by total spin. The code is a nonstabilizer code, and is also a nonlinear quantum error correcting code, meaning that quantum information is encoded in a parameterized family of quantum states, rather than a linear superposition of code words. Syndrome measurements are performed by projecting on states with differing total spin, with an associated correction to map states back to the maximum total spin space. We show that the code is asymptotically capable of protecting against any single qubit Pauli error for Gaussian distributed states such as spin coherent state. We directly evaluate the performance under the depolarizing channel, considering various cases, with and without initialization and measurement errors, as well as two qubit errors. We estimate the code-capacity threshold to be in the range of 32-75%, while the phenomenological threshold is in the range 9-75%.