Local-dimension-invariant Calderbank-Shor-Steane Codes with an Improved Distance Promise

TL;DR

This paper introduces a new family of quantum error-correcting codes based on local-dimension-invariant techniques, which work for any local dimension and improve the distance promise, reducing control complexity in quantum computing.

Contribution

It constructs a family of quantum codes with parameters $[[2^N,2^N-1-2N, geq 3]]_q$ for any prime $q$ and natural number $N$, using CSS code structures to lower local-dimension requirements.

Findings

Codes are applicable for any prime local dimension.

Achieves improved distance promise with reduced local-dimension constraints.

Supports fewer particles to control in quantum processors.

Abstract

Quantum computers will need effective error-correcting codes. Current quantum processors require precise control of each particle, so having fewer particles to control might be beneficial. Although traditionally quantum computers are considered as using qubits (2-level systems), qudits (systems with more than 2-levels) are appealing since they can have an equivalent computational space using fewer particles, meaning fewer particles need to be controlled. In this work we prove how to construct codes with parameters $[[2^N,2^N-1-2N,\geq 3]]_q$ for any choice of prime $q$ and natural number $N$. This is accomplished using the technique of local-dimension-invariant (LDI) codes. Generally LDI codes have the drawback of needing large local-dimensions to ensure the distance is at least preserved, and so this work also reduces this requirement by utilizing the structure of CSS codes, allowing for the aforementioned code family to be imported for any local-dimension choice.