Lift-Connected Surface Codes

TL;DR

This paper introduces lift-connected surface (LCS) codes, a new family of quantum error-correcting codes that outperform standard surface codes in logical error rate at similar or fewer qubits, with promising near-term implementation potential.

Contribution

The paper presents a novel construction of quantum LDPC codes using the lifted product, creating interconnected surface code stacks with improved error correction properties.

Findings

LCS codes have lower logical error rates than standard surface codes at similar sizes.

LCS codes achieve comparable thresholds to surface codes.

LCS codes are suitable for 3D-local connectivity implementations.

Abstract

We use the recently introduced lifted product to construct a family of Quantum Low Density Parity Check Codes (QLDPC codes). The codes we obtain can be viewed as stacks of surface codes that are interconnected, leading to the name lift-connected surface (LCS) codes. LCS codes offer a wide range of parameters - a particularly striking feature is that they show interesting properties that are favorable compared to the standard surface code. For example, already at moderate numbers of physical qubits in the order of tens, LCS codes of equal size have lower logical error rate or similarly, require fewer qubits for a fixed target logical error rate. We present and analyze the construction and provide numerical simulation results for the logical error rate under code capacity and phenomenological noise. These results show that LCS codes attain thresholds that are comparable to corresponding (non-connected) copies of surface codes, while the logical error rate can be orders of magnitude lower, even for representatives with the same parameters. This provides a code family showing the potential of modern product constructions at already small qubit numbers. Their amenability to 3D-local connectivity renders them particularly relevant for near-term implementations.