A Fault-Tolerant Honeycomb Memory

TL;DR

This paper evaluates the robustness of the honeycomb quantum memory code, demonstrating its potential for fault-tolerant quantum computing with fewer qubits compared to traditional codes.

Contribution

It quantifies the honeycomb code's error threshold using a correlated decoder and compares its performance to the surface code across different error models.

Findings

Honeycomb code threshold of 0.2%-0.3% in circuit model

Surface code threshold of 0.5%-0.7% in circuit model

Honeycomb code can reach teraquop regime with 600 qubits at 10^-3 error rate

Abstract

Recently, Hastings & Haah introduced a quantum memory defined on the honeycomb lattice. Remarkably, this honeycomb code assembles weight-six parity checks using only two-local measurements. The sparse connectivity and two-local measurements are desirable features for certain hardware, while the weight-six parity checks enable robust performance in the circuit model. In this work, we quantify the robustness of logical qubits preserved by the honeycomb code using a correlated minimum-weight perfect-matching decoder. Using Monte Carlo sampling, we estimate the honeycomb code's threshold in different error models, and project how efficiently it can reach the "teraquop regime" where trillions of quantum logical operations can be executed reliably. We perform the same estimates for the rotated surface code, and find a threshold of $0.2\%-0.3\%$ for the honeycomb code compared to a threshold of $0.5\%-0.7\%$ for the surface code in a controlled-not circuit model. In a circuit model with native two-body measurements, the honeycomb code achieves a threshold of $1.5\% < p <2.0\%$, where $p$ is the collective error rate of the two-body measurement gate - including both measurement and correlated data depolarization error processes. With such gates at a physical error rate of $10^{-3}$, we project that the honeycomb code can reach the teraquop regime with only $600$ physical qubits.