A Fault-Tolerant Honeycomb Memory

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.

17 pages, 10 figures, 2 tables

References in corpus (13)

• Surface codes: Towards practical large-scale quantum computation
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Exponential suppression of bit or phase flip errors with repetitive error correction
• Stim: a fast stabilizer circuit simulator
• Initialization by measurement of a two-qubit superconducting circuit
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Two-Qubit State Tomography using a Joint Dispersive Read-Out
• Dynamically Generated Logical Qubits
• Experimental demonstration of continuous quantum error correction
• Fault-Tolerant Weighted Union-Find Decoding on the Toric Code
• Physical model of continuous two-qubit parity measurement in a cavity-QED network
• Three-qubit direct dispersive parity measurement with Tunable Coupling Qubits
• Single-shot quantum error correction with the three-dimensional subsystem toric code

Cited by in corpus (57)

• Sparse Blossom: correcting a million errors per core second with minimum-weight matching
• Biology and medicine in the landscape of quantum advantages
• Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network
• Calibrated decoders for experimental quantum error correction
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes
• Floquet codes without parent subsystem codes
• Anyon condensation and the color code
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes
• Boundaries for the Honeycomb Code
• Performance of planar Floquet codes with Majorana-based qubits
• Pauli topological subsystem codes from Abelian anyon theories
• Benchmarking the Planar Honeycomb Code
• Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
• Quantum computation from dynamic automorphism codes
• Engineering 3D Floquet codes by rewinding
• Stability Experiments: The Overlooked Dual of Memory Experiments
• Crystalline Quantum Circuits
• Inplace Access to the Surface Code Y Basis
• The XYZ${}^2$ hexagonal stabilizer code
• Efficient Magic State Distillation by Zero-Level Distillation
• A Pair Measurement Surface Code on Pentagons
• Fermionic approach to variational quantum simulation of Kitaev spin models
• Single-Step Parity Check Gate Set for Quantum Error Correction
• Fault-tolerant quantum architectures based on erasure qubits
• Comparative study of quantum error correction strategies for the heavy-hexagonal lattice
• ERASER: Towards Adaptive Leakage Suppression for Fault-Tolerant Quantum Computing
• Designing fault-tolerant circuits using detector error models
• Fault-tolerant hyperbolic Floquet quantum error correcting codes
• Dynamical Logical Qubits in the Bacon-Shor Code
• XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime
• Local Clustering Decoder as a fast and adaptive hardware decoder for the surface code
• Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays
• LUCI in the Surface Code with Dropouts
• Hexagonal matching codes with 2-body measurements
• Low-overhead quantum error correction codes with a cyclic topology
• Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements
• Snakes and Ladders: Adapting the surface code to defects
• Quantum Computation by Spin Parity Measurements with Encoded Spin Qubits
• Error Correction in Dynamical Codes
• Almost fault-tolerant quantum machine learning with drastic overhead reduction
• Decoding across transversal Clifford gates in the surface code
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code
• Distributed quantum error correction based on hyperbolic Floquet codes
• High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory
• Distance-four quantum codes with combined postselection and error correction
• Quantum control without quantum states
• Contextuality of Quantum Error-Correcting Codes
• Planar Floquet Codes
• Multiqubit Rydberg Gates for Quantum Error Correction
• Logical operations with a dynamical qubit in Floquet-Bacon-Shor code
• A dynamic circuit for the honeycomb Floquet code
• Increasing the distance of topological codes with time vortex defects
• Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
• Pinball: A Cryogenic Predecoder for Surface Code Decoding Under Circuit-Level Noise
• Generalized Code Distance through Rotated Logical States in Quantum Error Correction
• Phases of Floquet code under local decoherence