# A Fault-Tolerant Honeycomb Memory

@article{Gidney2021AFH, title={A Fault-Tolerant Honeycomb Memory}, author={Craig Gidney and Michael Newman and Austin G. Fowler and Mick Broughton}, journal={Quantum}, year={2021}, volume={5}, pages={605} }

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…

## 19 Citations

### Hexagonal matching codes with two-body measurements

- Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2022

Here it is shown how the stabilizers of the code can be measured solely through two-body measurements that are native to the architecture, and how this achieves a result similar to the recently introduced Floquet codes, but via a completely different method.

### Fragile boundaries of tailored surface codes

- Physics
- 2022

Biased noise is common in physical qubits, and tailoring a quantum code to the bias by locally modifying stabilizers or changing boundary conditions has been shown to greatly increase error…

### Fragile boundaries of tailored surface codes and improved decoding of circuit-level noise

- Computer Science
- 2022

This work introduces e-cient and fault-tolerant decoders, belief-matching and belief-ﬁnd, which exploit correlated hyperedge fault mechanisms present in circuit-level noise, and suggests that fragility could remain a signi ﬁcant obstacle, even for other tailored codes.

### Planar Floquet Codes

- Computer Science
- 2021

This work shows a way to introduce boundaries to the system which curiously presents a rotating dynamics but has constant distance and is therefore not faulttolerant.

### Performance of planar Floquet codes with Majorana-based qubits

- Physics, Computer Science
- 2022

Two variants of Floquet codes can be implemented on MZM-based architectures without any auxiliary qubits for syndrome measurement and with shallow syndrome extraction sequences and it is shown that they improve the threshold for scalable quantum computation in MZm-based systems by an order of magnitude, and reduces space and time overheads below threshold.

### Benchmarking the Planar Honeycomb Code

- PhysicsQuantum
- 2022

We improve the planar honeycomb code by describing boundaries that need no additional physical connectivity, and by optimizing the shape of the qubit patch. We then benchmark the code using Monte…

### Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model

- Physics
- 2022

We consider a paradigmatic solvable model of topological order in two dimensions, Kitaev’s honeycomb Hamiltonian, and turn it into a measurement-only dynamics consisting of stochastic measurements of…

### Floquet codes without parent subsystem codes

- Physics
- 2022

We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS…

### Crystalline Quantum Circuits

- Computer Science
- 2022

This work constructs classes of nonrandom unitary Cliﬀord circuits by imposing translation invariance in both time and space and breaks unitarity by adding spacetime-translation-invariant measurements and a class of circuits with fractal dynamics.

### Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes

- MathematicsPhysical Review B
- 2022

The recent “honeycomb code” is a fault-tolerant quantum memory deﬁned by a sequence of checks which implements a nontrivial automorphism of the toric code. We argue that a general framework to…

## References

SHOWING 1-10 OF 44 REFERENCES

### Triangular color codes on trivalent graphs with flag qubits

- Computer Science
- 2019

This work numerically estimates the threshold of the triangular color code to be 0.2%, and proves that 1-flag stabilizer measurement circuits are sufficient to preserve the full code distance, which may be used to find simpler syndrome extraction circuits of the color code.

### Subsystem surface codes with three-qubit check operators

- Computer Science, PhysicsQuantum Inf. Comput.
- 2013

A simplified version of the Kitaev's surface code in which error correction requires only three-qubit parity measurements for Pauli operators XXX and ZZZ is proposed and the new subsystem surface code (SSC) gives rise to an exactly solvable Hamiltonian with 3-qubits interactions, topologically ordered ground state, and a constant energy gap.

### Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits

- Computer Science, PhysicsPhysical Review X
- 2020

This work modify minimum weight perfect matching decoding to efficiently and scalably incorporate information from measurements of the flag qubits and correct up to the full code distance while respecting the limited connectivity.

### Constructions and noise threshold of topological subsystem codes

- Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2011

It is demonstrated that topological subsystem codes (TSCs) can be viewed as generalizations of Kitaev's honeycomb model to 3-valent hypergraphs, which provides a systematic way of constructing TSCs and analyzing their properties.

### Single-shot quantum error correction with the three-dimensional subsystem toric code

- Computer ScienceNature Communications
- 2022

It is proved that one round of parity-check measurements suffices to perform reliable QEC with the 3D STC even in the presence of measurement errors, and an efficient single-shot QEC decoding strategy is proposed.

### Fault-tolerant weighted union-find decoding on the toric code

- Computer Science
- 2020

This work benchmarked a weighted variant of the union-find decoder on the toric code under circuit-level depolarizing noise, which preserves the almost-linear time complexity of the original while significantly increasing the performance in the fault-tolerance setting.

### Topological quantum error correction in the Kitaev honeycomb model

- Physics
- 2017

The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is…

### Surface codes: Towards practical large-scale quantum computation

- Physics, Computer Science
- 2012

The concept of the stabilizer, using two qubits, is introduced, and the single-qubit Hadamard, S and T operators are described, completing the set of required gates for a universal quantum computer.

### Modeling noise and error correction for Majorana-based quantum computing

- Physics, Computer ScienceQuantum
- 2018

Stochastic Majorana noise models are developed that are generalizations of the standard qubit-based models and connected to parameters of the physical system to emphasize the importance of correlated errors induced in multi-qubit measurements.

### Experimental demonstration of continuous quantum error correction

- PhysicsNature communications
- 2022

The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction.…