Fault-tolerant error correction with the gauge color code

Abstract

The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a universal set of computational operations with the minimal cost in quantum resources remains an important and ongoing challenge. One proposal of significant recent interest is the gauge color code. Notably, this code may offer a reduced resource cost over other well-studied fault-tolerant architectures using a new method, known as gauge fixing, for performing the non-Clifford logical operations that are essential for universal quantum computation. Here we examine the gauge color code when it is subject to noise. Specifically we make use of single-shot error correction to develop a simple decoding algorithm for the gauge color code, and we numerically analyse its performance. Remarkably, we find threshold error rates comparable to those of other leading proposals. Our results thus provide encouraging preliminary data of a comparative study between the gauge color code and other promising computational architectures.

v1 - 5+4 pages, 11 figures, comments welcome; v2 - minor revisions, new supplemental including a discussion on correlated errors and details on threshold calculations; v3 - Author accepted manuscript. Accepted on 21/06/16. Deposited on 29/07/16. 9+5 pages, 17 figures, new version includes resource scaling analysis in below threshold regime, see eqn. (4) and methods section

References in corpus (15)

• Surface codes: Towards practical large-scale quantum computation
• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Restrictions on Transversal Encoded Quantum Gate Sets
• Magic state distillation with low overhead
• Topological quantum computing with a very noisy network and local error rates approaching one percent
• Topological Computation without Braiding
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Unfolding the color code
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Universal transversal gates with color codes - a simplified approach
• A magic state's fidelity can be superior to the operations that created it
• Fault-tolerant quantum computation versus Gaussian noise
• Improved HDRG decoders for qudit and non-Abelian quantum error correction
• Active error correction for Abelian and non-Abelian anyons

Cited by in corpus (72)

• Roads towards fault-tolerant universal quantum computation
• A Neural Decoder for Topological Codes
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Quantum computation with realistic magic state factories
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Factoring 2048-bit RSA Integers in 177 Days with 13436 Qubits and a Multimode Memory
• A theory of single-shot error correction for adversarial noise
• A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost
• Triangular color codes on trivalent graphs with flag qubits
• Advantages of versatile neural-network decoding for topological codes
• Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
• Parallel window decoding enables scalable fault tolerant quantum computation
• A fault-tolerant non-Clifford gate for the surface code in two dimensions
• Cellular-automaton decoders with provable thresholds for topological codes
• Single-shot error correction of three-dimensional homological product codes
• Parallelized quantum error correction with fracton topological codes
• Analysing correlated noise on the surface code using adaptive decoding algorithms
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Three-dimensional color code thresholds via statistical-mechanical mapping
• Error Rates and Resource Overheads of Repetition Cat Qubits
• A logical qubit in a linear array of semiconductor quantum dots
• Unifying gate-synthesis and magic state distillation
• Combining hard and soft decoders for hypergraph product codes
• Pauli topological subsystem codes from Abelian anyon theories
• Universal fault-tolerant measurement-based quantum computation
• Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
• Improved single-shot decoding of higher dimensional hypergraph product codes
• Characterization of solvable spin models via graph invariants
• Fault-tolerant interface between quantum memories and quantum processors
• Symmetry-protected self-correcting quantum memories
• An efficient magic state approach to small angle rotations
• Cellular automaton decoders of topological quantum memories in the fault tolerant setting
• Temporal-mode continuous-variable 3-dimensional cluster state for topologically-protected measurement-based quantum computation
• Beyond single-shot fault-tolerant quantum error correction
• Morphing quantum codes
• A decoder for the triangular color code by matching on a Möbius strip
• Optimization of Lattice Surgery is NP-Hard
• QVECTOR: an algorithm for device-tailored quantum error correction
• Efficient color code decoders in $d\ge 2$ dimensions from toric code decoders
• Renormalization group decoder for a four-dimensional toric code
• Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code
• Tailoring three-dimensional topological codes for biased noise
• The role of entropy in topological quantum error correction
• Resilience to time-correlated noise in quantum computation
• Fault-tolerant fermionic quantum computation based on color code
• Achieving fault tolerance on capped color codes with few ancillas
• Decoding of Quantum Data-Syndrome Codes via Belief Propagation
• Projecting 3D color codes onto 3D toric codes
• Dual correspondence between classical spin models and quantum CSS states
• Symmetry protected self correcting quantum memory in three space dimensions
• Experiments with the 4D Surface Code on a QCCD Quantum Computer
• Doubled Color Codes
• Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models
• Correcting spanning errors with a fractal code
• Nonlocal discrete time crystals in periodically driven surface codes
• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
• On maximum-likelihood decoding with circuit-level errors
• Quantum convolutional data-syndrome codes
• Fault-tolerant compiling of classically hard IQP circuits on hypercubes
• Local Probabilistic Decoding of a Quantum Code
• Phase diagram of the three-dimensional subsystem toric code
• Generalized quantum data-syndrome codes and belief propagation decoding for phenomenological noise
• Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma
• Single-shot and measurement-based quantum error correction via fault complexes
• Enhancing Quantum Memory Lifetime with Measurement-Free Local Error Correction and Reinforcement Learning
• High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory
• Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
• Accurate Leakage Speculation for Quantum Error Correction
• Quantum repetition codes as building blocks of large period discrete time crystals
• Planar fault-tolerant circuits for non-Clifford gates on the 2D color code
• Color code with a logical control-$S$ gate using transversal $T$ rotations
• Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory