Deep neural decoders for near term fault-tolerant experiments

Abstract

Finding efficient decoders for quantum error correcting codes adapted to realistic experimental noise in fault-tolerant devices represents a significant challenge. In this paper we introduce several decoding algorithms complemented by deep neural decoders and apply them to analyze several fault-tolerant error correction protocols such as the surface code as well as Steane and Knill error correction. Our methods require no knowledge of the underlying noise model afflicting the quantum device making them appealing for real-world experiments. Our analysis is based on a full circuit-level noise model. It considers both distance-three and five codes, and is performed near the codes pseudo-threshold regime. Training deep neural decoders in low noise rate regimes appears to be a challenging machine learning endeavour. We provide a detailed description of our neural network architectures and training methodology. We then discuss both the advantages and limitations of deep neural decoders. Lastly, we provide a rigorous analysis of the decoding runtime of trained deep neural decoders and compare our methods with anticipated gate times in future quantum devices. Given the broad applications of our decoding schemes, we believe that the methods presented in this paper could have practical applications for near term fault-tolerant experiments.

arXiv comment26 pages, 8 tables, 28 figures. Comments welcome! v2 includes fixes to minor typos and expanded discussions

References in corpus (39)

• Fault-tolerant quantum computation by anyons
• Surface codes: Towards practical large-scale quantum computation
• Good Quantum Error-Correcting Codes Exist
• Topological quantum memory
• Quantum Error Correction for Quantum Memories
• Quantum Computing with Very Noisy Devices
• Quantum information processing with superconducting circuits: a review
• Elucidating Reaction Mechanisms on Quantum Computers
• Topological Quantum Distillation
• Experimental Comparison of Two Quantum Computing Architectures
• Quantum orders in an exact soluble model
• Active stabilisation, quantum computation and quantum state synthesis
• Low-distance Surface Codes under Realistic Quantum Noise
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• Fast Decoders for Topological Quantum Codes
• Universal fault-tolerant quantum computation with only transversal gates and error correction
• A Neural Decoder for Topological Codes
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Machine-learning-assisted correction of correlated qubit errors in a topological code
• Effective fault-tolerant quantum computation with slow measurements
• Anyon computers with smaller groups
• Flag fault-tolerant error correction with arbitrary distance codes
• Decoding Small Surface Codes with Feedforward Neural Networks
• Optimal and Efficient Decoding of Concatenated Quantum Block Codes
• High threshold error correction for the surface code
• Using concatenated quantum codes for universal fault-tolerant quantum gates
• The surface code with a twist
• Tensor-Network Simulations of the Surface Code under Realistic Noise
• Universal fault-tolerant gates on concatenated stabilizer codes
• Fault-Tolerant Quantum Computing in the Pauli or Clifford Frame with Slow Error Diagnostics
• Scalable Neural Network Decoders for Higher Dimensional Quantum Codes
• Overhead analysis of universal concatenated quantum codes
• Thresholds for universal concatenated quantum codes
• Towards practical classical processing for the surface code: timing analysis
• Topological code Autotune
• Linear-time general decoding algorithm for the surface code
• Hard decoding algorithm for optimizing thresholds under general Markovian noise
• Efficient simulation of quantum error correction under coherent error based on non-unitary free-fermionic formalism
• The Small Stellated Dodecahedron Code and Friends

Cited by in corpus (50)

• Experimental quantum speed-up in reinforcement learning agents
• Optimizing Quantum Error Correction Codes with Reinforcement Learning
• Machine Learning for Quantum Matter
• Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes
• Quantum error correction for the toric code using deep reinforcement learning
• Triangular color codes on trivalent graphs with flag qubits
• Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network
• The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
• Neural-Network Decoders for Quantum Error Correction using Surface Codes:A Space Exploration of the Hardware Cost-Performance Trade-Offs
• Advantages of versatile neural-network decoding for topological codes
• Comparing neural network based decoders for the surface code
• Reinforcement Learning Decoders for Fault-Tolerant Quantum Computation
• Neural network decoder for topological color codes with circuit level noise
• Fault-tolerant preparation of approximate GKP states
• Quantum Error Correction with the Semion Code
• Fault-Tolerant Weighted Union-Find Decoding on the Toric Code
• Scalable Neural Decoder for Topological Surface Codes
• Decoding algorithms for surface codes
• A scalable and fast artificial neural network syndrome decoder for surface codes
• Artificial Intelligence for Quantum Computing
• Reinforcement learning for optimal error correction of toric codes
• Neural Network Decoders for Large-Distance 2D Toric Codes
• Deep Q-learning decoder for depolarizing noise on the toric code
• Techniques for combining fast local decoders with global decoders under circuit-level noise
• Neural ensemble decoding for topological quantum error-correcting codes
• Symmetries for a High Level Neural Decoder on the Toric Code
• Achieving fault tolerance on capped color codes with few ancillas
• Determination of the Semion Code Threshold using Neural Decoders
• Enhancing variational Monte Carlo using a programmable quantum simulator
• Data-driven decoding of quantum error correcting codes using graph neural networks
• Neural network decoder for near-term surface-code experiments
• Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes
• Artificial Neural Network Syndrome Decoding on IBM Quantum Processors
• On maximum-likelihood decoding with circuit-level errors
• Error-rate-agnostic decoding of topological stabilizer codes
• Efficient diagnostics for quantum error correction
• Concatenate codes, save qubits
• Check-Agnosia based Post-Processor for Message-Passing Decoding of Quantum LDPC Codes
• Low-overhead quantum error correction codes with a cyclic topology
• Synergy between noisy quantum computers and scalable classical deep learning
• Rescaling decoder for 2D topological quantum color codes on 4.8.8 lattices
• A NEAT Quantum Error Decoder
• Introduction to Quantum Error Correction with Stabilizer Codes
• Efficient Syndrome Decoder for Heavy Hexagonal QECC via Machine Learning
• Towards a Cryogenic CMOS-Memristor Neural Decoder for Quantum Error Correction
• Self-attention U-Net decoder for toric codes
• Challenges and opportunities in the supervised learning of quantum circuit outputs
• Neural Decoders for Universal Quantum Algorithms
• Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
• On the interpretability of neural network decoders