Techniques for combining fast local decoders with global decoders under circuit-level noise

Abstract

Implementing algorithms on a fault-tolerant quantum computer will require fast decoding throughput and latency times to prevent an exponential increase in buffer times between the applications of gates. In this work we begin by quantifying these requirements. We then introduce the construction of local neural network (NN) decoders using three-dimensional convolutions. These local decoders are adapted to circuit-level noise and can be applied to surface code volumes of arbitrary size. Their application removes errors arising from a certain number of faults, which serves to substantially reduce the syndrome density. Remaining errors can then be corrected by a global decoder, such as Blossom or Union Find, with their implementation significantly accelerated due to the reduced syndrome density. However, in the circuit-level setting, the corrections applied by the local decoder introduce many vertical pairs of highlighted vertices. To obtain a low syndrome density in the presence of vertical pairs, we consider a strategy of performing a syndrome collapse which removes many vertical pairs and reduces the size of the decoding graph used by the global decoder. We also consider a strategy of performing a vertical cleanup, which consists of removing all local vertical pairs prior to implementing the global decoder. Lastly, we estimate the cost of implementing our local decoders on Field Programmable Gate Arrays (FPGAs).

arXiv comment28 pages, 24 figures. Comments welcome! V2 Contains a more detailed FPGA analysis

References in corpus (56)

• Fault-tolerant quantum computation by anyons
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Quantum Mechanics helps in searching for a needle in a haystack
• Surface codes: Towards practical large-scale quantum computation
• Good Quantum Error-Correcting Codes Exist
• Topological quantum memory
• Quantum Error Correction for Quantum Memories
• Multiple Particle Interference and Quantum Error Correction
• Quantum Computing with Very Noisy Devices
• A Theory of Fault-Tolerant Quantum Computation
• Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Low-distance Surface Codes under Realistic Quantum Noise
• Building a fault-tolerant quantum computer using concatenated cat codes
• Fast Decoders for Topological Quantum Codes
• Universal fault-tolerant quantum computation with only transversal gates and error correction
• Almost-linear time decoding algorithm for topological codes
• Magic State Distillation: Not as Costly as You Think
• A Neural Decoder for Topological Codes
• Skip Connections Matter: On the Transferability of Adversarial Examples Generated with ResNets
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Machine-learning-assisted correction of correlated qubit errors in a topological code
• Fault-tolerant quantum computation
• Decoding Small Surface Codes with Feedforward Neural Networks
• Deep Neural Network Probabilistic Decoder for Stabilizer Codes
• Quantum error correction for the toric code using deep reinforcement learning
• Triangular color codes on trivalent graphs with flag qubits
• Universal quantum computing with twist-free and temporally encoded lattice surgery
• Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes
• Deep neural decoders for near term fault-tolerant experiments
• Comparing neural network based decoders for the surface code
• Universal fault-tolerant gates on concatenated stabilizer codes
• Reinforcement Learning Decoders for Fault-Tolerant Quantum Computation
• Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
• Cellular-automaton decoders with provable thresholds for topological codes
• Low overhead quantum computation using lattice surgery
• Fault-Tolerant Weighted Union-Find Decoding on the Toric Code
• Code Deformation and Lattice Surgery Are Gauge Fixing
• Scalable Neural Decoder for Topological Surface 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
• Graph Based Convolutional Neural Network
• A scalable and fast artificial neural network syndrome decoder for surface codes
• Cellular automaton decoders of topological quantum memories in the fault tolerant setting
• Reinforcement learning for optimal error correction of toric codes
• Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
• Neural Network Decoders for Large-Distance 2D Toric Codes
• A local pre-decoder to reduce the bandwidth and latency of quantum error correction
• Deep Q-learning decoder for depolarizing noise on the toric code
• A circuit-level protocol and analysis for twist-based lattice surgery
• Neural ensemble decoding for topological quantum error-correcting codes
• Hierarchical decoding to reduce hardware requirements for quantum computing
• Symmetries for a High Level Neural Decoder on the Toric Code

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