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Concatenated Quantum Codes
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abstract
One of the main problems for the future of practical quantum computing is to stabilize the computation against unwanted interactions with the environment and imperfections in the applied operations. Existing proposals for quantum memories and quantum channels require gates with asymptotically zero error to store or transmit an input quantum state for arbitrarily long times or distances with fixed error. In this report a method is given which has the property that to store or transmit a qubit with maximum error $\epsilon$ requires gates with error at most $c\epsilon$ and storage or channel elements with error at most $\epsilon$, independent of how long we wish to store the state or how far we wish to transmit it. The method relies on using concatenated quantum codes with hierarchically implemented recovery operations. The overhead of the method is polynomial in the time of storage or the distance of the transmission. Rigorous and heuristic lower bounds for the constant $c$ are given.
Forward citations
Cited by 13 Pith papers
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Blocklet concatenation: Low-overhead fault-tolerant protocols for fusion-based quantum computation
Blocklet concatenation yields fusion-based quantum computing protocols with constant-sized resource states, erasure thresholds up to 19.1%, and footprint per logical qubit scaling better than surface codes.
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A local automaton for the 2D toric code
A strictly local measurement-and-feedback decoder for the 2D toric code is built from hierarchical Tsirelson-type automata, preserving a logical qubit for times exponential in system size.
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Merging-Based Quantum Repeater
A merging-based quantum repeater that patches failed operations by recycling entanglement achieves higher simulated secret key rates than swapping-based repeaters.
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Oraqle: An Empirical Analysis of Qubit Readout and Discriminators in Quantum Error Correction
Using real 5-qubit traces, this study shows readout windows can be cut to ~600 ns with negligible QEC penalty and small discriminators match large ones.
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Arbitrary-Distance Quantum Error Correction with Gauss's Law for $\mathbb Z_2$ Lattice Gauge Theory
Gauss's law constraints in Z2 lattice gauge theory can be made into quantum error-correcting codes of arbitrary distance, with provably optimal encoding rate within the constructed family.
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Synthesis and Optimization of Encoding Circuits for Fault-Tolerant Quantum Computation
New search algorithms over stabilizer tableaus and modular assembly techniques yield encoders with up to 43% fewer two-qubit gates and 70% lower depth than prior constructions on tested stabilizer codes including qLDP...
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Coupled-Layer Construction of Quantum Product Codes
Tensor and balanced product codes arise from a coupled-layer construction via anyon condensation on stacked constituent codes.
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Growing Sparse Quantum Codes from a Seed
Conjoining only bit-flip and phase-flip repetition codes can generate any CSS code, and an iterative algorithm grows sparse subsystem codes with kd^2=O(n) worst-case scaling.
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Enhancing Decoding Performance using Efficient Error Learning
Using about 1% of Pauli error rates from Cycle Error Reconstruction plus a heuristic completion, maximum-likelihood decoding of concatenated Steane codes achieves roughly 5 to 10 times lower logical error rates than f...
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Quantum Error Correction Exploiting Degeneracy to Approach the Hashing Bound
A proposed quantum LDPC code with degeneracy-aware post-processing reaches FER 10^-4 at 9.45% depolarizing noise, approaching the hashing bound.
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Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction
VarQEC uses a distinguishability loss as a machine-learning objective to variationally discover resource-efficient encoding circuits optimized for given noise models.
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Entanglement-Assisted Concatenated Quantum Codes: Parameters and Asymptotic Performance
New families of concatenated entanglement-assisted quantum codes are claimed to beat known code tables, and the paper attempts to show such codes asymptotically reach the entanglement-assisted Gilbert-Varshamov bound.
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Design Automation in Quantum Error Correction
A comprehensive review of automated tools and methods for designing quantum error-corrected circuits, with case studies on T-gate optimization, surface-code layout, ML decoders, and verification.
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