Classical codes plus SAT search yield no-go theorems limiting error detection in sub-8-qubit distillation and new minimal-qubit protocols for T-to-T (distances 4-5 on 10-11 qubits) and T-to-CCZ (distances 3-4 on 9-10 qubits).
Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead through high-rate encodings, yet finite-size instances with practical logical error rates often achieve encoding rates only around or below $1/10$. Here, building on a recent ultra-high-rate construction by Kasai, we identify new structural conditions on the underlying affine permutation matrices that make encoding rates exceeding $1/2$ compatible with efficient implementation on reconfigurable neutral atom arrays. These conditions define a co-designed family of ultra-high-rate quantum codes that supports efficient syndrome extraction and atom rearrangement under realistic parallel control constraints. Using a hierarchical decoder with high accuracy and good throughput, we study the performance under a circuit-level noise model with $p=0.1\%$, achieving per-logical-per-round error rates of $1.3_{-0.9}^{+3.0} \times 10^{-13}$ with a $[[2304,1156,\leq 14]]$ code and $2.9_{-1.5}^{+3.1} \times 10^{-11}$ with a $[[1152,580,\leq 12]]$ code. We compare these codes against a heuristic Pareto frontier for finite-blocklength codes relating block length, encoding rate, and logical error rates, and find that our codes lie near the frontier. These results approach the teraquop regime, highlighting the promise of this code family for practical ultra-high-rate quantum error correction.
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GB codes are expressed as cyclic submodules of R_ℓ² to derive necessary and sufficient conditions for block-separable automorphisms and fold-transversal gates, with the new MCR family demonstrated to generate the 2-qubit Clifford group for k=2 codes up to distance 13.
Neutral atom platform achieves repeated toric code syndrome extraction with qubit reloading, preserving logical information over 90 cycles and showing distance-dependent logical error suppression.
Full extractors for HGP codes are built to enable logical processing via PBC without compilation overhead, with sizes 50-80% of base codes and low error rates in simulations.
PIQC proposes a distributed FTQC architecture based on molecular quantum nodes with photonic integration, nuclear registers, loss-tolerant entanglement, and Floquetified qLDPC codes.
A forced-gap post-selection strategy using repeated Relay-BP decoder runs improves logical error rates by over 4x on 72- and 144-qubit bivariate bicycle codes at fixed post-selection rate.
A new [[16384,4142,≤40]] quantum LDPC code family is obtained by CPM-lifting a girth-8 base CSS code, achieving frame error rate ~10^{-8} at depolarizing noise p=0.085.
citing papers explorer
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Exploring the landscape of compact magic-state distillation factories
Classical codes plus SAT search yield no-go theorems limiting error detection in sub-8-qubit distillation and new minimal-qubit protocols for T-to-T (distances 4-5 on 10-11 qubits) and T-to-CCZ (distances 3-4 on 9-10 qubits).
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Generalized Bicycle Codes as Cyclic Submodules and their Automorphism Structure
GB codes are expressed as cyclic submodules of R_ℓ² to derive necessary and sufficient conditions for block-separable automorphisms and fold-transversal gates, with the new MCR family demonstrated to generate the 2-qubit Clifford group for k=2 codes up to distance 13.
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Quantum error correction with the toric code
Neutral atom platform achieves repeated toric code syndrome extraction with qubit reloading, preserving logical information over 90 cycles and showing distance-dependent logical error suppression.
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Full Extractors for Logical Processing in Hypergraph Product Codes
Full extractors for HGP codes are built to enable logical processing via PBC without compilation overhead, with sizes 50-80% of base codes and low error rates in simulations.
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PIQC: Scalable Distributed Quantum Computing via Photonic Integration of Designed Molecular Quantum Nodes
PIQC proposes a distributed FTQC architecture based on molecular quantum nodes with photonic integration, nuclear registers, loss-tolerant entanglement, and Floquetified qLDPC codes.
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Forced Gap Post-Selection for Quantum LDPC Codes and their Operations
A forced-gap post-selection strategy using repeated Relay-BP decoder runs improves logical error rates by over 4x on 72- and 144-qubit bivariate bicycle codes at fixed post-selection rate.
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High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures
A new [[16384,4142,≤40]] quantum LDPC code family is obtained by CPM-lifting a girth-8 base CSS code, achieving frame error rate ~10^{-8} at depolarizing noise p=0.085.