Space-group codes—CSS codes whose stabilizers use crystallographic point-group symmetries—can be topologically ordered and geometrically local, and some match or beat bivariate-bicycle benchmarks.
Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays
13 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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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2026 13roles
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Presents planar open-boundary quantum LDPC codes with nearest-neighbor iSWAP-based syndrome extraction that outperform rotated surface codes in code-efficiency and logical error rate on finite instances like [[323,14,15]].
Classical repetition-code framing plus SAT search yields no-go theorems (no d>3 T-to-T on <8 qubits) and the smallest known unitary factories for d=4,5 T-states (10–11 qubits) and d=3,4 CCZ-states (9–10 qubits).
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.
A symmetry-co-designed high-rate QEC architecture with parallel STAR injection on bivariate bicycle codes achieves ~5.5x space savings for TFIM and Fermi-Hubbard simulations versus surface-code STAR.
A new RL-LS BP decoder for QLDPC codes combines learned variable-node scheduling with list-based search and cumulative path metrics, showing improved performance over standard BP on the depolarizing channel.
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.
New structural conditions on affine permutation matrices yield ultra-high-rate quantum LDPC codes (rate >1/2) with near-teraquop logical error rates under circuit-level noise on reconfigurable atom arrays.
Constructs a [[34542,23032,d≤310]] rate-2/3 girth-8 quantum LDPC CSS code from two-branch finite-field bases and CPM lifts with no decoder failures in 10^8 trials at p=0.01.
citing papers explorer
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Topological Codes from Space Groups: A Route beyond Translation Invariance
Space-group codes—CSS codes whose stabilizers use crystallographic point-group symmetries—can be topologically ordered and geometrically local, and some match or beat bivariate-bicycle benchmarks.
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Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid
Presents planar open-boundary quantum LDPC codes with nearest-neighbor iSWAP-based syndrome extraction that outperform rotated surface codes in code-efficiency and logical error rate on finite instances like [[323,14,15]].
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Exploring the landscape of compact magic-state distillation factories
Classical repetition-code framing plus SAT search yields no-go theorems (no d>3 T-to-T on <8 qubits) and the smallest known unitary factories for d=4,5 T-states (10–11 qubits) and d=3,4 CCZ-states (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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Fast and Parallel High-Rate STAR Architecture for Megaquop Quantum Simulation
A symmetry-co-designed high-rate QEC architecture with parallel STAR injection on bivariate bicycle codes achieves ~5.5x space savings for TFIM and Fermi-Hubbard simulations versus surface-code STAR.
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Learning-Based List Sequential Belief Propagation Decoding of Quantum LDPC Codes
A new RL-LS BP decoder for QLDPC codes combines learned variable-node scheduling with list-based search and cumulative path metrics, showing improved performance over standard BP on the depolarizing channel.
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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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Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays
New structural conditions on affine permutation matrices yield ultra-high-rate quantum LDPC codes (rate >1/2) with near-teraquop logical error rates under circuit-level noise on reconfigurable atom arrays.
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Rate-2/3 Girth-8 (3,18)-Regular Quantum LDPC Codes from Two-Branch Finite-Field Bases and CPM Lifts
Constructs a [[34542,23032,d≤310]] rate-2/3 girth-8 quantum LDPC CSS code from two-branch finite-field bases and CPM lifts with no decoder failures in 10^8 trials at p=0.01.
- High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures