Biased-Noise Quantum Reed-Solomon Codes and a Tornado Concatenation for Cat Qubits

• URL: http://arxiv.org/abs/2607.13105v3
• Date: Tue, 21 Jul 2026 22:49:23 GMT
• Title: Biased-Noise Quantum Reed-Solomon Codes and a Tornado Concatenation for Cat Qubits
• Abstract summary: We build a bit-flip-only quantum Reed-Solomon (RS) code.<n>Errors are decoded by an optimal bounded-distance syndrome-lookup table.<n>Monte-Carlo simulation shows that at a physical bit-flip rate $p = 0.1$ the Tornado code reaches a logical error rate $p_L approx 5.3 times 10-3$, below both parent codes.
• Score: 0.9485024320296608
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Dissipative cat qubits exponentially suppress one Pauli error channel with the mean photon number, leaving the conjugate bit-flip error as the dominant failure mode. This strong noise bias makes the full machinery of general quantum error correction unnecessary: a code need only protect against a single error type, and any classical linear code can be promoted to a Clifford stabilizer code that does exactly this. We use this observation to build a bit-flip-only quantum Reed-Solomon (RS) code. Starting from the maximum-distance-separable RS code [7, 3, 5] over GF($2^3$), we binary-expand it to the linear code [21, 9, 6] over GF(2) and realize it as a [[21, 9, $d_X = 6, d_Z = 1$]] bit-flip code whose stabilizers are products of $Z$ operators. Because no phase-flip correction is attempted, the construction discards the redundancy that standard quantum RS codes spend on correcting $Z$ errors -- which a strongly biased cat qubit renders unnecessary -- and yields a shallow Clifford circuit that samples directly in Stim. Errors are decoded by an optimal bounded-distance syndrome-lookup table. We then introduce a Tornado architecture: a two-layer concatenation that wraps every position of the outer RS code in an inner distance-three repetition code, yielding a [[63, 9, 18]] code decoded by a two-stage inner majority vote and outer lookup decoder. Monte-Carlo simulation shows that at a physical bit-flip rate $p = 0.1$ the Tornado code reaches a logical error rate $p_L \approx 5.3 \times 10^{-3}$, below both parent codes, and that its logical error rate scales as $p_L \propto p^6$ at low $p$, in contrast to $p^2$ for the repetition code and $p^3$ for the standalone RS code. We give the exact construction, the error and circuit model, an asymptotic scaling analysis, and an honest account of the overhead cost and single-shot assumptions.

Related papers

• The Gain-Engineered Transmon [68.89136228609398]
  We introduce and experimentally realize a noise-biased qubit in a standard transmon-readout resonator circuit.<n>Our results open a path towards using this system as a simple building-block for hardware-efficient quantum error detection and correction schemes.
  arXiv  Detail & Related papers  (2026-08-26T17:00:42Z)
• Quantum error correction at ultra-low overhead [0.0]
  Suppressing errors is the central challenge for useful large-scale quantum computing.<n>We introduce Cornucopia codes, a family of practical, hardware-efficient quantum low-density parity-check codes.<n>Results bring demonstrations of ultra-low overhead quantum error correction within the reach of near-term quantum processors.
  arXiv  Detail & Related papers  (2026-08-03T18:13:57Z)
• A polynomial-time approximation scheme for minimum-weight decoding of topological codes [42.44256445495892]
  Two-dimensional topological translationally in (2D TTI) stabilizer codes lie at the heart of fault-tolerant quantum computation.<n>Minimum-weight decoding of these codes was recently shown to be NP-hard, even in basic settings.
  arXiv  Detail & Related papers  (2026-06-16T16:44:08Z)
• High-threshold decoding of non-Pauli codes for 2D universality [0.15999407512883507]
  Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead.<n>A core challenge for these codes is to achieve a low-overhead universal gate set with limited connectivity.<n>We explore a non-Pauli stabilizer code that can be used to complete a universal gate set on topological toric and surface codes in strictly two dimensions.
  arXiv  Detail & Related papers  (2026-04-02T13:39:46Z)
• Mirror codes: High-threshold quantum LDPC codes beyond the CSS regime [0.0]
  This work makes two contributions towards error-corrected quantum devices.<n>First, we introduce mirror codes, a simple yet flexible construction of LDPC stabilizer codes.<n>Second, we construct syndrome extraction circuits that trade overhead for provable fault tolerance.
  arXiv  Detail & Related papers  (2026-03-05T18:58:58Z)
• Elevator Codes: Concatenation for resource-efficient quantum memory under biased noise [0.0]
  Biased-noise qubits can significantly reduce the overhead of quantum error correction.<n>Codes such as the rectangular surface code or XZZX code substantially reduce the qubit overhead under biased noise.<n>We introduce a 2D local code construction that outperforms these codes for noise biases $ge 7times104$.
  arXiv  Detail & Related papers  (2026-01-15T19:00:00Z)
• Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction [44.698141103370546]
  GraphQEC is a code-agnostic decoder leveraging machine-learning on the graph structure of stabilizer codes with linear time complexity.<n>Our approach represents the first universal solution for real-time quantum error correction across arbitrary stabilizer codes.
  arXiv  Detail & Related papers  (2025-02-27T10:56:53Z)
• Universal quantum computation via scalable measurement-free error correction [45.29832252085144]
  We show that universal quantum computation can be made fault-tolerant in a scenario where the error-correction is implemented without mid-circuit measurements.<n>We introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $mathitCCZ$ gate.<n>In particular, our findings support that below-breakeven logical performance is achievable with a circuit-level error rate below $10-3$.
  arXiv  Detail & Related papers  (2024-12-19T18:55:44Z)
• Demonstrating dynamic surface codes [118.67046728951689]
  We experimentally demonstrate three time-dynamic implementations of the surface code.<n>First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three.<n>Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors.<n>Third, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead.
  arXiv  Detail & Related papers  (2024-12-18T21:56:50Z)
• Hardware-efficient quantum error correction via concatenated bosonic qubits [41.6475446744259]
  Quantum computers will need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits.<n>Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits.<n>We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold.
  arXiv  Detail & Related papers  (2024-09-19T18:00:53Z)
• Quantum error correction below the surface code threshold [107.92016014248976]
  Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit. We present two surface code memories operating below a critical threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.
  arXiv  Detail & Related papers  (2024-08-24T23:08:50Z)
• Exact results on finite size corrections for surface codes tailored to biased noise [0.0]
  We study the XY and XZZX surface codes under phase-biased noise. We find exact solutions at a special disordered point. We show that calculating thresholds based not only on the total logical failure rate, but also independently on the phase- and bit-flip logical failure rates, gives a more confident estimate.
  arXiv  Detail & Related papers  (2024-01-08T16:38:56Z)
• Local Probabilistic Decoding of a Quantum Code [0.0]
  flip is an extremely simple and maximally local classical decoder. Lowest-weight uncorrectable errors for this decoder are closer to correctable errors than to other uncorrectable errors. Introducing randomness into the decoder can allow it to correct these "uncorrectable" errors with finite probability.
  arXiv  Detail & Related papers  (2022-12-14T02:44:26Z)
• Avoiding coherent errors with rotated concatenated stabilizer codes [6.85316573653194]
  We integrate stabilizer codes with constant-excitation codes by code concatenation. We analyze this code's potential as a quantum memory.
  arXiv  Detail & Related papers  (2020-10-01T16:39:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.