QDistRnd: A GAP package for computing the distance of quantum error-correcting codes

• URL: http://arxiv.org/abs/2308.15140v1
• Date: Tue, 29 Aug 2023 09:17:57 GMT
• Title: QDistRnd: A GAP package for computing the distance of quantum error-correcting codes
• Abstract summary: GAP package QDistRnd implements a probabilistic algorithm for finding the minimum distance of a quantum low-density parity-check code linear over a finite field GF(q)
• Score: 0.029541734875307393
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The GAP package QDistRnd implements a probabilistic algorithm for finding the minimum distance of a quantum low-density parity-check code linear over a finite field GF(q). At each step several codewords are randomly drawn from a distribution biased toward smaller weights. The corresponding weights are used to update the upper bound on the distance, which eventually converges to the minimum distance of the code. While there is no performance guarantee, an empirical convergence criterion is given to estimate the probability that a minimum weight codeword has been found. In addition, a format for storing matrices associated with q-ary quantum codes is introduced and implemented via the provided import/export functions. The format, MTXE, is based on the well established MaTrix market eXchange (MTX) Coordinate format developed at NIST, and is designed for full backward compatibility with this format. Thus, MTXE files are readable by any software package which supports MTX.

Related papers

• SSTQ:Privacy-Preserving Vector Quantization via Subsampled Stochastic TurboQuant [79.24089819400126]
  Subsampled TurboQuant (SSTQ) is a framework that combines overcomplete equal-width tight frames, coordinate subsampling, and privacy-aware quantization.<n>SSTQ achieves mean squared error scaling while using only $lceil log N il + b$ bits per client, where $N = (d)$ is the frame size.<n>We also derive a surrogate privacy-aware codebook objective that reduces the codebook-dependent MSE scaling from $O(4b)$ to $O(2b)$.
  arXiv  Detail & Related papers  (2026-08-05T17:51:25Z)
• Approximating optimal decoding of quantum LDPC codes with narrow frontiers [1.8907108368038215]
  We introduce the Frontier decoder, a dynamic-programming decoder for sparse quantum decoding problems.<n>In the code-capacity setting, the decoder reaches thresholds close to optimal for the surface code and the color code.<n>When the list size is constant, the decoder has linear complexity, suggesting the possibility of low-latency implementations.
  arXiv  Detail & Related papers  (2026-06-18T17:34:11Z)
• Measurement Geometry for Quantum Random Access Codes: Beyond Nayak Bound and Toward Optimality [0.13999481573773068]
  Quantum random access codes (QRACs) ask how well N classical bits can be encoded into M qubits while allowing any single bit to be recovered.<n>We formulate the optimal decoding probability in terms of decoding measurements.<n>We show that decoding measurement of any two-qubit QRAC attaining the conjectured bound must form MUPVMs.
  arXiv  Detail & Related papers  (2026-06-10T21:41:58Z)
• Decoded Quantum Interferometry Beyond Hamming: Rank-Metric and Translation Association Schemes [39.146761527401424]
  Decoded Quantum Interferometry (DQI) uses coherent decoding and a quantum Fourier transform to find high-quality solutions of structured optimisation problems.<n>We extend the core DQI mechanism beyond Hamming space to finite geometries with translation symmetry.<n>We find solutions with an effective-rank proxy near min(m,n)-l, and the corresponding expected score can be converted into a constant-probability bound on the residual rank of a sample.
  arXiv  Detail & Related papers  (2026-06-03T13:12:15Z)
• Mitigating Bias in Locally Constrained Decoding via Tractable Proposals [73.78736135699953]
  Existing locally constrained decoding approaches enforce constraints by myopically masking out next tokens.<n>Recent work uses sequential Monte Carlo methods to mitigate such biases, but designing effective proposal distributions or potential functions remains a key challenge.<n>We propose a generic approach to construct proposals and potentials for SMC sampling from $p_mathrmlm( cdot mid mathrmconstraint)$.
  arXiv  Detail & Related papers  (2026-06-01T08:58:18Z)
• Towards Scalable Quaternary Message-Passing Decoding for Quantum Error Correction [6.120106694667796]
  This work takes a step toward a more principled and interpretable MP decoding framework.<n>We introduce a dilution method, which allows a quaternary Min-Sum (MS) decoder to exhibit an apparent depolarizing threshold.<n>For $X$-noise, the standard MS decoder under dilution has worst-case complexity $O(N log2 d)$ and outperforms BP-OSD at $d=65$.
  arXiv  Detail & Related papers  (2026-05-22T19:57:24Z)
• MatGPTQ: Accurate and Efficient Post-Training Matryoshka Quantization [35.18619976978831]
  Matryoshka Quantization (MatQuant) is a recent quantization approach showing that a single integer-quantized model can be served across multiple precisions.<n>We introduce Post-Training Matryoshka Quantization (MatGPTQ), a new PTQ pipeline that produces a single parent model jointly optimized for multiple target precisions in one-shot.
  arXiv  Detail & Related papers  (2026-02-03T13:52:18Z)
• Learning Grouped Lattice Vector Quantizers for Low-Bit LLM Compression [57.54335545892155]
  We introduce a Grouped Lattice Vector Quantization (GLVQ) framework that assigns each group of weights a customized lattice codebook.<n>Our approach achieves a better trade-off between model size and accuracy compared to existing post-training quantization baselines.
  arXiv  Detail & Related papers  (2025-10-23T20:19:48Z)
• Measurement incompatibility and quantum steering via linear programming [18.995314010885533]
  We develop a hierarchy of linear programs that compute upper and lower bounds on the robustness of quantum measurements.<n>We show how our methods can be used to construct local hidden state models for states, or conversely to certify that a given state exhibits steering.
  arXiv  Detail & Related papers  (2025-06-03T16:28:25Z)
• Robust Conformal Prediction with a Single Binary Certificate [58.450154976190795]
  Conformal prediction (CP) converts any model's output to prediction sets with a guarantee to cover the true label with (adjustable) high probability. We propose a robust conformal prediction that produces smaller sets even with significantly lower MC samples.
  arXiv  Detail & Related papers  (2025-03-07T08:41:53Z)
• Conditional Distribution Quantization in Machine Learning [83.54039134248231]
  Conditional expectation mathbbE(Y mid X) often fails to capture the complexity of multimodal conditional distributions mathcalL(Y mid X) We propose using n-point conditional quantizations--functional mappings of X that are learnable via gradient descent--to approximate mathcalL(Y mid X)
  arXiv  Detail & Related papers  (2025-02-11T00:28:24Z)
• MultiMax: Sparse and Multi-Modal Attention Learning [60.49318008131978]
  SoftMax is a ubiquitous ingredient of modern machine learning algorithms. We show that sparsity can be achieved by a family of SoftMax variants, but they often require an alternative loss function and do not preserve multi-modality. We propose MultiMax, which adaptively modulates the output distribution according to input entry range.
  arXiv  Detail & Related papers  (2024-06-03T10:51:43Z)
• Determining the upper bound of code distance of quantum stabilizer codes through Monte Carlo method based on fully decoupled belief propagation [19.39678519027849]
  In this paper, employing the idea of Monte Carlo method, we propose the algorithm of determining the upper bound of code distance of QSCs. Our algorithm shows high precision - the upper bound of code distance determined by the algorithm of a variety of QSCs whose code distance is known is consistent with actual code distance.
  arXiv  Detail & Related papers  (2024-02-09T15:40:55Z)
• The closed-branch decoder for quantum LDPC codes [0.0]
  Real-time decoding is a necessity for implementing arbitrary quantum computations on the logical level. We present a new decoder for Quantum Low Density Parity Check (QLDPC) codes, named the closed-branch decoder.
  arXiv  Detail & Related papers  (2024-02-02T16:22:32Z)
• DGR: Tackling Drifted and Correlated Noise in Quantum Error Correction via Decoding Graph Re-weighting [14.817445452647588]
  We propose an efficient decoding graph edge re-weighting strategy with no quantum overhead. DGR reduces the logical error rate by 3.6x on average-case noise mismatch with exceeding 5000x improvement under worst-case mismatch.
  arXiv  Detail & Related papers  (2023-11-27T18:26:16Z)
• Gaussian conversion protocol for heralded generation of qunaught states [66.81715281131143]
  bosonic codes map qubit-type quantum information onto the larger bosonic Hilbert space. We convert between two instances of these codes GKP qunaught states and four-foldsymmetric binomial states corresponding to a zero-logical encoded qubit. We obtain GKP qunaught states with a fidelity of over 98% and a probability of approximately 3.14%.
  arXiv  Detail & Related papers  (2023-01-24T14:17:07Z)
• Huber-energy measure quantization [0.0]
  We describe an algorithm which finds the best approximation of a target probability law by a sum of $Q$ Dirac masses. The procedure is implemented by minimizing the statistical distance between the original measure and its quantized version.
  arXiv  Detail & Related papers  (2022-12-15T21:50:54Z)
• Single-shot quantum error correction with the three-dimensional subsystem toric code [77.34726150561087]
  We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC) The 3D STC can be realized by measuring geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions.
  arXiv  Detail & Related papers  (2021-06-04T17:35:00Z)
• PyMatching: A Python package for decoding quantum codes with minimum-weight perfect matching [0.0]
  PyMatching is a package for decoding quantum error-correcting codes with the minimum-weight perfect matching (MWPM) algorithm. PyMatching supports the use of weighted edges, hook errors, boundaries and measurement errors, enabling fast decoding and simulation of fault-tolerant quantum computing.
  arXiv  Detail & Related papers  (2021-05-27T12:10:37Z)
• Q-Match: Iterative Shape Matching via Quantum Annealing [64.74942589569596]
  Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) This paper proposes Q-Match, a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm. Q-Match can be applied for shape matching problems iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems.
  arXiv  Detail & Related papers  (2021-05-06T17:59:38Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model [50.38446482252857]
  This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator) We first consider $gamma$-discounted infinite-horizon Markov decision processes (MDPs) with state space $mathcalS$ and action space $mathcalA$. We prove that a plain model-based planning algorithm suffices to achieve minimax-optimal sample complexity given any target accuracy level.
  arXiv  Detail & Related papers  (2020-05-26T17:53:18Z)

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.