585 research outputs found

    Neural network decoder for near-term surface-code experiments

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    Neural-network decoders can achieve a lower logical error rate compared to conventional decoders, like minimum-weight perfect matching, when decoding the surface code. Furthermore, these decoders require no prior information about the physical error rates, making them highly adaptable. In this study, we investigate the performance of such a decoder using both simulated and experimental data obtained from a transmon-qubit processor, focusing on small-distance surface codes. We first show that the neural network typically outperforms the matching decoder due to better handling errors leading to multiple correlated syndrome defects, such as YY errors. When applied to the experimental data of [Google Quantum AI, Nature 614, 676 (2023)], the neural network decoder achieves logical error rates approximately 25%25\% lower than minimum-weight perfect matching, approaching the performance of a maximum-likelihood decoder. To demonstrate the flexibility of this decoder, we incorporate the soft information available in the analog readout of transmon qubits and evaluate the performance of this decoder in simulation using a symmetric Gaussian-noise model. Considering the soft information leads to an approximately 10%10\% lower logical error rate, depending on the probability of a measurement error. The good logical performance, flexibility, and computational efficiency make neural network decoders well-suited for near-term demonstrations of quantum memories.Comment: 15 pages, 8 figures, 1 tabl

    On Capacity Optimality of OAMP: Beyond IID Sensing Matrices and Gaussian Signaling

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    This paper investigates a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrarily fixed signal distribution, and forward error control (FEC) coding. A universal Gram-Schmidt orthogonalization is considered for the construction of orthogonal approximate message passing (OAMP), which renders the results applicable to general prototypes without the differentiability restriction. For OAMP with Lipschitz continuous local estimators, we develop two variational single-input-single-output transfer functions, based on which we analyze the achievable rate of OAMP. Furthermore, when the state evolution of OAMP has a unique fixed point, we reveal that OAMP reaches the constrained capacity predicted by the replica method of the LUIS with an arbitrary signal distribution based on matched FEC coding. The replica method is rigorous for LUIS with Gaussian signaling and for certain sub-classes of LUIS with arbitrary signal distributions. Several area properties are established based on the variational transfer functions of OAMP. Meanwhile, we elaborate a replica constrained capacity-achieving coding principle for LUIS, based on which irregular low-density parity-check (LDPC) codes are optimized for binary signaling in the simulation results. We show that OAMP with the optimized codes has significant performance improvement over the un-optimized ones and the well-known Turbo linear MMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, replica constrained capacity-approaching bit error rate (BER) performances are observed under various channel conditions.Comment: Single column, 34 pages, 9 figure

    Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network

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    Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our decoder outperforms state-of-the-art algorithmic decoders on real-world data from Google's Sycamore quantum processor for distance 3 and 5 surface codes. On distances up to 11, the decoder maintains its advantage on simulated data with realistic noise including cross-talk, leakage, and analog readout signals, and sustains its accuracy far beyond the 25 cycles it was trained on. Our work illustrates the ability of machine learning to go beyond human-designed algorithms by learning from data directly, highlighting machine learning as a strong contender for decoding in quantum computers

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Spatially-Coupled QDLPC Codes

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    Spatially-coupled (SC) codes is a class of convolutional LDPC codes that has been well investigated in classical coding theory thanks to their high performance and compatibility with low-latency decoders. We describe toric codes as quantum counterparts of classical two-dimensional spatially-coupled (2D-SC) codes, and introduce spatially-coupled quantum LDPC (SC-QLDPC) codes as a generalization. We use the convolutional structure to represent the parity check matrix of a 2D-SC code as a polynomial in two indeterminates, and derive an algebraic condition that is both necessary and sufficient for a 2D-SC code to be a stabilizer code. This algebraic framework facilitates the construction of new code families. While not the focus of this paper, we note that small memory facilitates physical connectivity of qubits, and it enables local encoding and low-latency windowed decoding. In this paper, we use the algebraic framework to optimize short cycles in the Tanner graph of 2D-SC HGP codes that arise from short cycles in either component code. While prior work focuses on QLDPC codes with rate less than 1/10, we construct 2D-SC HGP codes with small memory, higher rates (about 1/3), and superior thresholds.Comment: 25 pages, 7 figure

    Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning

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    The paper introduces the application of information geometry to describe the ground states of Ising models by utilizing parity-check matrices of cyclic and quasi-cyclic codes on toric and spherical topologies. The approach establishes a connection between machine learning and error-correcting coding. This proposed approach has implications for the development of new embedding methods based on trapping sets. Statistical physics and number geometry applied for optimize error-correcting codes, leading to these embedding and sparse factorization methods. The paper establishes a direct connection between DNN architecture and error-correcting coding by demonstrating how state-of-the-art architectures (ChordMixer, Mega, Mega-chunk, CDIL, ...) from the long-range arena can be equivalent to of block and convolutional LDPC codes (Cage-graph, Repeat Accumulate). QC codes correspond to certain types of chemical elements, with the carbon element being represented by the mixed automorphism Shu-Lin-Fossorier QC-LDPC code. The connections between Belief Propagation and the Permanent, Bethe-Permanent, Nishimori Temperature, and Bethe-Hessian Matrix are elaborated upon in detail. The Quantum Approximate Optimization Algorithm (QAOA) used in the Sherrington-Kirkpatrick Ising model can be seen as analogous to the back-propagation loss function landscape in training DNNs. This similarity creates a comparable problem with TS pseudo-codeword, resembling the belief propagation method. Additionally, the layer depth in QAOA correlates to the number of decoding belief propagation iterations in the Wiberg decoding tree. Overall, this work has the potential to advance multiple fields, from Information Theory, DNN architecture design (sparse and structured prior graph topology), efficient hardware design for Quantum and Classical DPU/TPU (graph, quantize and shift register architect.) to Materials Science and beyond.Comment: 71 pages, 42 Figures, 1 Table, 1 Appendix. arXiv admin note: text overlap with arXiv:2109.08184 by other author

    Physical Layer Secret Key Agreement Using One-Bit Quantization and Low-Density Parity-Check Codes

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    Physical layer approaches for generating secret encryption keys for wireless systems using channel information have attracted increased interest from researchers in recent years. This paper presents a new approach for calculating log-likelihood ratios (LLRs) for secret key generation that is based on one-bit quantization of channel measurements and the difference between channel estimates at legitimate reciprocal nodes. The studied secret key agreement approach, which implements advantage distillation along with information reconciliation using Slepian-Wolf low-density parity-check (LDPC) codes, is discussed and illustrated with numerical results obtained from simulations. These results show the probability of bit disagreement for keys generated using the proposed LLR calculations compared with alternative LLR calculation methods for key generation based on channel state information. The proposed LLR calculations are shown to be an improvement to the studied approach of physical layer secret key agreement.Comment: Officially Published on ODU Digital Commons at https://digitalcommons.odu.edu/ece_etds/1

    New perspectives in statistical mechanics and high-dimensional inference

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    The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it

    4-Cycle Free Spatially Coupled LDPC Codes with an Explicit Construction

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    Spatially coupled low-density parity-check (SC-LDPC) codes are a class of capacity approaching LDPC codes with low message recovery latency when a sliding window decoding is used. In this paper, we first present a new method for the construction of a class of SC-LDPC codes by the incidence matrices of a given non-negative integer matrix EE, and then the relationship of 4-cycles between matrix EE and the corresponding SC-LDPC code are investigated. Finally, by defining a new class of integer finite sequences, called {\it good sequences}, for the first time, we give an explicit method for the construction of a class of 4-cycle free SC-LDPC codes that can achieve (in most cases) the minimum coupling width

    Single-Frequency Network Terrestrial Broadcasting with 5GNR Numerology

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