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We consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli…
An arbitrarily reliable quantum computer can be efficiently constructed from noisy components using a recursive simulation procedure, provided that those components fail with probability less than the fault-tolerance threshold. Recent…
Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline…
The error floor phenomenon, associated with iterative decoders, is one of the most significant limitations to the applications of low-density parity-check (LDPC) codes. A variety of techniques from code design to decoder implementation have…
Spatially coupled, parallel concatenated codes (SC-PCCs) have been shown to approach channel capacity when decoded using optimal iterative methods. However, under complexity constraints such decoding strategies can result in unacceptable…
Quantum computers must meet extremely stringent qualitative and quantitative requirements on their qubits in order to solve real-life problems. Quantum circuit fragmentation techniques divide a large quantum circuit into a number of…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
We introduce generalized spatially coupled parallel concatenated codes (GSC-PCCs), a class of spatially coupled turbo-like codes obtained by coupling parallel concatenated codes (PCCs) with a fraction of information bits repeated before the…
The ultimate goal of quantum error correction is to create logical qubits with very low error rates (e.g. 1e-12) and assemble them into large-scale quantum computers capable of performing many (e.g. billions) of logical gates on many (e.g.…
The error-pattern correcting code (EPCC) is incorporated in the design of a turbo equalizer (TE) with aim to correct dominant error events of the inter-symbol interference (ISI) channel at the output of its matching Viterbi detector. By…
Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore…
In this paper, we investigate the performance of a class of spatially coupled codes, namely partially information coupled turbo codes (PIC-TCs) over the binary erasure channel (BEC). This class of codes enjoy flexible code rate adjustment…
Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a $(2,3)$-regular compact graph. In this paper, we introduce a family of $(d_v,d_c)$-regular GLDPC codes with convolutional code…
Contemporary methods for benchmarking noisy quantum processors typically measure average error rates or process infidelities. However, thresholds for fault-tolerant quantum error correction are given in terms of worst-case error rates --…
We consider analog error-correcting codes (analog ECCs) that are designed to correct/detect outlying errors arising in analog implementations of vector-matrix multiplication. The error-correction/detection capability of an analog ECC can be…
Quantum computers are inhibited by physical errors that occur during computation. For this reason, the development of increasingly sophisticated error characterization and error suppression techniques is central to the progress of quantum…
Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
Prompting with natural language instructions has recently emerged as a popular method of harnessing the capabilities of large language models. Given the inherent ambiguity present in natural language, it is intuitive to consider the…