Related papers: Two-sided Robustly Testable Codes
Unlike the surface code, quantum low-density parity-check (QLDPC) codes can have a finite encoding rate, potentially lowering the error correction overhead. However, finite-rate QLDPC codes have nonlocal stabilizers, making it difficult to…
We construct a family of constant-rate highly-symmetric self-dual qLDPC codes on high dimensional expanders. This is the first self-dual code constructed on high dimensional expanders and also the first such code with a rich (e.g.…
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
Variable selection can be performed by testing conditional independence (CI) between each predictor and the response, given the other predictors. A doubly robust and powerful option for these CI tests is the projected covariance measure…
This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust…
A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective way to prove that a set is locally…
This brief paper: (1) Discusses strategies to generate random test cases that can be used to extensively test any Linear Distance Program (LDP) software. (2) Gives three numerical examples of input cases generated by this strategy that…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also…
We continue the study of classical and quantum low-density parity check (LDPC) codes from a physical perspective. We focus on constructive approaches and formulate a general framework for systematically constructing codes with various…
Several recent results provide theoretical insights into the phenomena of adversarial examples. Existing results, however, are often limited due to a gap between the simplicity of the models studied and the complexity of those deployed in…
The generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion…
The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either…
We study the design of computationally efficient algorithms with provable guarantees, that are robust to adversarial (test time) perturbations. While there has been an proliferation of recent work on this topic due to its connections to…
Several notions of code products are known in quantum error correction, such as hyper-graph products, homological products, lifted products, balanced products, to name a few. In this paper we introduce a new product code construction which…
Minimum distance is an important parameter of a linear error correcting code. For improved performance of binary Low Density Parity Check (LDPC) codes, we need to have the minimum distance grow fast with n, the codelength. However, the best…
Linear complementary pairs (LCPs) of codes have been studied since they were introduced in the context of discussing mitigation measures against possible hardware attacks to integrated circuits. In this situation, the security parameters…
Classical low-density parity-check (LDPC) codes are a widely deployed and well-established technology, forming the backbone of modern communication and storage systems. It is well known that, in this classical setting, increasing the girth…
We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasi-cyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized…