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This paper introduces Rewired Sequential Greedy (ResQue Greedy), an enhanced approach for submodular maximization under cardinality constraints. By integrating a novel set curvature metric within a lattice-based framework, ResQue Greedy…
In this paper, we prove how to extend a subset of quantum stabilizer codes into a qudit hybrid code storing $\log_2 p$ classical bits over a qudit space with dimension $p$, with $p$ prime. Our proof also gives an explicit procedure for…
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error…
We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…
In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…
One-way quantum repeaters where loss and operational errors are counteracted by quantum error correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such…
The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in applications of networked control systems. Although the work of Schulman and Sahai over the past two decades, and…
Let $q$ be a prime power. Let $\lambda>1$ be a divisor of $q-1$, and let $\tau>1$ and $\rho>1$ be divisors of $q+1$. Under certain conditions we prove that there exists an MDS stabilizer quantum code with length $n=\lambda \tau \sigma$…
Gottesman, Kitaev and Preskill have proposed a scheme to encode a qubit in a harmonic oscillator, which is called the GKP code. It is designed to be resistant to small shift errors contained in momentum and position quadratures. Thus…
In this work, we propose a fully differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
In this paper, we study the problem of robust phase recovery. We investigate a novel approach based on extremely quantized (one-bit) phase-less measurements and a corresponding recovery scheme. The proposed approach has surprising…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a numerically stable binary coding method which overcomes the drawbacks of the \textit{Fractional…
We present a simple performance bound for the greedy scheme in string optimization problems that obtains strong results. Our approach vastly generalizes the group of previously established greedy curvature bounds by Conforti and…
Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic…
Classical $(r,\delta)$-locally recoverable codes are designed for avoiding loss of information in large scale distributed and cloud storage systems. We introduce the quantum counterpart of those codes by defining quantum…
The continuous improvements on image compression with variational autoencoders have lead to learned codecs competitive with conventional approaches in terms of rate-distortion efficiency. Nonetheless, taking the quantization into account…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of $Z$- or $X$-rotations of individual qubits. We find that, similarly to the case of incoherent bit- and phase-flips, a trade-off between…