Related papers: Almost-linear time decoding algorithm for topologi…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
Accuracy thresholds of quantum error correcting codes, which exploit topological properties of systems, defined on two different arrangements of qubits are predicted. We study the topological color codes on the hexagonal lattice and on the…
The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these…
We show that for all $\varepsilon>0$, for sufficiently large $q\in\mathbb{N}$ power of $2$, for all $\delta>0$, it is NP-hard to distinguish whether a given $2$-Prover-$1$-Round projection game with alphabet size $q$ has value at least…
Error-correcting codes are one of the most fundamental objects in pseudorandomness, with applications in communication, complexity theory, and beyond. Codes are useful because of their ability to support decoding, which is the task of…
The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the…
We present a classical algorithm that, for any 3D geometrically-local, polylogarithmic-depth quantum circuit $C$ acting on $n$ qubits, and any bit string $x\in\{0,1\}^n$, can compute the quantity $|< x |C|0^{\otimes n}>|^2$ to within any…
Detecting and counting copies of permutation patterns are fundamental algorithmic problems, with applications in the analysis of rankings, nonparametric statistics, and property testing tasks such as independence and quasirandomness…
We study the traveling salesman problem in the hyperbolic plane of Gaussian curvature $-1$. Let $\alpha$ denote the minimum distance between any two input points. Using a new separator theorem and a new rerouting argument, we give an…
We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, however, we focus on the three-dimensional (3D) toric…
In the $k$-Cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. Prior work on this problem gives, for all $h…
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…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
We present a decoding algorithm for quantum convolutional codes that finds the class of degenerate errors with the largest probability conditioned on a given error syndrome. The algorithm runs in time linear with the number of qubits.…
The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum…
Designing algorithms for space bounded models with restoration requirements on the space used by the algorithm is an important challenge posed about the catalytic computation model introduced by Buhrman et al. (2014). Motivated by the…
Quantum computers hold the potential to surpass classical computers in solving complex computational problems. However, the fragility of quantum information and the error-prone nature of quantum operations make building large-scale,…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including…