Related papers: Syndrome decoding meets multiple instances
It is common for search and optimization problems to have alternative equivalent encodings in ASP. Typically none of them is uniformly better than others when evaluated on broad classes of problem instances. We claim that one can improve…
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give…
QR decomposition is an essential operation for solving linear equations and obtaining least-squares solutions. In high-performance computing systems, large-scale parallel QR decomposition often faces node faults. We address this issue by…
Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the…
The Benders' decomposition algorithm is a technique in mathematical programming for complex mixed-integer linear programming (MILP) problems with a particular block structure. The strategy of Benders' decomposition can be described as a…
Shor's algorithm efficiently solves factoring and discrete logarithm problems using quantum computers, compromising all public key schemes used today. These schemes rely on assumptions on their computational complexity, which quantum…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
Entanglement plays a crucial role in quantum physics and is the key resource in quantum information processing. However, entanglement detection and quantification are believed to be hard due to the operational impracticality of existing…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
Decoding a quantum error correction code is generally NP-hard, but corrections must be applied at a high frequency to suppress noise successfully. Matchable codes, like the surface code, exhibit a special structure that makes it possible to…
We propose a novel parallel algorithm for decomposing hard CircuitSAT instances. The technique employs specialized constraints to partition an original SAT instance into a family of weakened formulas. Our approach is implemented as a…
Number partitioning is one of the classical NP-hard problems of combinatorial optimization. It has applications in areas like public key encryption and task scheduling. The random version of number partitioning has an "easy-hard" phase…
Fast classical processing is essential for most quantum fault-tolerance architectures. We introduce a sliding-window decoding scheme that provides fast classical processing for the surface code through parallelism. Our scheme divides the…
We consider the problem of stabilizing an unstable plant driven by bounded noise over a digital noisy communication link, a scenario at the heart of networked control. To stabilize such a plant, one needs real-time encoding and decoding…
A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a…
Post-quantum cryptography is essential for securing digital communications against threats posed by quantum computers. Re-searchers have focused on developing algorithms that can withstand attacks from both classical and quantum computers,…
Analogy has been shown to be important in many key cognitive abilities, including learning, problem solving, creativity and language change. For cognitive models of analogy, the fundamental computational question is how its inherent…
Large language models have shown impressive capabilities across a variety of NLP tasks, yet their generating text autoregressively is time-consuming. One way to speed them up is speculative decoding, which generates candidate segments (a…
We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based…