Related papers: Classical and Quantum Algorithms for the Boolean S…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
We develop a new algorithm for the quantisation of systems with first-class constraints. Our approach lies within the (History Projection Operator) continuous-time histories quantisation programme. In particular, the Hamiltonian treatment…
Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum…
The topical quantum computation paradigm is a transposition of the Turing machine into the quantum framework. Implementations based on this paradigm have limitations as to the number of: qubits, computation steps, efficient quantum…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
In this paper we detail a classical algorithmic approach to the k-satisfiability (k-SAT) problem that is inspired by the quantum amplitude amplification algorithm. This work falls under the emerging field of quantum-inspired classical…
In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…
The new model of quantum computation is proposed, for which an effective algorithm of solving any task in NP is described. The work is based and inspired be the Grover's algorithm for solving NP-tasks with quadratic speedup compared to the…
This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…
The accelerated development of quantum technology has reached a pivotal point. Early in 2014, several results were published demonstrating that several experimental technologies are now accurate enough to satisfy the requirements of…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
We study the classical complexity of the exact Boson Sampling problem where the objective is to produce provably correct random samples from a particular quantum mechanical distribution. The computational framework was proposed by Aaronson…
Three algorithms are presented that determine the existence of satisfying assignments for 3SAT Boolean satisfiability expressions. One algorithm is presented for determining an instance of a satisfying assignment, where such exists. The…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
Bayesian implementation concerns decision making problems when agents have incomplete information. This paper proposes that the traditional sufficient conditions for Bayesian implementation shall be amended by virtue of a quantum Bayesian…
Composition is something we take for granted in classical algorithms design, and in particular, we take it as a basic axiom that composing ``efficient'' algorithms should result in an ``efficient'' algorithm -- even using this intuition to…