Related papers: BQP $=$ PSPACE
This paper is an attempt to incorporate the idea of spiking neural P systems as an early seed into the area of Operating System Design, regarding their capability to solve some classical computer science problems. It is reflecting the power…
Machine learning and quantum computing are being progressively explored to shed light on possible computational approaches to deal with hitherto unsolvable problems. Classical methods for machine learning are ubiquitous in pattern…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.
Energy games belong to a class of turn-based two-player infinite-duration games}played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in ${\sf NP} \cap {\sf co\mbox{-}NP}$, but are not…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
The maximum clique problem is a classical NP-complete problem in graph theory and has important applications in many domains. In this paper we show, in a partially non-constructive way, the existence of an exact polynomial-time algorithm…
Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
The maximum parsimony phylogenetic tree reconstruction problem is NP-hard, presenting a computational bottleneck for classical computing and motivating the exploration of emerging paradigms like quantum computing. To this end, we design…
In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups $\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_q$, for p and q prime. We first present a classification of these groups in five classes. Then, we…
In this paper, we have discussed a quantum approach for the all-pair multiclass classification problem. We have shown that the multiclass support vector machine for big data classification with a quantum all-pair approach can be implemented…
The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
Polylogarithmic time delineates a relevant notion of feasibility on several classical computational models such as Boolean circuits or parallel random access machines. As far as the quantum paradigm is concerned, this notion yields the…
It has recently been shown (Burer, Math. Program Ser. A 120:479-495, 2009) that a large class of NP-hard nonconvex quadratic programming problems can be modeled as so called completely positive programming problems, which are convex but…
An approach to the solution of NP-complete problems based on quantum computing and chaotic dynamics is proposed. We consider the satisfiability problem and argue that the problem, in principle, can be solved in polynomial time if we combine…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
Recently, Renes proposed a quantum algorithm called belief propagation with quantum messages (BPQM) for decoding classical data encoded using a binary linear code with tree Tanner graph that is transmitted over a pure-state CQ channel…