Related papers: Quantum algorithm based on the $\varepsilon$-rando…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
Quantum algorithm is constructed which verifies the formulas of predicate calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the time required for classical algorithms. This algorithm uses the polynomial number of…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
The ultimate objective of this paper is to create a stepping stone to the development of new quantum algorithms. The strategy chosen is to begin by focusing on the class of abelian quantum hidden subgroup algorithms, i.e., the class of…
We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation…
In this paper we study quantum algorithms for NP-complete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic…
We present a quantum algorithm solving the greatest common divisor (GCD) problem. This quantum algorithm possesses similar computational complexity with classical algorithms, such as the well-known Euclidean algorithm for GCD. This…
Quantum Annealing, or Quantum Stochastic Optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an…
We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training…
Quantum algorithms have begun to surpass classical ones in several computation fields, yet practical application remains challenging due to hardware and software limitations. Here, we introduce a quantum algorithm that quadratically…
Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its…
Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum…