Related papers: Quantum query complexity with matrix-vector produc…
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…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…
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…
Classical algorithms for market equilibrium computation such as proportional response dynamics face scalability issues with Internet-based applications such as auctions, recommender systems, and fair division, despite having an almost…
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…
Along with the development of quantum technology, finding useful applications of quantum computers has been a central pursuit. Despite various quantum algorithms have been developed, many of them often require strong input assumptions,…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
We consider algorithms with access to an unknown matrix $M\in\mathbb{F}^{n \times d}$ via matrix-vector products, namely, the algorithm chooses vectors $\mathbf{v}^1, \ldots, \mathbf{v}^q$, and observes $M\mathbf{v}^1,\ldots,…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
Quantum machine learning promises to efficiently solve important problems. There are two persistent challenges in classical machine learning: the lack of labeled data, and the limit of computational power. We propose a novel framework that…