Related papers: A Panoply of Quantum Algorithms

Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…

The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of…

It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…

Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…

In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…

We develop the first quantum algorithm for the constrained portfolio optimization problem. The algorithm has running time $\widetilde{O} \left( n\sqrt{r} \frac{\zeta \kappa}{\delta^2} \log \left(1/\epsilon\right) \right)$, where $r$ is the…

Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…

Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases,…

Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…

We describe a general method to obtain quantum speedups of classical algorithms which are based on the technique of backtracking, a standard approach for solving constraint satisfaction problems (CSPs). Backtracking algorithms explore a…

Linear regression is one of the most fundamental linear algebra problems. Given a dense matrix $A \in \mathbb{R}^{n \times d}$ and a vector $b$, the goal is to find $x'$ such that $ \| Ax' - b \|_2^2 \leq (1+\epsilon) \min_{x} \| A x - b…

Studies on Quantum Computing have been developed since the 1980s, motivating researches on quantum algorithms better than any classical algorithm possible. An example of such algorithms is Grover's algorithm, capable of finding $k$ (marked)…

There exist quantum algorithms that are more efficient than their classical counterparts; such algorithms were invented by Shor in 1994 and then Grover in 1996. A lack of invention since Grover's algorithm has been commonly attributed to…

Many computational problems are subject to a quantum speed-up: one might find that a problem having an O(n^3)-time or O(n^2)-time classic algorithm can be solved by a known O(n^1.5)-time or O(n)-time quantum algorithm. The question…

Search is one of the most commonly used primitives in quantum algorithm design. It is known that quadratic speedups provided by Grover's algorithm are optimal, and no faster quantum algorithms for Search exist. While it is known that at…

We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact…

There is an ongoing effort to find quantum speedups for learning problems. Recently, [Y. Liu et al., Nat. Phys. $\textbf{17}$, 1013--1017 (2021)] have proven an exponential speedup for quantum support vector machines by leveraging the…

We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…

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…

The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…