Related papers: Span-program-based quantum algorithm for evaluatin…
We consider the task of estimating the expectation value of an $n$-qubit tensor product observable $O_1\otimes O_2\otimes \cdots \otimes O_n$ in the output state of a shallow quantum circuit. This task is a cornerstone of variational…
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,…
Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…
Variational quantum algorithms use non-convex optimization methods to find the optimal parameters for a parametrized quantum circuit in order to solve a computational problem. The choice of the circuit ansatz, which consists of…
Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
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)…
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…
Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm,…
Quantum computer is extensively used in solving financial problems. Quantum amplitude estimation, an algorithm that aims to estimate the amplitude of a given quantum state, can be utilized to determine the expectation value of bonds as the…
Comparative analyses of protein-protein interaction networks play important roles in the understanding of biological processes. However, the growing enormity of available data on the networks becomes a computational challenge for the…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
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…
Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…
The negative-AND (NAND) gate is universal for classical computation making it an important target for development. A seminal quantum computing algorithm by Farhi, Goldstone and Gutmann has demonstrated its realization by means of quantum…
Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…