Related papers: Quantum Algorithm for Matrix Logarithm by Integral…
Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with…
Black-box quantum state preparation is a fundamental primitive in quantum algorithms. Starting from Grover, a series of techniques have been devised to reduce the complexity. In this work, we propose to perform black-box state preparation…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…
Computing the unit group and solving the principal ideal problem for a number field are two of the main tasks in computational algebraic number theory. This paper proposes efficient quantum algorithms for these two problems when the number…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
Block-encodings of matrices have become an essential element of quantum algorithms derived from the quantum singular value transformation. This includes a variety of algorithms ranging from the quantum linear systems problem to quantum…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
We present a classical protocol, using the matrix product state representation, to simulate cluster-state quantum computation at a cost polynomial in the number of qubits in the cluster and exponential in d -- the width of the cluster. We…
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…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of a NP-Complete…
In this paper, we present Q# implementations for arbitrary single-variabled fixed-point arithmetic operations for a gate-based quantum computer based on lookup tables (LUTs). In general, this is an inefficent way of implementing a function…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs…
We transform the problem of solving linear system of equations $A\mathbf{x}=\mathbf{b}$ to a problem of finding the right singular vector with singular value zero of an augmented matrix $C$, and present two quantum algorithms for solving…