相关论文: Product Decomposition of Periodic Functions in Qua…
Recently, there has been a surge of interest for quantum computation for its ability to exponentially speed up algorithms, including machine learning algorithms. However, Tang suggested that the exponential speed up can also be done on a…
Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based…
The computation of a matrix function $f(A)$ is an important task in scientific computing appearing in machine learning, network analysis and the solution of partial differential equations. In this work, we use only matrix-vector products…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we…
The characterization of a unitary gate is experimentally accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to reconstruct the underlying operator. The process matrix is typically…
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…
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…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
We describe the first strongly subquadratic time algorithm with subexponential approximation ratio for approximately computing the Fr\'echet distance between two polygonal chains. Specifically, let $P$ and $Q$ be two polygonal chains with…
We present a quantum algorithm to evaluate matrix elements of functions of unitary operators. The method is based on calculating quadrature nodes and weights using data collected from a quantum processor. Given a unitary $U$ and quantum…
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…
This paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing…
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…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
The degrees of polynomials representing or approximating Boolean functions are a prominent tool in various branches of complexity theory. Sherstov recently characterized the minimal degree deg_{\eps}(f) among all polynomials (over the…
Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the Carmichael function for any integer $N$ with a…
In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a…
Submodular functions are set functions mapping every subset of some ground set of size $n$ into the real numbers and satisfying the diminishing returns property. Submodular minimization is an important field in discrete optimization theory…
In some applications, one is interested in reconstructing a function $f$ from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we…