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We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p([0,1))$, which allows to identify a univariate function with…
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…
We initiate the study of quantum algorithms for optimizing approximately convex functions. Given a convex set ${\cal K}\subseteq\mathbb{R}^{n}$ and a function $F\colon\mathbb{R}^{n}\to\mathbb{R}$ such that there exists a convex function…
In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as…
We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive semi-definite Hamiltonians, our method has expected running-time that is almost linear in $(M/(\epsilon_{\rm…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states. Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the…
We present a method for classically simulating quantum circuits based on the tensor contraction model of Markov and Shi (quant-ph/0511069). Using this method we are able to classically simulate the approximate quantum Fourier transform in…
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.…
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
We develop a quantum-classical hybrid algorithm for function optimization that is particularly useful in the training of neural networks since it makes use of particular aspects of high-dimensional energy landscapes. Due to a recent…
Quantum circuit simulation provides the foundation for the development of quantum algorithms and the verification of quantum supremacy. Among the various methods for quantum circuit simulation, tensor network contraction has been increasing…
A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…
We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…
Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum…
Tensor network methods strike a middle ground between fully-fledged quantum computing and classical computing, as they take inspiration from quantum systems to significantly speed up certain classical operations. Their strength lies in…
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…