Related papers: Quantum computation of multifractal exponents thro…
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the…
The application of quantum computing to the field of image processing has produced several promising applications: quantum image representation techniques have been developed showing how, by taking advantage of quantum properties like…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
The development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation, and sensing. This poses severe challenges in efficient control,…
We show that quantum wavepackets exhibit a sharp macroscopic peak as they spread in the vicinity of the critical point of the Anderson transition. The peak gives a direct access to the mutifractal properties of the wavefunctions and…
A universal quantum simulator would enable efficient simulation of quantum dynamics by implementing quantum-simulation algorithms on a quantum computer. Specifically the quantum simulator would efficiently generate qubit-string states that…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
The simultaneous quantum estimation of multiple parameters can provide a better precision than estimating them individually. This is an effect that is impossible classically. We review the rich background of multi-parameter quantum…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…
Entanglement is essential for quantum computation. However, disentanglement is also necessary. It can be achieved without the need of classical operations (measurements). Two examples are analyzed: the discrete Fourier transform and error…
We show how to implement a Rindler transformation of coordinates with an embedded quantum simulator. A suitable mapping allows to realise the unphysical operation in the simulated dynamics by implementing a quantum gate on an enlarged…
An algorithm is proposed which transfers the quantum information of a wave function (analogue signal) into a register of qubits (digital signal) such that $n$ qubits describe the amplitudes and phases of $2^n$ points of a sufficiently…
The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…