Related papers: NISQ algorithm for the matrix elements of a generi…
Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…
An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. Here, the genuinely quantum mechanical approach is considered in detail for (2x2) matrices. The method is based on the measurement of…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum…
Hybrid quantum-classical variational algorithms such as the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) are promising applications for noisy, intermediate-scale quantum (NISQ) computers.…
In recent years, Noisy Intermediate Scale Quantum (NISQ) computers have been widely used as a test bed for quantum dynamics. This work provides a new hardware-agnostic framework for modelling the Markovian noise and dynamics of quantum…
Currently available noisy intermediate-scale quantum (NISQ) devices are limited by the number of qubits that can be used for quantum chemistry calculations on molecules. We show herein that the number of qubits required for simulations on a…
We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy…
Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in the development of quantum technologies. We propose an efficient protocol based on the estimation of the time derivatives of few qubit…
Grover search is a renowned quantum search algorithm that leverages quantum superposition to find a marked item with quadratic speedup. However, when implemented on Noisy Intermediate-scale Quantum (NISQ) hardware, the required repeated…
To assess whether a gate-based quantum algorithm can be executed successfully on a noisy intermediate-scale quantum (NISQ) device, both complexity and actual value of quantum resources should be considered carefully. Based on quantum phase…
The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenvalues and eigenvectors of a given Hamiltonian on noisy intermediate-scale quantum (NISQ) devices. A particular application is to obtain ground…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
When noisy intermediate scalable quantum (NISQ) devices are applied in information processing, all of the stages through preparation, manipulation, and measurement of multipartite qubit states contain various types of noise that are…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal…
Random unitaries are an important resource for quantum information processing. While their universal properties have been thoroughly analyzed, it is not known what happens to these properties when the unitaries are sampled on the…