Related papers: Contour-integral based quantum eigenvalue transfor…
We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the…
We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for new ones. Existing implementations of QSVT rely on block…
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
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…
Reflections are omnipresent tools in quantum algorithms. We consider the task of reflecting through the eigenspace of an implementable unitary. Such reflections are generally designed using phase estimation or linear combination of…
Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…
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…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
A practical computation method to find the eigenvalues and eigenspinors of quantum mechanical Hamiltonian is presented. The method is based on reduction of the eigenvalue equation to well known geometric algebra rotor equation and,…
Quasi-degenerate eigenvalue problems are central to quantum chemistry and condensed-matter physics, where low-energy spectra often form manifolds of nearly degenerate states that determine physical properties. Standard quantum algorithms,…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…
Quantum signal processing allows for quantum eigenvalue transformation with Hermitian matrices, in which each eigenspace component of an input vector gets transformed according to its eigenvalue. In this work, we introduce the multivariate…