Related papers: A Lower Bound for the Sturm-Liouville Eigenvalue P…
Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and…
The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1}^n, we show a lower bound of Omega(2^{n/4}/n) on…
The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
The efficient management of energy communities relies on the solution of the "prosumer problem", i.e., the problem of scheduling the household loads on the basis of the user needs, the electricity prices, and the availability of local…
Quantum computers have the potential for an exponential speedup of classical molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) algorithms are intractable on current hardware while…
The electronic structure problem is one of the main problems in modern theoretical chemistry. While there are many already-established methods both for the problem itself and its applications like semi-classical or quantum dynamics, it…
The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision $\epsilon$, QPE…
Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship…
In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schroedinger equation for them is solved by using a generalized series solution for the bound states (using the Froebenius method) and then an…
We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j^{-k} with k>1. For the Wiener measure…
In this study, we give the variation of parameters method from a different viewpoint for the Nth order inhomogeneous linear ordinary difference equations with constant coefficient by means of delta exponential function . Advantage of this…
Power grid partitioning is an important requirement for resilient distribution grids. Since electricity production is progressively shifted to the distribution side, dynamic identification of self-reliant grid subsets becomes crucial for…
The working of a quantum computer is described in the concrete example of a quantum simulator of the single-particle Schrodinger equation. We show that a register of 6-10 qubits is sufficient to realize a useful quantum simulator capable of…
We consider a scattering problem generated by the Sturm-Liouville equation on a tree which consists of an equilateral compact subtree and a half-infinite lead attached to its root. We assume that the potential on the lead is identically…
We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example…
Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and…
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…
Given a finite set of eigenvalues of a regular Sturm-Liouville problem for the equation -y{\prime}{\prime}+q(x)y={\lambda}y, the potential q(x) of which is unknown. We show the possibility to compute more eigenvalues without any additional…