Related papers: Virtual states in the coupled-channel problems wit…
Quantum simulation - the use of one quantum system to simulate a less controllable one - may provide an understanding of the many quantum systems which cannot be modeled using classical computers. Impressive progress on control and…
Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using…
We develop a multiscale hybrid scheme for simulations of soft condensed matter systems, which allows one to treat the system at the particle level in selected regions of space, and at the continuum level elsewhere. It is derived…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
We propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regularized by a third-order dispersive term in the momentum…
We present a theoretical method to determine the multipartite entanglement between different partitions of multimode, fully or partially symmetric Gaussian states of continuous variable systems. For such states, we determine the exact…
We establish quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators in situations where, in addition to power-law upper bounds on solutions corresponding to energies in the spectrum, one also has lower bounds…
Solving linear and nonlinear differential equations with large degrees of freedom is an important task for scientific and industrial applications. In order to solve such differential equations on a quantum computer, it is necessary to embed…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce…
The projection-based quantum embedding method is applied to electronically excited states of valence, Rydberg, and charge-transfer character, valence- and core-ionized states, as well as bound and temporary radical anions. We embed…
We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the $d$-dimensional fractional equation is reformulated as a local partial differential equation in…
Resonance phenomena are central to many quantum systems, where resonant states are typically characterized by pole singularities of the S-matrix. In this work, we employ the complex scaling method (CSM) in conjunction with exact WKB…
The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes,…
In recent years, the development of quantum annealers has enabled experimental demonstrations and has increased research interest in applications of quantum annealing, such as in quantum machine learning and in particular for the popular…
We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations.…
We present a novel approach to accelerate iterative methods to solve nonlinear Schr\"odinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional…
The characterization of continuous-variable quantum states is crucial for applications in quantum communication, sensing, simulation and computing. However, a full characterization of multimode quantum states requires a number of…
We introduce the concept of strong quantum speedup. We prove that approximating the ground state energy of an instance of the time-independent Schr\"odinger equation, with $d$ degrees of freedom, $d$ large, enjoys strong exponential quantum…
Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating…