相关论文: A unified approach for exactly solvable potentials…

We define rewinding operators that invert quantum measurements. Then, we define complexity classes ${\sf RwBQP}$, ${\sf CBQP}$, and ${\sf AdPostBQP}$ as sets of decision problems solvable by polynomial-size quantum circuits with a…

Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal…

Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…

Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular…

In this paper we present a supervised machine learning quantum classifier. It consists of a quantum data re-uploading classifier with binary trainable parameters, the optimal values of which are found by a quantum search algorithm. We show…

Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES).…

Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and…

The potential of the exact quantum information processing is an interesting, important and intriguing issue. For examples, it has been believed that quantum tools can provide significant, that is larger than polynomial, advantages in the…

We extend the exactly solvable Hamiltonian describing $f$ quantum oscillators considered recently by J. Dorignac et al. by means of a new interaction which we choose as quasi exactly solvable. The properties of the spectrum of this new…

A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…

A few quasi-exactly solvable models are studied within the quantum Hamilton-Jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition…

Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity…

Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…

Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…

We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…

In a pre-selected Hilbert space of quantum states the unitarity of the evolution is usually guaranteed via a pre-selection of the generator (i.e., of the Hamiltonian operator) in self-adjoint form. In fact, the simultaneous use of both of…

Consider the following generalized hidden shift problem: given a function f on {0,...,M-1} x Z_N satisfying f(b,x)=f(b+1,x+s) for b=0,1,...,M-2, find the unknown shift s in Z_N. For M=N, this problem is an instance of the abelian hidden…

We prove that the inverse scattering problem for the Schr\"odinger operator with the separable potential can be reduced to the solving of a certain singular integral equation. We establish the uniqueness of the potential corresponding to…

Recently developed simple approach for the exact/approximate solution of Schrodinger equations with constant/position-dependent mass, in which the potential is considered as in the perturbation theory, is shown to be equivalent to the one…

We consider a recently proposed generalisation of the abelian hidden subgroup problem: the shifted subset problem. The problem is to determine a subset S of some abelian group, given access to quantum states of the form |S+x>, for some…