相关论文: An efficient and accurate quantum algorithm for th…
A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the…
Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method,…
Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…
We obtain exact solution of the Dirac equation for a charged particle with position-dependent mass in the Coulomb field. The effective mass of the spinor has a relativistic component which is proportional to the square of the Compton…
We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
A first-order relativistic wave equation is constructed in five dimensions. Its solutions are eight-component spinors, which are interpreted as single-particle fermion wave functions in four-dimensional spacetime. Use of a ``cylinder…
The two-dimensional Dirac equation has been widely used in graphene physics, the surface of topological insulators, and especially quantum scarring. Although a numerical approach to tackling an arbitrary confining problem was proposed…
We present a software package DiracQ, for use in quantum many-body Physics. It is designed for helping with typical algebraic manipulations that arise in quantum Condensed Matter Physics and Nuclear Physics problems, and also in some…
We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to…
We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto a…
A universal quantum simulator would enable efficient simulation of quantum dynamics by implementing quantum-simulation algorithms on a quantum computer. Specifically the quantum simulator would efficiently generate qubit-string states that…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Last years witnessed a remarkable interest in application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, even first proof-of-principle experimental realizations…