Related papers: A new approximation scheme in quantum mechanics
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
The dynamics of the nuclear-spin quantum computer with large number (L=1000) of qubits is considered using a perturbation approach, based on approximate diagonalization of exponentially large sparse matrices. Small parameters are introduced…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is…
We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.
We present a new short-time approximation scheme for evaluation of decoherence. At low temperatures, the approximation is argued to apply at intermediate times as well. It then provides a tractable approach complementary to Markovian-type…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
Here, we propose a new modified quantum mechanics and its new algorithms of atomic fine-structure,asymmetric variational method based on hydrogen-like atom orbit. In addition, as we all know, the ab initio calculation of atomic…
In strongly coupled field theories, perturbation theory cannot be employed to study the low-energy spectrum. Thus, non-perturbative techniques are required. We employ the variational method, a rigorous, non-perturbative approach which…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
Utilizing quantum computer to investigate quantum chemistry is an important research field nowadays. In addition to the ground-state problems that have been widely studied, the determination of excited-states plays a crucial role in the…
The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise…
Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum…
Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
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…
We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear…
We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…