Simulation of many-body interactions by conditional geometric phases

Simulation of many-body interactions by conditional geometric phases

It is shown how to exactly simulate many-body interactions and multiqubit gates by coupling finite dimensional systems, e.g., qubits with a continuous variable. Cyclic evolution in the phase space of such a variable gives rise to a geometric phase, depending on a product of commuting operators. The latter allows one to simulate many-body Hamiltonians and nonlinear Hamiltonians, and to implement...

A geometric study of many body systems

An n-body system is a labelled collection of n point masses in a Euclidean space, and their congruence and internal symmetry properties involve a rich mathematical structure which is investigated in the framework of equivariant Riemannian geometry. Some basic concepts are nconfiguration, configuration space, internal space, shape space, Jacobi transformation and weighted root system. The latter...

Minimizing Effective Many-Body Interactions

A simple two-level model is developed and used to test the properties of effective interactions for performing nuclear structure calculations in truncated model spaces. It is shown that the effective manybody interactions sensitively depend on the choice of the single-particle basis and they appear to be minimized when a self-consistent HartreeFock basis is used.

MCMC curve sampling and geometric conditional simulation

We present an algorithm to generate samples from probability distributions on the space of curves. Traditional curve evolution methods use gradient descent to find a local minimum of a specified energy functional. Here, we view the energy functional as a negative log probability distribution and sample from it using a Markov chain Monte Carlo (MCMC) algorithm. We define a proposal distribution ...

Curve sampling and geometric conditional simulation