Differential Evolution for Many-Particle Adaptive Quantum Metrology

Differential evolution for many-particle adaptive quantum metrology.

We devise powerful algorithms based on differential evolution for adaptive many-particle quantum metrology. Our new approach delivers adaptive quantum metrology policies for feedback control that are orders-of-magnitude more efficient and surpass the few-dozen-particle limitation arising in methods based on particle-swarm optimization. We apply our method to the binary-decision-tree model for q...

Kinetic Equations for Quantum Many-Particle Systems

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in tim...

Fractional Quantum Field Theory, Path Integral, and Stochastic Differential Equation for Strongly Interacting Many-Particle Systems

While free and weakly interacting particles are well described by a second-quantized nonlinear Schrödinger field, or relativistic versions of it, with various approximations, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal Lévy walks rather than Gaussian ran...

Groups of Operators for Evolution Equations of Quantum Many-Particle Systems

The aim of this work is to study the properties of groups of operators for evolution equations of quantum many-particle systems, namely, the von Neumann hierarchy for correlation operators, the BBGKY hierarchy for marginal density operators and the dual BBGKY hierarchy for marginal observables. We show that the concept of cumulants (semi-invariants) of groups of operators for the von Neumann eq...