Newton algorithm for Hamiltonian characterization in quantum control

Quantum Algorithm Processors to Reveal Hamiltonian Cycles

Professor J. R. Burger Summary – Quantum computer versus quantum algorithm processor in CMOS are compared to find (in parallel) all Hamiltonian cycles in a graph with m edges and n vertices, each represented by k bits. A quantum computer uses quantum states analogous to CMOS registers. With efficient initialization, number of CMOS registers is proportional to (n-1)! Number of qubits in a quantu...

A Quantum Algorithm for the Hamiltonian NAND Tree

The NAND trees in this paper are perfectly bifurcating trees with N leaves at the top and depth n = log2(N). Each leaf is assigned a value of 0 or 1 and the value of any other node is the NAND of the two connected nodes just above. The goal is to evaluate the value at the root of the tree. An example is shown in figure (1). Classically there is a randomized algorithm that succeeds after evaluat...

Optimization flow control with Newton-like algorithm

We proposed earlier an optimization approach to reactive ow control where the objective of the control is to maximize the total utility of all sources over their transmission rates. The control mechanism is derived as a gradient projection algorithm to solve the dual problem. In this paper we extend the algorithm to a scaled gradient projection. The diagonal scaling matrix approximates the diag...

Quasi-Newton Hamiltonian Monte Carlo

The Hamiltonian Monte Carlo (HMC) method has become significantly popular in recent years. It is the state-of-the-art MCMC sampler due to its more efficient exploration to the parameter space than the standard random-walk based proposal. The key idea behind HMC is that it makes use of first-order gradient information about the target distribution. In this paper, we propose a novel dynamics usin...

Modified Newton - Raphson methods for optimal control of quantum systems