Time-Energy Uncertainty Relations for Driven Dynamics and Adiabatic Quantum Computation

A new class of time-energy uncertainty relations is directly derived from the Schroedinger equations for time-dependent Hamiltonian H(t). Only the initial states and the Hamiltonians are required for our time-energy relations, with no requirement of a full solution for a time-dependent Hamiltonian.

The general relations we find could be applied to a particular sub-case of time-varying Hamiltonians in Adiabatic Quantum Computation in estimating lower bounds on computational time. We particularly emphasise the role of required energy resources, besides the space and time complexity, for the physical process of (quantum) computation in general.

If time permits I will present some Adiabatic Quantum Algorithm either for the Travelling Salesman Problem or for the problem of factorising a positive integer N into two integer factors x and y as an optimisation problem of one of the Diophantine polynomials.