The adiabatic theorem in the presence of noise

TL;DR

This paper rigorously analyzes the adiabatic theorem in quantum mechanics considering various experimental errors, providing bounds and applying them to practical quantum systems like spin-1/2 particles and flux qubits.

Contribution

It introduces explicit bounds for the adiabatic approximation error under multiple noise sources, including decoherence, with applications to real quantum systems.

Findings

Bounds on evolution time for adiabatic approximation with noise

Application to spin-1/2 particle in magnetic field

Comparison of theoretical bounds with flux qubit simulations

Abstract

We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian, coupling to low-energy quantum systems, and decoherent time-dependent perturbations in the Hamiltonian. For decoherent perturbations, we find both upper and lower bounds on the evolution time to guarantee the adiabatic approximation performs within a prescribed tolerance. Our new results include explicit definitions of constants, and we apply them to the spin-1/2 particle in a rotating magnetic field, and to the superconducting flux qubit. We compare the theoretical bounds on the superconducting flux qubit to simulation results.