The Energy Cost of Controlling Mesoscopic Quantum Systems

TL;DR

This paper establishes the fundamental minimum energy required to control mesoscopic quantum systems under noise, providing insights into the efficiency and power consumption of quantum control protocols and devices.

Contribution

It derives the theoretical lower bound on control energy for mesoscopic quantum systems with noise, enabling evaluation of control protocol efficiency.

Findings

Calculated energy cost for maintaining a qubit in the ground state

Assessed efficiency of resolved-sideband cooling in nano-mechanical resonators

Discussed energy implications for quantum information processing

Abstract

We determine the minimum energy required to control the evolution of any mesoscopic quantum system in the presence of arbitrary Markovian noise processes. This result provides the mesoscopic equivalent of the fundamental cost of refrigeration, sets the minimum power consumption of mesoscopic devices that operate out of equilibrium, and allows one to calculate the efficiency of any control protocol, whether it be open-loop or feedback control. As examples we calculate the energy cost of maintaining a qubit in the ground state, the efficiency of resolved-sideband cooling of nano-mechanical resonators, and discuss the energy cost of quantum information processing.