From quantum speed limits to energy-efficient quantum gates

Abstract

While recent breakthroughs in quantum computing promise the nascence of the quantum information age, quantum states remain delicate to control. Moreover, the required energy budget for large scale quantum applications has only sparely been considered. Addressing either of these issues necessitates a careful study of the most energetically efficient implementation of elementary quantum operations. In the present analysis, we show that this optimal control problem can be solved within the powerful framework of quantum speed limits. To this end, we derive state-independent lower bounds on the energetic cost, from which we find the universally optimal implementation of unitary quantum gates, for both single and N -qubit operations.

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…2.2.6. The energetic cost in quantum thermodynamics is reflected by the first law [530]; and the cost of quantum gates has been analyzed [9,175]. A different viewpoint is accounting for irreversible entropy generation required for control [316,330].…”

“…8 Munich Centre for Quantum Science and Technology (MCQST), München, Germany. 9 The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel. 10 Department of Physics and Astronomy 'G.…”