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 [536]; and the cost of quantum gates has been analyzed [9,179]. A different viewpoint is accounting for irreversible entropy generation required for control [320,334].…”

“…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.…”

Quantum Correlations and Speed Limit of Central Spin Systems

“…[37] Furthermore, the speed limit for driven quantum systems that are valid for arbitrary initial and final states, as well as for arbitrary unitary driving, was derived. [38] QSL time for the evolution between arbitrary states in open quantum systems finds many potential applications [39][40][41][42] in the field of quantum information and computation and is an active research topic. [43][44][45] In general, comprehending the subtlety of the environment's impact on the quantum system is a non-trivial task.…”

Affinity-based geometric discord and quantum speed limits of its creation and decay

“…Due to the wide range of applications of QSL in quantum information theory, the researchers got enormous interest on characterization of QSL for nonunitary dynamics. QSL has been studied from the different perspectives such as decay rate of quantum states, parameter estimation, rate of information transfer and processing, entropy production [28], precision in quantum metrology, state preparation and time scales of quantum optimal control, many-body open system [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Recently, QSL for the states with a bounded energy spectrum is also studied [28] and realizable using different candidates such as on single photons [29], trapped ions [30], trapped atoms [31], and artificial atoms in superconducting quantum circuits [32,33].…”