Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control

By Sebastian Deffner, Steve Campbell. 2017

632 citations recorded by the source corpus.

One of the most widely known building blocks of modern physics is Heisenberg’s indeterminacy principle. Among the different statements of this fundamental property of the full quantum mechanical nature of physical reality, the uncertainty relation for energy and time has a special place. Its interpretation and its consequences have inspired continued research efforts for almost a century. In its modern formulation, the uncertainty relation is understood as setting a fundamental bound on how fast any quantum system can evolve. In this topical review we describe important milestones, such as the Mandelstam–Tamm and the Margolus–Levitin bounds on the quantum speed limit, and summarise recent applications in a variety of current research fields—including quantum information theory, quantum computing, and quantum thermodynamics amongst several others. To bring order and to provide an access point into the many different notions and concepts, we have grouped the various approaches into the minimal time approach and the geometric approach, where the former relies on quantum control theory, and the latter arises from measuring the distinguishability of quantum states. Due to the volume of the literature, this topical review can only present a snapshot of the current state-of-the-art and can never be fully comprehensive. Therefore, we highlight but a few works hoping that our selection can serve as a representative starting point for the interested reader.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ac62e4512d888f5053c7b8767b03b5ed854df46e

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Citations in the corpus

Observing the Space- and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions (2017, background): “Answering these questions also informs us about the minimal time required to build up highly correlated states starting from a product state [4], a notion which is closely related to “quantum speed limits” in an optimal control context [41,42].”
Quantum Fisher information matrix and multiparameter estimation (2019, methodology): “trics on quantum states indicates that the QFIM can be used to quantify the evolution time. As a matter of fact, the QFI and the QFIM have been used to bound the quantum speed limit in recent studies [7,36,75,76]. For a unitary evolution, U = exp( iHt), to steer a state away from the initial positio”
Speed limit for open quantum systems (2018, background): “Quantum speed limit (QSL) is an inequality relation which sets a lower bound on the operation time required to transform a given initial state to a given final state [1].”
Quantum Technologies Need a Quantum Energy Initiative (2021, neutral): “quantum speed limits [42] and shortcuts to adiabaticity [43].”
Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “for the control task [330] and is sometimes also referred to as controllability time [8] or the quantum speed limit (qsl) [181, 465].”