1. Entangling Power and Quantum Circuit Complexity
- Author
-
Eisert, J.
- Subjects
High Energy Physics - Theory ,Computer science ,FOS: Physical sciences ,General Physics and Astronomy ,Quantum simulator ,Context (language use) ,Quantum entanglement ,Topology ,01 natural sciences ,Unitary state ,Quantum circuit ,Quantum gate ,Quantum computation ,0103 physical sciences ,Circuit complexity ,010306 general physics ,Quantum computer ,Quantum aspects of black holes ,Quantum Physics ,500 Naturwissenschaften und Mathematik::530 Physik::539 Moderne Physik ,010308 nuclear & particles physics ,TheoryofComputation_GENERAL ,Mathematical physics methods ,Condensed Matter - Other Condensed Matter ,Computational complexity ,High Energy Physics - Theory (hep-th) ,Entanglement entropy ,Quantum Physics (quant-ph) ,Other Condensed Matter (cond-mat.other) - Abstract
Notions of circuit complexity and cost play a key role in quantum computing and simulation where they capture the (weighted) minimal number of gates that is required to implement a unitary. Similar notions also become increasingly prominent in high energy physics in the study of holography. While notions of entanglement have in general little implications for the quantum circuit complexity and the cost of a unitary, in this note, we discuss a simple such relationship when both the entanglement of a state and the cost of a unitary take small values, building on ideas on how values of entangling power of quantum gates add up. This bound implies that if entanglement entropies grow linearly in time, so does the cost. The implications are two-fold: It provides insights into complexity growth for short times. In the context of quantum simulation, it allows to compare digital and analog quantum simulators. The main technical contribution is a continuous-variable small incremental entangling bound., 7 pages, 1 figure, typos corrected
- Published
- 2021
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