Journal
NEW JOURNAL OF PHYSICS
Volume 19, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/aa8242
Keywords
speed limits; quantum control; unitary gates; quantum information
Categories
Funding
- NSF [CHE-1464569]
- EPSRC [EP/M01634X/1]
- DOE [DE-FG-02ER15344]
- ARO [W911NF-16-1-0014]
- Engineering and Physical Sciences Research Council [EP/M01634X/1] Funding Source: researchfish
- EPSRC [EP/M01634X/1] Funding Source: UKRI
- Direct For Mathematical & Physical Scien
- Division Of Chemistry [1464569] Funding Source: National Science Foundation
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In this work we derive a lower bound for the minimumtime required to implement a target unitary transformation through a classical time-dependent field in a closed quantum system. The bound depends on the target gate, the strength of the internal Hamiltonian and the highest permitted control field amplitude. These findings reveal some properties of the reachable set of operations, explicitly analyzed for a single qubit. Moreover, for fully controllable systems, we identify a lower bound for the time at which all unitary gates become reachable. Weuse numerical gate optimization in order to study the tightness of the obtained bounds. It is shown that in the single qubit case our analytical findings describe the relationship between the highest control field amplitude and the minimum evolution timeremarkably well. Finally, we discuss both challenges and ways forward for obtaining tighter bounds for higher dimensional systems, offering a discussion about the mathematical form and the physical meaning of the bound.
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