Time-optimal navigation through quantum wind

Brody, Dorje C.; Gibbons, G. W.; Meier, David M.

doi:10.1088/1367-2630/17/3/033048

Cited by 53 publications

(71 citation statements)

References 35 publications

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“…However, finding the shortest possible control pulses in general remains challenging. It is broadly equivalent to finding geodesics of Randers type Finsler metrics on either (special) unitary groups or complex projective spaces for the tasks of implementing gates or preparing states, respectively [36][37][38][39][40]. Other approaches also exist including brachistochrone equations [41], however as of yet these can only be addressed by numerical approaches and they are not geometrically intrinsic rendering analytical solutions harder to obtain.…”

Section: Introductionmentioning

confidence: 99%

The roles of drift and control field constraints upon quantum control speed limits

et al. 2017

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In this work we derive a lower bound for the minimum time 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. We use 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 time remarkably 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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Section: Introductionmentioning

confidence: 99%

The roles of drift and control field constraints upon quantum control speed limits

et al. 2017

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“…The modern formulation of QSL for unitary processes takes into account an alternative expression as an upper bound for the speed of evolution, the mean energy of the system, that can replace the role of energy dispersion Δ E 1232021. A geometric interpretation provides an intuitive understanding of the QSL bound as a brachistochrone22 where the geodesic2324 set by the Fubini-Study metric in (projective) Hilbert space is travelled at the maximum speed of evolution achievable under a given Hamiltonian dynamics25262728. Time-optimal evolutions are often explored in the context of quantum control theory, where the existence of a QSL has been shown to limit the performance of algorithms aimed at identifying optimal driving protocols1112.…”

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confidence: 99%

Fundamental Speed Limits to the Generation of Quantumness

Jing

Campo

2016

Sci Rep

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Quantum physics dictates fundamental speed limits during time evolution. We present a quantum speed limit governing the generation of nonclassicality and the mutual incompatibility of two states connected by time evolution. This result is used to characterize the timescale required to generate a given amount of quantumness under an arbitrary physical process. The bound is found to be tight under pure dephasing dynamics. More generally, our analysis reveals the dependence on the initial and final states and non-Markovian effects.

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“…Another area where the geometry of CP n comes to the aid of physics is in quantum control theory [45].…”

Section: Jhep01(2016)135mentioning

confidence: 99%

Compactifications of deformed conifolds, branes and the geometry of qubits

Cvetič

Gibbons

Pope

2016

J. High Energ. Phys.

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We present three families of exact, cohomogeneity-one Einstein metrics in (2n + 2) dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces CP n+1 , written in a Stenzel form, whose principal orbits are the Stiefel manifolds V 2 (R n+2 ) = SO(n+2)/SO(n) divided by Z 2 . The second family are also Einstein-Kähler metrics, now on the Grassmannian manifolds G 2 (R n+3 ) = SO(n+3)/((SO(n+1)×SO(2)), whose principal orbits are the Stiefel manifolds V 2 (R n+2 ) (with no Z 2 factoring in this case). The third family are Einstein metrics on the product manifolds S n+1 × S n+1 , and are Kähler only for n = 1. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. We also elaborate on the geometric approach to quantum mechanics based on the Kähler geometry of Fubini-Study metrics on CP n+1 , and we apply the formalism to study the quantum entanglement of qubits.

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Time-optimal navigation through quantum wind

Cited by 53 publications

References 35 publications

The roles of drift and control field constraints upon quantum control speed limits

The roles of drift and control field constraints upon quantum control speed limits

Fundamental Speed Limits to the Generation of Quantumness

Compactifications of deformed conifolds, branes and the geometry of qubits

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