Time- and frequency-domain solutions in an optical analogue of Grover's search algorithm

Abstract

We present new results on an optical implementation of Grover's quantum search algorithm. This extends previous work in which the transverse spatial mode of a light beam oscillates between a broad initial input shape and a highly localized spike, which reveals the position of the tagged item. The spike reaches its maximum intensity after ∼ √ N round trips in a cavity equipped with two phase plates, where N is the ratio of the surface area of the original beam and the area of the phase spot or tagged item. In our redesigned experiment the search space is now two-dimensional. In the time domain we demonstrate for the first time a multiple item search where the items appear directly as bright spots on the images of a gated camera. In a complementary experiment we investigate the searching cavity in the frequency domain. The oscillatory nature of the search algorithm can be seen as a splitting of cavity eigenmodes, each of which concentrates up to 50% of its power in the bright spot corresponding to the solution.

Considerations for the extension of coherent optical processors into the quantum computing regime

“…In contrast, the Grover quantum algorithm can complete the search in O(N 1/2 ). Interestingly, the Grover quantum algorithm employs quantum interference but not entanglement 6 . Each data item is associated with a quantum state and a system of the superposition of all N quantum states is generated.…”

“…An iterative process is implemented that amplifies the amplitude of the target object to near unity at which point measurement of the wavefront leads its collapse at a position corresponding to the location of the target object in the database with near certainty. Bhattacharia et al 7 , and Hijmans et al 6 have shown, however, that a classical coherent optical system can implement the search in a very similar way by employing a classical optical wavefront, in contrast to a wavefunction. Their proposed system is iterative, to mimic more closely the Grover algorithm but, essentially, it is very closely related to a classical Zernike phase contrast arrangement which has been used for many years to detect spatial density changes in microscopy by converting phase changes generated by the spatial density variations of cells in the input field of view to intensity changes which are clearly visible.…”

Effect of geometry on the classical entanglement in a chaotic optical fiber

“…In Refs. [24][25][26], it was shown that the Grover and Deutsch algorithms can be implemented using classical entanglement and the cryptographic application was also pointed out in Ref. [30].…”

“…It was Spreeuw who realized the existence of classical entanglement [22,23]. Further research on this area revealed that classical entanglement can indeed be used as a resource [24][25][26][27]. In Refs.…”

Robust Quantum Searching with Spontaneously Decaying Qubits

“…(Color online) Steady state population in the solution, ρ00, as a function of the decay rate Γ. The data sets are for different numbers of qubits, from the top down: q = 6, 8,10,12,16,20,24, 28. The decay rate has been scaled by the frequency of the quantum search oscillation, ∼ 2 −q/2 .…”