Optical simulation of quantum algorithms using programmable liquid-crystal displays

We present a scheme to perform an all optical simulation of quantum algorithms and maps. The main components are lenses to efficiently implement the Fourier transform and programmable liquid-crystal displays to introduce space dependent phase changes on a classical optical beam. We show how to simulate Deutsch-Jozsa and Grover’s quantum algorithms using essentially the same optical array programmed in two different ways.

Figure 1

Configuration for Deutsch–Jozsa’s algorithm. The $457\text{nm}$ line of an Argon Laser is filtered, expanded, and collimated in order to illuminate homogeneously the oracle simulated by the spatial light modulator (SLM). In the focal plane of the second lens, a CCD captures the intensity distribution around the axis.

Figure 2

Top: Different oracle configurations in Deutsch–Jozsa algorithm corresponding to various setups of the programmable LCTV. They are associated with constant (a) or balanced functions (b), (c), and (d). Bottom: The intensity in the CCD camera is nonzero at the zero frequency only if the function is constant, as predicted by the algorithm. The center of the dotted crosses indicates this frequency.

Figure 3

(a) Oracle configuration in Deutsch-Jozsa algorithm corresponding to a random balanced function. (b) Intensity in the CCD camera, (c) intensity profile corresponding to the dashed line marked in (b).

Figure 4

Convergent optical processor for the simulation of Grover’s algorithm. The first SLM modulates the phase of the initial homogenous wave front to mark the items being searched for. Next, the IAA operation is carried out by the second SLM. The CCD1 captures the output signal. In dotted line we show how the addition of a flipper mirror allows us to simulate the Deustch-Jozsa algorithm by using the same configuration.

Figure 5

(a) The different items of the four-state database. The upper images (b) are registered when the oracle marks one by one the four items. The lower intensity profiles (c) correspond to the lines marked on the images.

Figure 6

(a) Squared entrance pupil, where the different numbers label the items of the 2D 16–state database. (b) Intensity output, and the corresponding profile, when the oracle marks 1–2, 1–4, 3–2, and 3–4 labeled states.