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Demonstração óptica do algoritmo de Deutsch-Jozsa com 1 qubit

Mariana R. Barros

Published May 7, 2010• 0 citations
OpenAlex

Abstract

In this work we implement the Deutsch-Jozsa algorithm with one qubit by removing a redundancy on it, which reduces the size of the register and simpli es the function evaluation. In order to do this, we used a pair of photons produced by down convertion, where one of them is used as triguer and the other passes trougth a double slit; as result its output is in a superposition of paths, i.e., one qubit. Using a spatial light modulator (SLM) that puts phases on the paths of the photons, and detecting in coincidence, we demonstrate the Deutsch-Jozsa algorithm with photons, and using only one qubit.

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In this work we implement the Deutsch-Jozsa algorithm with one qubit by removing a redundancy on it, which reduces the size of the register and simpli es the function evaluation. In order to do this, we used a pair of photons produced by down convertion, where one of them is used as triguer and the other passes trougth a double slit; as result its output is in a superposition of paths, i.e., one qubit. Using a spatial light modulator (SLM) that puts phases on the paths of the photons, and detecting in coincidence, we demonstrate the Deutsch-Jozsa algorithm with photons, and using only one qubit.
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In this thesis we demonstrate experimentally the implementation of quantum processes and simulation of complex dynamics, through the manipulation of a quantum system. Pairs of entangled photons generated by spontaneous parametric down conversion (SPDC) were used as the quantum system. The entangled state in the transversal path has been manipulated using programmable spatial light modulators (SLM). A nonlinear crystal with phase matching type I and a continuouslaser beam with wavelength in the violet region were used for the generation of twin photons in entangled path states that allow us to vary the Hilbert space dimension. Three quantum protocols were experimentally studied in this thesis: minimum Deutsch algorithm, entanglement concentration and simulation of dissipative dynamics. In the Deutsch algorithm implementation were used twin photons generated by SPDC and a double slit to encode a spatial qubit were used. The second photon was used as a trigger to prepare a conditional state of the first. The SLM was used as the oracle mentioned in the algorithm, i. e., it is responsible for implementing the balancedand constant functions. The entanglement concentration protocol for two-qutrit states was also implemented. Partially entangled path states were generated using SPDC along with a SLM that modules amplitude only. A second SLM phase modulator inside a Sagnac interferometer was used to implement the protocol using the method known as Procustean. The third protocol demonstrated experimentally was the simulation of two dissipative dynamics in qudits: dephasing and amplitude. One of the photons passes through a noisy channel, implemented using a SLM, and the transmitted state is characterized allowing us to identify the noisy channel properties.
We show that deterministic quantum computing with one qubit (DQC1) can be experimentally implemented with a spatial light modulator, using the polarization and the transverse spatial degrees of freedom of light. The scheme allows the computation of the trace of a high-dimension matrix, being limited by the resolution of the modulator panel and the technical imperfections. In order to illustrate the method, we compute the normalized trace of unitary matrices and implement the Deutsch-Jozsa algorithm. The largest matrix that can be manipulated with our setup is $1080\ifmmode\times\else\texttimes\fi{}1920$, which is able to represent a system with approximately 21 qubits.