Photon gates in atomic ensembles
نویسندگان
چکیده
Quantum computers operate with qubits, which are entities that can be in the state |0〉, state |1〉 or any superposition (linear combination) of those. One of the essential parts of a quantum computer is a controlled two-qubit gate. An example of such gate is the controlled phase gate, which imparts a phase of π (i.e. multiplies by −1) to the state, where both qubits are in |1〉. In this thesis we shall look at three different schemes to implement a controlled phase gate for qubits stored in photons. The photons are special in the sense that they normally do not interact with each other, which makes it hard to make controlled two-qubit gates with them. This is why the usual role of the photons in quantum computing is to carry quantum information over long distances instead of being the registers of a quantum computer that the quantum algorithms are run on directly. However, the single-qubit gates for photons work very well, and if an efficient two-qubit gate was constructed, the photons could also possibly function in the latter role. We are going to use atoms with a certain energy level structure to make an effective interaction between the photons. In the first of the three controlled phase gate schemes, only one such atom will be used. The description of the first scheme consists of an intuitive derivation based on physical arguments which is then verified by running the numerical simulations. Afterwards we look at two modifications that make use of an ensemble of those atoms and the collective enhancement effects that it can give. The second scheme builds upon the analytical results of the first one. The last scheme is treated using a different effective theory of the interaction and under a number of approximations. Hence as the last topic in this thesis we take the first steps towards verifying this effective theory and the other approximations by running the numerical simulations. Resumé p̊a dansk Kvantecomputere opererer med qubits, som er enheder, der kan være i tilstanden |0〉, tilstanden |1〉 eller en vilk̊arlig superposition (lineær kombination) af disse. En af de nødvendige dele af en kvantecomputer er en kontrolleret to-qubit gate. Et eksempel af s̊adan en gate er den kontrollerede fase gate, som giver en fase af π (dvs. ganger med −1) til tilstanden, hvor begge qubits er i |1〉. I denne afhandling skal vi kigge p̊a tre forskellige tilgange til at realisere en kontrolleret fase gate for qubits gemt i fotoner. Fotonerne er specielle i den forstand, at de normalt ikke vekselvirker med hinanden, hvilket gør det svært at lave kontrollerede to-qubit gates med dem. Derfor er fotonernes sædvanlinge rolle i kvantedatabehandling at overføre kvanteinformation over lange afstande i stedet for at være registre i en kvantecomputer, som kvantealgoritmer er kørt p̊a direkte. Fra den anden side virker enkelt-qubit gates for fotoner godt, og hvis en effektiv to-qubit gate var konstrueret, s̊a ville fotoner ogs̊a kunne fungere i den sidstenævnte rolle. Vi skal bruge atomer med en bestemt energiniveaustruktur for at lave en effektiv vekselvirkning mellem fotoner. I den første af de tre tilgange til at lave en kontrollet fase gate vil kun ét s̊adant atom blive brugt. Beskrivelsen af den første tilgang best̊ar af en intuitiv udledning baseret p̊a fysiske argumenter, hvilket er dernæst verificeret ved at køre numeriske simulationer. Efterfølgende kigger vi p̊a to modifikationer, som benytter et ensemble af disse atomer og de kollektive forstærkningseffekter, som det kan give. Den anden tilgang g̊ar ud fra de analytiske resultater af den første. Den sidste tilgang er behandlet vha. en anden effektiv teori af vekselvirkningen og en række af approksimationer. Derfor som det sidste emne af denne afhandling tager vi de første skridt imod verificering af denne effektive teori og de andre approksimationer ved at køre numeriske simulationer.
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