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Quantum Computing

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    $\begingroup$ I have added a comment clarifying what I mean by 'existence'. The first paper you link to is not an experiment that creates and manipulates anyons: the abstract says that they use polarized photons (bosons) to simulate the behavior of anyons by encoding a model of anyons in the photonic qubits (analog quantum simulation). Likewise is the case for your paper, except with superconducting qubits instead of photonic ones. The question remains, whether or not an exchange factor different from $\pm1$ has ever been confirmed experimentally in a peer reviewed journal! $\endgroup$ Commented May 14, 2018 at 23:26
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    $\begingroup$ I don’t see much of a difference between a ‘simulation’ and a realization with a Hamiltonian. Is the latter not also something like a simulation, since the anyons are only quasiparticles? As long as topologically ordered states are used, I think they are both equally valid. $\endgroup$ Commented May 15, 2018 at 5:35
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    $\begingroup$ +1 Thanks @JamesWotton. This at least partly answers what I wanted to know. If I interpreted this correctly, for performing topological quantum computing, all we need to do is simulate "anyonic" behaviour/statistics. The world lines of these "simulated anyons" can be used to create logic gates which make up the computer (although I'm not aware of the exact method and might ask that as a fresh question). That is, as far as I understand: it isn't necessary for anyonic statistics to exist "in nature" for performing topological quantum computing; a simulation of that kind of statistics suffices. $\endgroup$ Commented May 15, 2018 at 6:11
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    $\begingroup$ @JamesWootton: If I simulate a 10 qubit quantum computer by diagonalizing a $2^{10} \times 2^{10}$ matrix on a classical computer, have I made a quantum computer, or have I simulated one? The latter is not scalable in this case. Imagine that quantum theory existed without any experimental evidence (i.e. entangled states or superpositions were never confirmed in experiment, and neither was anything else quantum, such as discrete levels in the H atom). Then we can still use a classical computer to show that a 3-qubit Deutsch-Josza algorithm works, but still we have no evidence that qubits [cont] $\endgroup$ Commented May 15, 2018 at 17:32
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    $\begingroup$ This isn’t the same kind of simulation though. We aren’t just describing the quantum states involved on a classical computer, we are creating them using actual quantum systems. The only difference with a ‘true’ implementation is the lack of the Hamiltonian. But since the only job of the Hamiltonian is to create and protect the states (which we are doing manually instead) and not to induce dynamics, I don’t see why it’s absence makes the anyons any less anyonic. $\endgroup$ Commented May 15, 2018 at 18:39