Quantum Computing in Plato’s Cave

Abstract: We show that the mere observation of a quantum system can turn its dynamics from a very simple one into a universal quantum computation. This effect, which occurs if the system is regularly observed at short time intervals, can be rephrased as a modern version of Plato's Cave allegory. More precisely, in the original version of the myth, the reality perceived within the Cave is described by the projected shadows of some more fundamental dynamics (the Ideals) which is intrinsically simpler (intelligible). We found that in the quantum world the "projected" reality perceived through sequences of measurements is even more complex than in a classical world. After discussing examples we go on to show that this effect is generally to be expected: almost any quantum dynamics will become universal once "observed" as outlined above. Conversely, we show that any complex quantum dynamics can be "purified" into a simpler one in larger dimensions. Reference: [1] D. Burgarth, P. Facchi, V. Giovannetti, H. Nakazato, S. Pascazio, K. Yuasa, "Exponential Rise of Dynamical Complexity in Quantum Computing through Projections," Nature Communications 5, 5173 (2014). http://dx.doi.org/10.1038/ncomms6173 [2] D. Orsucci, D. Burgarth, P. Facchi, H. Nakazato, S. Pascazio, K. Yuasa, V. Giovannetti, "Hamiltonian Purification," arXiv:1411.0316 [quant-ph]. http://arxiv.org/abs/1411.0316 -------------------------------------------------------------------------