Quantum computational speedup and retrocausality

Abstract

Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a classical logic description, with surprising consequences. In the classical logic description of the quantum algorithm, very simply, it is as if the problem-solver knew in advance, before beginning her problem-solving action, one of the possible halves of the information that specifies the solution of the problem she will produce and measure in the future and could use this knowledge to produce the solution with fewer computation steps. This is a causal loop whose retrocausal character turns out to be implicit in the very notion of quantum state superposition, both an essential ingredient of the quantum computational speedup and one of the pillars of quantum mechanics. Indeed, the key point of the work is that the classical logic description of a quantum state superposition must resort to a logical form of retrocausality that in turn must be physically implicit in the superposition itself. The existence of retrocausality in ordinary quantum physics implies e different way of viewing physical reality. It explains in a unified way all quantum speedups and quantum nonlocality. It highlights the teleological character of quantum algorithms, that is, their being evolutions toward a goal (the solution of the problem) with an attractor in the solution they will produce in the future (the solution again). Under the quantum cosmological assumption, it provides a plausible physical basis to the teleological character of natural evolutions.