The Role of Interference and Entanglement in Quantum Computing.

Anwar Y. Shiekh

Arun Kumar Pati, Samuel L. Braunstein

Benoît Vermersch

Alexandr Alexandrovich Ezhov, G. P. Berman

The role of interference and entanglement in quantum neural processing is discussed. It is argued that on contrast to the quantum computing the problem of the use of exponential resources as the payment for the absence of entanglement does not exist for quantum neural processing. This is because of corresponding systems, as any modern classical artificial neural system, do not realize functions precisely, but approximate them by training on small sets of examples. It can permit to implement quantum neural systems optically, because in this case there is no need in exponential resources of optical devices (beam-splitters etc.). On the other hand, the role of entanglement in quantum neural processing is still very important, because it actually associates qubit states: this is necessary feature of quantum neural memory models.

Hugo Thomas, Pierre-Emmanuel Emeriau, Rawad Mezher +3 more

Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness, and coherence are arguably of great significance. We introduce "path coherence" as a measure of the coherent path interferences arising in a quantum computation. Leveraging the sum-over-paths formalism, we obtain a classical algorithm for estimating quantum transition amplitudes, the complexity of which scales with path coherence. As path coherence relates to the hardness of classical estimation of quantum transition amplitudes, it provides a new perspective on the role of coherence in quantum computational advantage. Beyond their fundamental significance, our results have practical applications for simulating large classes of quantum computations with classical computers.