Computing scalar products via a two-terminal quantum transmission line
arXiv:1905.10093 · doi:10.1016/j.physleta.2019.125978
Abstract
The scalar product of two vectors with real components can be computed using two quantum channels, that is, information transmission lines in the form of spin-1/2 XX chains. Each channel has its own -qubit sender and both channels share a single two-qubit receiver. The elements of each vector are encoded in the pure single-excitation initial states of the senders. After time evolution, a bi-linear combination of these elements appears in the only matrix element of the second-order coherence matrix of the receiver state. An appropriate local unitary transformation of the extended receiver turns this combination into a renormalized version of the scalar product of the original vectors. The squared absolute value of this scaled scalar product is the intensity of the second-order coherence which consequently can be measured, for instance, employing multiple-quantum NMR. The unitary transformation generating the scalar product of two-element vectors is presented as an example.
16 pages, 2 figures, accepted for publication in Phys. Lett. A, 2019
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