Computing scalar products via a two-terminal quantum transmission line

Publication date: Available online 12 September 2019Source: Physics Letters AAuthor(s): J. Stolze, A.I. ZenchukAbstractThe scalar product of two vectors with K 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 K-qubit sender and both channels share a single two-qubit receiver. The K 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.

Source: Physics Letters A - September 13, 2019 Category: Physics Source Type: research