Supervised Quantum Learning without Measurements

We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation that introduces feedback in the dynamics and eliminates the necessity of intermediate measurements. The performance of the quantum algorithm is analyzed by comparing the results obtained in numerical simulations with the outcome of classical machine learning methods for the same problem. The use of time-delayed equations enhances the toolbox of the field of quantum machine learning, which may enable unprecedented applications in quantum technologies. The authors acknowledge support from Basque Government grants BFI-2012-322 and IT986-16, Spanish MINECO/FEDER FIS2015-69983-P, Ramon y Cajal Grant RYC-2012-11391, and UPV/EHU UFI 11/55.