Universal discriminative quantum neural networks
Abstract
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train nearterm quantum circuits to classify data represented by nonorthogonal quantum probability distributions using the Adam stochastic optimization algorithm. This is achieved by iterative interactions of a classical device with a quantum processor to discover the parameters of an unknown nonunitary quantum circuit. This circuit learns to simulates the unknown structure of a generalized quantum measurement, or PositiveOperatorValueMeasure (POVM), that is required to optimally distinguish possible distributions of quantum inputs. Notably we use universal circuit topologies, with a theoretically motivated circuit design, which guarantees that our circuits can in principle learn to perform arbitrary inputoutput mappings. Our numerical simulations show that shallow quantum circuits could be trained to discriminate among various pure and mixed quantum states exhibiting a tradeoff between minimizing erroneous and inconclusive outcomes with comparable performance to theoretically optimal POVMs. We train the circuit on different classes of quantum data and evaluate the generalization error on unseen mixed quantum states. This generalization power hence distinguishes our work from standard circuit optimization and provides an example of quantum machine learning for a task that has inherently no classical analogue.
 Publication:

arXiv eprints
 Pub Date:
 May 2018
 arXiv:
 arXiv:1805.08654
 Bibcode:
 2018arXiv180508654C
 Keywords:

 Quantum Physics;
 Computer Science  Neural and Evolutionary Computing;
 Statistics  Machine Learning
 EPrint:
 19 pages, 10 figures