  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 near-term quantum circuits to
classify data represented by non-orthogonal 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 non-unitary quantum circuit. This circuit learns to
simulates the unknown structure of a generalized quantum measurement, or
Positive-Operator-Value-Measure (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
input-output mappings. Our numerical simulations show that shallow quantum
circuits could be trained to discriminate among various pure and mixed quantum
states exhibiting a trade-off 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.
