Universal discriminative quantum neural networks

TL;DR

This paper introduces universal discriminative quantum neural networks trained to classify non-orthogonal quantum states, demonstrating their ability to learn optimal quantum measurements with shallow circuits and generalize to unseen data.

Contribution

It presents a novel approach using universal quantum circuit topologies to learn optimal quantum measurements for state discrimination, applicable to both pure and mixed states.

Findings

Shallow quantum circuits can effectively discriminate quantum states.

The method achieves performance comparable to optimal POVMs.

The approach demonstrates strong generalization to unseen quantum data.

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 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.