# Universal discriminative quantum neural networks

arXiv: https://arxiv.org/abs/1805.08654 · HTML: https://mlsanity.com/paper/1805.08654/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2018.

## Built on by (most cited first, 16 of 16)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Concentration of Data Encoding in Parameterized Quantum Circuits](https://mlsanity.com/paper/2206.08273/) (2022)
- [A Leap among Quantum Computing and Quantum Neural Networks: A Survey](https://mlsanity.com/paper/2107.03313/) (2021)
- [Toward Physically Realizable Quantum Neural Networks](https://mlsanity.com/paper/2203.12092/) (2022)
- [RGB Image Classification with Quantum Convolutional Ansaetze](https://mlsanity.com/paper/2107.11099/) (2021)
- [Unleashing the Expressive Power of Pulse-Based Quantum Neural Networks](https://mlsanity.com/paper/2402.02880/) (2024)
- [Quantum Machine Learning For Classical Data](https://mlsanity.com/paper/2105.03684/) (2021)
- [QFCNN: Quantum Fourier Convolutional Neural Network](https://mlsanity.com/paper/2106.10421/) (2021)
- [Quantum-machine-learning channel discrimination](https://mlsanity.com/paper/2206.09933/) (2022)
- [Energy-dependent barren plateau in bosonic variational quantum circuits](https://mlsanity.com/paper/2305.01799/) (2023)
- [Quantum Natural Stochastic Pairwise Coordinate Descent](https://mlsanity.com/paper/2407.13858/) (2024)
- [Computing Graph Edit Distance with Algorithms on Quantum Devices](https://mlsanity.com/paper/2111.10183/) (2021)
- [Fourier series weight in quantum machine learning](https://mlsanity.com/paper/2302.00105/) (2023)
- [Quantum-data-driven dynamical transition in quantum learning](https://mlsanity.com/paper/2410.01955/) (2024)
- [Machine Learning for Quantum Noise Reduction](https://mlsanity.com/paper/2509.16242/) (2025)

## Abstract (arXiv)

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.