# Quantum-machine-learning channel discrimination

arXiv: https://arxiv.org/abs/2206.09933 · HTML: https://mlsanity.com/paper/2206.09933/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 80 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 13 of 13)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Experimental neural network enhanced quantum tomography](https://mlsanity.com/paper/1904.05902/) (2019)
- [Universal discriminative quantum neural networks](https://mlsanity.com/paper/1805.08654/) (2018)
- [Machine Learning Phase Transitions with a Quantum Processor](https://mlsanity.com/paper/1906.10155/) (2019)
- [Variational Quantum Eigensolver for Frustrated Quantum Systems](https://mlsanity.com/paper/2005.00544/) (2020)
- [Probing Criticality in Quantum Spin Chains with Neural Networks](https://mlsanity.com/paper/2005.02104/) (2020)

## Built on by (most cited first, 1 of 1)

- [Tensor networks in machine learning](https://mlsanity.com/paper/2207.02851/) (2022)

## Abstract (arXiv)

In the problem of quantum channel discrimination, one distinguishes between a given number of quantum channels, which is done by sending an input state through a channel and measuring the output state. This work studies applications of variational quantum circuits and machine learning techniques for discriminating such channels. In particular, we explore (i) the practical implementation of embedding this task into the framework of variational quantum computing, (ii) training a quantum classifier based on variational quantum circuits, and (iii) applying the quantum kernel estimation technique. For testing these three channel discrimination approaches, we considered a pair of entanglement-breaking channels and the depolarizing channel with two different depolarization factors. For the approach (i), we address solving the quantum channel discrimination problem using widely discussed parallel and sequential strategies. We show the advantage of the latter in terms of better convergence with less quantum resources. Quantum channel discrimination with a variational quantum classifier (ii) allows one to operate even with random and mixed input states and simple variational circuits. The kernel-based classification approach (iii) is also found effective as it allows one to discriminate depolarizing channels associated not with just fixed values of the depolarization factor, but with ranges of it. Additionally, we discovered that a simple modification of one of the commonly used kernels significantly increases the efficiency of this approach. Finally, our numerical findings reveal that the performance of variational methods of channel discrimination depends on the trace of the product of the output states. These findings demonstrate that quantum machine learning can be used to discriminate channels, such as those representing physical noise processes.