# Towards interpretable quantum machine learning via single-photon quantum walks

arXiv: https://arxiv.org/abs/2301.13669 · HTML: https://mlsanity.com/paper/2301.13669/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 57 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)
- [Optimizing Quantum Error Correction Codes with Reinforcement Learning](https://mlsanity.com/paper/1812.08451/) (2018)
- [Reprogrammable Electro-Optic Nonlinear Activation Functions for Optical Neural Networks](https://mlsanity.com/paper/1903.04579/) (2019)
- [A Review of Modularization Techniques in Artificial Neural Networks](https://mlsanity.com/paper/1904.12770/) (2019)
- [Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learning](https://mlsanity.com/paper/2301.09138/) (2023)
- [Machine learning for long-distance quantum communication](https://mlsanity.com/paper/1904.10797/) (2019)
- [Multiqubit and multilevel quantum reinforcement learning with quantum technologies](https://mlsanity.com/paper/1709.07848/) (2017)
- [Basic protocols in quantum reinforcement learning with superconducting circuits](https://mlsanity.com/paper/1701.05131/) (2017)
- [Photonic architecture for reinforcement learning](https://mlsanity.com/paper/1907.07503/) (2019)
- [How a minimal learning agent can infer the existence of unobserved variables in a complex environment](https://mlsanity.com/paper/1910.06985/) (2019)
- [Projective simulation for classical learning agents: a comprehensive investigation](https://mlsanity.com/paper/1305.1578/) (2013)
- [Projective simulation with generalization](https://mlsanity.com/paper/1504.02247/) (2015)
- [Speeding-up the decision making of a learning agent using an ion trap quantum processor](https://mlsanity.com/paper/1709.01366/) (2017)
- [Development of swarm behavior in artificial learning agents that adapt to different foraging environments](https://mlsanity.com/paper/2004.00552/) (2020)
- [Robotic Playing for Hierarchical Complex Skill Learning](https://mlsanity.com/paper/1603.00794/) (2016)

## Built on by (most cited first, 4 of 4)

- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Multi-Excitation Projective Simulation with a Many-Body Physics Inspired Inductive Bias](https://mlsanity.com/paper/2402.10192/) (2024)
- [Free Energy Projective Simulation (FEPS): Active inference with interpretability](https://mlsanity.com/paper/2411.14991/) (2024)
- [Predictive control of blast furnace temperature in steelmaking with hybrid depth-infused quantum neural networks](https://mlsanity.com/paper/2504.12389/) (2025)

## Abstract (arXiv)

Variational quantum algorithms represent a promising approach to quantum machine learning where classical neural networks are replaced by parametrized quantum circuits. However, both approaches suffer from a clear limitation, that is a lack of interpretability. Here, we present a variational method to quantize projective simulation (PS), a reinforcement learning model aimed at interpretable artificial intelligence. Decision making in PS is modeled as a random walk on a graph describing the agent's memory. To implement the quantized model, we consider quantum walks of single photons in a lattice of tunable Mach-Zehnder interferometers trained via variational algorithms. Using an example from transfer learning, we show that the quantized PS model can exploit quantum interference to acquire capabilities beyond those of its classical counterpart. Finally, we discuss the role of quantum interference for training and tracing the decision making process, paving the way for realizations of interpretable quantum learning agents.