Machine learning the arrow of time in solid-state spins

TL;DR

This paper demonstrates how machine learning techniques can identify the thermodynamic arrow of time in quantum spin systems by analyzing experimental trajectories, revealing entropy production and energy flow with high accuracy.

Contribution

It introduces machine learning methods to detect time asymmetry and entropy production in quantum thermodynamics experiments, a novel approach in the field.

Findings

Unsupervised clustering separates trajectories by time direction.

Neural network identifies trajectory direction with ~92% accuracy.

Generative model reproduces energy flow and entropy signatures.

Abstract

Understanding the emergence of the thermodynamic arrow of time in microscopic systems is of fundamental importance, particularly given that unitary evolution preserves time-reversal symmetry. While projective measurements introduce temporal irreversibility, identifying this asymmetry from single evolution trajectories in the presence of stochastic fluctuations presents a considerable challenge. Here, we harness machine learning to identify the arrow of time from individual trajectories generated by a programmable ten-qubit quantum processor based on a nitrogen-vacancy center in diamond. We implement quantum circuits that realize unitary evolutions where heat flows from hotter to colder subsystems and their time-reversed counterparts. Projective measurements inserted in these processes induce entropy production, and their outcomes constitute the evolution trajectory. We demonstrate that an unsupervised clustering algorithm autonomously divides the experimental trajectories into two distinct groups without prior knowledge, while a convolutional neural network identifies the temporal direction of these trajectories with approximately 92% accuracy. In addition, we show that a diffusion-based generative model reproduces essential signatures of directional energy flow and entropy production. Our results establish machine learning as a powerful tool for uncovering underlying physical processes from complex experimental data, advancing the interface between quantum thermodynamics and artificial intelligence.