Improving thermal state preparation of Sachdev-Ye-Kitaev model with reinforcement learning on quantum hardware

TL;DR

This paper introduces a reinforcement learning approach to efficiently prepare thermal states of the SYK model on quantum hardware, significantly reducing circuit complexity and maintaining accuracy even in noisy environments.

Contribution

It presents a novel RL-based framework that optimizes quantum circuits for thermal state preparation, outperforming traditional methods in complexity and scalability.

Findings

Reduces CNOT gates by two orders of magnitude for N≥12

Maintains high accuracy in both noiseless and noisy hardware

Demonstrates scalability for large SYK systems

Abstract

The Sachdev-Ye-Kitaev (SYK) model, known for its strong quantum correlations and chaotic behavior, serves as a key platform for quantum gravity studies. However, variationally preparing thermal states on near-term quantum processors for large systems ($N>12$, where $N$ is the number of Majorana fermions) presents a significant challenge due to the rapid growth in the complexity of parameterized quantum circuits. This paper addresses this challenge by integrating reinforcement learning (RL) with convolutional neural networks, employing an iterative approach to optimize the quantum circuit and its parameters. The refinement process is guided by a composite reward signal derived from entropy and the expectation values of the SYK Hamiltonian. This approach reduces the number of CNOT gates by two orders of magnitude for systems $N\geq12$ compared to traditional methods like first-order Trotterization. We demonstrate the effectiveness of the RL framework in both noiseless and noisy quantum hardware environments, maintaining high accuracy in thermal state preparation. This work advances a scalable, RL-based framework with applications for quantum gravity studies and out-of-time-ordered thermal correlators computation in quantum many-body systems on near-term quantum hardware. The code is available at https://github.com/Aqasch/solving_SYK_model_with_RL.