Meta-Algorithms Efficiently Prepare Thermal States on Noisy Intermediate-Scale Quantum Devices

Preparing the quantum states that describe systems at finite temperature presents a significant hurdle in modern computation, with implications for modelling complex physical systems and advancing quantum machine learning. Ruchira V Bhat, Rahul Bhowmick, Avinash Singh, and colleagues at Fujitsu Research of India address this challenge by introducing new meta-learning algorithms, Meta-Variational Thermalizer and Neural Network Meta-VQT, designed to efficiently prepare these thermal states on current quantum computers. These methods learn from a range of different system parameters, allowing them to quickly and accurately generate thermal states even for systems they haven’t encountered before, a capability demonstrated on systems up to eight qubits. Importantly, the team showcases the practical application of these algorithms by training a Quantum Boltzmann Machine with a substantial speedup over existing methods, paving the way for more efficient and scalable quantum machine learning applications.

Inspired by previous work, researchers have developed two new meta-learning algorithms, Meta-Variational Quantum Thermalizer (Meta-VQT) and Neural Network Meta-VQT (NN-Meta VQT), for efficiently preparing thermal states on current quantum computers. Both algorithms leverage collective optimization over training sets to generalize Gibbs state preparation to unseen parameters, demonstrating effectiveness on systems up to eight qubits.

Metropolis Algorithm for Thermal State Preparation

This research addresses the challenge of preparing thermal states, crucial for many quantum algorithms, on near-term quantum computers. The authors introduce Meta-VQT and NN-Meta VQT, which aim to learn how to efficiently prepare these states using variational quantum circuits. The key innovation is a meta-learning approach, where circuit parameters are optimized to minimize the difference between the prepared state and the target thermal state. Meta-VQT employs a variational quantum circuit with parameters to be optimized, minimizing a loss function that measures the distance between the prepared and target states.

NN-Meta VQT enhances this by using a neural network to map Hamiltonian parameters to circuit parameters, allowing for a more flexible and expressive parameterization. The team also demonstrates the application of NN-Meta VQT to train Quantum Boltzmann Machines (QBMs), preparing the Gibbs state of the QBM and updating its parameters to model a target probability distribution. The results demonstrate that NN-Meta VQT is more robust to the complexity of the Hamiltonian than traditional methods, and effectively trains QBMs. The research achieves improved accuracy and robustness in preparing thermal states, utilizes neural networks to enhance expressibility and training efficiency, and provides a thorough experimental setup and clear pseudoalgorithms.

Meta-Learning Optimizes Thermal State Preparation

Researchers have developed new techniques for preparing Gibbs states, crucial for simulating quantum systems and with broad applications in fields like materials science and drug discovery. These methods, termed Meta-Variational Thermalizer (Meta-VQT) and Neural Network Meta-VQT (NN-Meta VQT), address a fundamental challenge in quantum computing by efficiently preparing these states on current, noisy quantum hardware. The core innovation lies in a collective optimization approach, where the algorithms learn to prepare Gibbs states not just for specific parameter settings, but across a range of values, improving their ability to generalize beyond the initial training data. The team’s approach builds upon existing variational quantum algorithms, but introduces a meta-learning component, akin to “learning to learn” in classical machine learning.

Instead of training a quantum circuit for each new set of parameters defining a quantum system, the algorithms train a system that can quickly adapt to unseen parameters. This is achieved by training the algorithms on a set of parameters and then applying that learned knowledge to prepare Gibbs states for new, previously unseen parameters. Demonstrations on systems up to eight qubits, including the Transverse Field Ising and Heisenberg models, show that the meta-trained algorithms can accurately generate thermal states beyond the data used for training. For larger systems, the algorithms serve as effective starting points for optimization, significantly outperforming random initializations. For a three-qubit Kitaev ring model, the algorithms effectively captured the behavior of the system across different temperature ranges, demonstrating their ability to handle finite-temperature effects. The team observed a 30-fold speedup compared to existing techniques, alongside improved accuracy in preparing the Gibbs states needed for training, suggesting a pathway towards scalable and efficient quantum machine learning.

Meta-Algorithms Generalize Thermal State Preparation

Researchers have developed two new meta-algorithms, Meta-Variational Thermalizer (Meta-VQT) and Neural Network Meta-VQT (NN-Meta VQT), designed to efficiently prepare thermal states on near-term quantum computers. These methods move beyond traditional approaches by training the algorithms to learn the Gibbs state across a range of Hamiltonian parameters, rather than optimizing for each parameter individually. This collective optimization allows for generalization to unseen parameter configurations, reducing the quantum resources needed and accelerating the process of finding thermal states. Demonstrations on systems up to eight qubits, including the Transverse Field Ising and Heisenberg models, show that the meta-trained algorithms can accurately generate thermal states beyond the data used for training.

For larger systems, the algorithms serve as effective starting points for optimization, significantly outperforming random initializations. Furthermore, the approach successfully prepares Gibbs states across finite-temperature crossover regimes, as demonstrated with a Kitaev ring model, and enhances the training of a Boltzmann quantum machine, achieving a 30-fold runtime speedup compared to existing techniques. The authors acknowledge that their numerical results are currently based on two-qubit Hamiltonians, and scaling to larger systems and more complex models may require deeper quantum circuits. The research highlights the potential of meta-algorithms to overcome limitations in preparing thermal states on noisy intermediate-scale quantum devices.