Quantum computing continues to explore practical applications in machine learning, but challenges remain in efficiently loading classical data and training algorithms onto current hardware. Luca Candelori from Qognitive, Inc., Swarnadeep Majumder and Antonio Mezzacapo from IBM Quantum, along with Javier Robledo Moreno and others, demonstrated how to overcome these hurdles. Their work focuses on a linear Hamiltonian-based machine learning approach, which uses a k-local Hamiltonian ground state problem to represent classical data in a compact form. By employing a sample-based Krylov diagonalization method, the team was able to compute low-energy states and train parameters to represent a classical dataset. Experiments performed on IBM's Heron processor utilizing up to 50 qubits demonstrate the potential effectiveness and scalability of this new technology for quantum machine learning.
Quantum machine learning has long promised revolutionary advances in data analysis, but practical implementation remains difficult due to fundamental obstacles such as the enormous quantum cost of loading classical data and the poor trainability of many quantum machine learning algorithms designed for short-term quantum hardware. In this work, we demonstrate how to overcome these obstacles by employing a linear Hamiltonian-based machine learning approach, providing a compact quantum representation of classical data via the k-local Hamiltonian ground state problem. The researchers utilize a sample-based Krylov quantum diagonalization method to compute the low-energy states of the data Hamiltonian, paving the way for practical applications and significantly contributing to realizing the potential of quantum machine learning with currently available quantum hardware.
Data embedding with data-induced Hamiltonian
Researchers have pioneered a linear Hamiltonian-based method for compact classical data representation that leverages the k-local Hamiltonian ground state problem to effectively encode data within the quantum system itself. This innovative approach avoids the huge quantum costs traditionally associated with loading data and alleviates trainability issues common with short-term quantum algorithms. The team designed a system in which each data point induces a unique Hamiltonian constructed from fixed feature operators and corresponding feature values, enabling expressive data embeddings suitable for today's quantum processors. To approximate the ground states of these data-specific Hamiltonians, scientists developed and implemented a sample-based Krylov quantum diagonalization (SKQD) algorithm.
This technique extracts quantum samples from the Krylov quantum state and then performs classical diagonalization within the subspace defined by the sampled bit string, providing provable convergence to approximate the ground state energy and, subject to the ground state sparsity assumption, providing both ground state and low energy spectral approximations. The experiments used an IBM Heron quantum processor and utilized up to 50 qubits to demonstrate the effectiveness and scalability of the methodology. In this work, we utilized local gradients to train the parameters of these data Hamiltonians, allowing us to represent classical datasets within a quantum framework. This process effectively coordinates feature and label operators with the underlying learning task and facilitates accurate classification based on ground state measurements. In this work, we learn data encoding as a Hamiltonian, which avoids the need for predefined analyses, avoids challenges associated with barren plateaus and unfavorable local minima in variational quantum algorithms, and thus enables robust and efficient embedding of classical data that is resistant to hardware noise and classical simulability.
Efficient quantum data embedding by linear Hamiltonian scientists
Scientists have achieved a breakthrough in quantum machine learning by demonstrating a linear Hamiltonian-based method that can efficiently embed classical data into quantum hardware. The research team was able to successfully train a model on a benchmark dataset using up to 50 qubits on an IBM Heron processor, overcoming a long-standing hurdle in quantum data analysis and leveraging a compact representation of classical data through the k-local Hamiltonian ground state problem. This study focused on approximating the ground state using the sample-based Krylov diagonalization (SKQD) algorithm, a technique in which sparse ground state convergence is provable. Measurements confirm that the SKQD algorithm can effectively compute the low-energy states of the data Hamiltonian using parameters trained to represent the classical dataset through local gradients, and learn the data encoding as a Hamiltonian constructed from feature operators and their corresponding feature values, resulting in a separate Hamiltonian for each data point.
The team recorded non-vanishing gradients during training on the Heron processor. This is an important indicator of model training success. The results demonstrate that the model can be trained on a binary classification problem with 10 features, demonstrating the scalability of current prefault-tolerant quantum computers. The workflow operates on sparse ground states obtained from SKQD and explores only a small subspace of the complete Hilbert space, minimizing computational demands. Classical features are embedded as weighted combinations of Pauli terms in single-qubit and two-qubit gates to generate Krylov states and facilitate efficient data representation. In this work, we introduce a new approach to quantum machine learning that encodes data into k-local Hamiltonians to achieve a compact representation and avoid optimization collapse. Tests demonstrate the method's robustness to hardware noise and its potential to operate beyond the limits of classically simulable circuits, providing a path to practical machine learning on near-term quantum processors, with applications spanning finance, healthcare, and general data science.
Enabling scalable quantum machine learning with Hamiltonian training Researchers
Researchers have demonstrated successful training of linear Hamiltonian-based machine learning models utilizing modern quantum processors. This work overcomes obstacles in quantum machine learning related to data loading and algorithm trainability by representing classical data as a k-local Hamiltonian ground state problem. The team employed a sample-based Krylov diagonalization method to compute these low-energy states and trained Hamiltonian parameters to effectively represent classical datasets through local gradients. Experiments conducted on a benchmark dataset utilizing up to 50 qubits on a Heron processor confirmed the effectiveness and scalability of this approach. In particular, this study shows that gradient calculations do not necessarily require a large number of energy terms to achieve high accuracy, suggesting that quantum resources may be used efficiently. Future research will focus on hyperparameter optimization and evaluation on larger and more complex datasets, in parallel with systematic comparisons with classical methods, in order to identify scenarios where Hamiltonian-based encoding offers clear advantages.
