A Few Constrain Many: Correlation-Enhanced Learning of Many-Body Quantum Systems

Abstract:Discovering properties of many-body quantum systems is challenging because of the large number of parameters to determine. Here, we show that correlations among quantum observables help reduce the complexity of quantum learning. A polynomial number of selected measurements can bound the values of exponentially many dependent yet unmeasured quantities, enabling efficient estimation of general functions of quantum states. We leverage this result to design correlation-informed learning algorithms that estimate key quantum resources, such as entanglement and magic, in systems of 100 qubits. They achieve a lower relative error than shadow tomography and neural-state methods by using information about a polynomial number of measured Pauli strings. These protocols are readily testable with today's quantum computers, as they do not require premeasurement entangling gates. Quantum constraints themselves are therefore a resource for exploring large quantum systems.

arXiv:2609.39935 [quant-ph]

(or arXiv:2609.39935v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.39935 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.