Entanglement is a phenomenon in quantum physics where two or more systems become interconnected in a manner that makes it impossible to describe their quantum states separately. When systems interact and become entangled, they exhibit strong correlations.

This concept is crucial for quantum computing, as the degree of entanglement directly influences the optimization and efficiency of a quantum computer. The more entangled the systems are, the better the performance of the quantum computer.

A study conducted by researchers affiliated with the Department of Physics at São Paulo State University’s Institute of Geosciences and Exact Sciences (IGCE-UNESP) in Rio Claro, Brazil, tested a novel method of quantifying entanglement and the conditions for its maximization. Applications include optimizing the construction of a quantum computer.

An article on the study is published as a Letter in Physical Review B.

Breaking Down the Hellmann-Feynman Theorem

The study showed how the Hellmann-Feynman theorem breaks down under specific conditions. The theorem describes the dependence of the system’s own energy on a control parameter and is a key part of quantum mechanics used across disciplines from quantum chemistry to particle physics.

“Simply put, we propose a quantum analog of the Grüneisen parameter widely used in thermodynamics to explore finite temperature and quantum critical points. In our proposal, the quantum Grüneisen parameter quantifies entanglement, or von Neumann entropy, in relation to a control parameter, which may be a magnetic field or a certain level of pressure, for example,” Valdeci Mariano de Souza, last author of the article and a professor at IGCE-UNESP, told Agência FAPESP. “Using our proposal, we demonstrate that entanglement will be maximized in the vicinity of quantum critical points and that the Hellmann-Feynman theorem breaks down at a critical point.”

For Souza, the results contribute to basic research in physics and could also have a direct impact on quantum computing. Recalling Intel cofounder Gordon Moore’s 1965 prediction that the number of transistors used in conventional computers would double every two years, he said this rapid growth in the power of classical computers cannot last, while recent technological advances are enabling quantum computing to progress by leaps and bounds, with giants like Google and IBM in the lead.

“In conventional computing, binary language in terms of zeroes and ones is used to process information. Quantum mechanics, however, superimposes states and hugely increases processing capacity. Hence the growing interest in research on quantum entanglement,” he explained.

Sources:
Published 6 October 2023, Physical Review B; “Grüneisen parameter as an entanglement compass and the breakdown of the Hellmann-Feynman theorem”
DOI: 10.1103/PhysRevB.108.L140403
Research leading to production of the article was supported by FAPESP via projects 11/22050-4 and 18/09413-0.

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