Researchers have developed a new quantum algorithm, the quantum Hermite transform, representing a move beyond the limited number of operations currently available for quantum computers to outperform classical systems. The collaborative effort between the U.S. Department of Energy’s Brookhaven National Laboratory, Northeastern University, Google Quantum AI, and University of Texas at Austin addresses a critical need for more versatile “primitives,” the fundamental building blocks of quantum computation. Hermite transforms are widely used in engineering and physics to describe the energy levels of the quantum harmonic oscillator and also underpin many Gaussian systems common in machine learning and data science, suggesting broad applications for this new capability. “The quantum Hermite transform is a quantum algorithm that implements the Hermite transform on a quantum state,” said Ning Bao, an assistant professor at Northeastern University with a joint appointment in Brookhaven Lab’s Computing and Data Sciences Directorate, whose DOE-funded project initiated the work. Quantum Hermite Transform as a Novel Primitive The development of genuinely useful quantum algorithms remains a significant hurdle in realizing the promise of quantum computing; currently, the field suffers from a limited number of standardized operations, or “primitives,” capable of delivering a quantum advantage. This innovation isn’t simply a quantum analogue of a classical mathematical tool, but a structurally distinct primitive poised to expand the scope of quantum computation, particularly in areas like artificial intelligence. Historically, performing these transforms on quantum computers has been inefficient. The team overcame this obstacle by designing a quantum circuit that executes the transform with logarithmic overhead, a substantial improvement even for large quantum states. This circuit leverages precise approximations of Hermite functions and a technique to the harmonic oscillator, allowing quantum computers to rapidly calculate future states. Combined with novel methods for configuring qubits, the quantum Hermite transform emerges as a practical and precise