en.Wedoany.com Reported - Researchers from the U.S. Department of Energy's Brookhaven National Laboratory, Northeastern University, Google Quantum AI, and the University of Texas at Austin have collaboratively developed a quantum algorithm known as the Quantum Hermite Transform, which overcomes the limitations on the number of operations current quantum computers can execute, enabling performance surpassing classical systems. The Hermite transform is widely used in engineering and physics to describe the energy levels of quantum harmonic oscillators and also forms the basis of common Gaussian systems in machine learning and data science, indicating broad application prospects for this new capability. Ning Bao, an assistant professor at Northeastern University who also holds a position in the Computational and Data Science Directorate at Brookhaven National Laboratory, stated that the Quantum Hermite Transform is a quantum algorithm that implements the Hermite transform on quantum states, and the project was initiated with funding from the U.S. Department of Energy.

The development of truly useful quantum algorithms remains a major obstacle to realizing the promise of quantum computing, as the field currently lacks a sufficient number of standardized operations to provide a quantum advantage. This innovation is not merely a quantum simulation of a classical mathematical tool but a structurally different new primitive that promises to expand the application scope of quantum computing in fields such as artificial intelligence. The research team overcame the previous inefficiency of executing these transforms on quantum computers by designing a quantum circuit with logarithmic overhead, a significant improvement even for large quantum states. This circuit leverages precise approximations of Hermite functions and a technique tailored for harmonic oscillators, enabling quantum computers to rapidly compute future states. Combined with new methods for configuring qubits, the Quantum Hermite Transform becomes a practical and precise quantum primitive. Bao explained that rapidly advancing a quantum system means directly calculating its state at a specific moment, which can substantially reduce the time required to prepare a quantum state if the time evolution lasts for a long duration. Bao emphasized that the significance of this work lies in the fact that quantum computing currently lacks a sufficient library of core algorithmic primitives, which are essential for more complex algorithms.

The development of the Quantum Hermite Transform addresses the critical bottleneck of the limited number of foundational algorithms available in quantum computing. Existing methods often rely on variants of mature techniques like the Quantum Fourier Transform, restricting the scope of quantum advantage, whereas the Quantum Hermite Transform offers a structurally different approach with the potential to unlock new computational pathways. This new algorithm efficiently transfers mathematical operations used in fields such as physics and machine learning onto quantum hardware. Its key innovation lies in performing the transform with logarithmic overhead, meaning the required computational steps scale proportionally to the logarithm of the problem size rather than linearly, thus providing exponential speedup for large quantum states. The research team also introduced a technique that enables quantum computers to directly calculate the future state of a system, bypassing lengthy simulations. Combined with new methods for correctly initializing qubits, the Quantum Hermite Transform creates a practical, high-precision primitive capable of analyzing and representing data in new ways. Bao stated that quantum computers are powerful, but without quantum algorithms, the scope of this power is very limited. The development of the Quantum Hermite Transform stems from a project funded by the U.S. Department of Energy, highlighting the importance of sustained investment in expanding the algorithmic foundation of quantum computing and broadening its potential impact across scientific disciplines. This efficiency is further enhanced by the Quantum Hermite Transform's ability to directly calculate the future state of a quantum system, significantly reducing preparation time.