DOE’s Northeastern & Brookhaven Lab Expand Quantum Computing Toolkit

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 quantum primitive. Bao clarified that “fast forwarding a quantum system means to directly compute its state at a specific moment in time.” She added that if the time evolution is over a very long duration, this can drastically reduce the amount of time needed to prepare a quantum state. Bao emphasizes the importance of this work because quantum computing currently lacks a sufficient library of core algorithmic primitives, essential for more complex algorithms.

This scarcity often leads to reliance on variations of existing techniques, limiting the range of solvable problems. “Having new primitives enables solving broader suites of problems, including those relevant to real-world science,” Bao added, positioning the quantum Hermite transform not as a final solution, but as a reusable operation, akin to a quantum gate, that empowers quantum computers to surpass classical systems.

The development of the quantum Hermite transform (QHT) addresses a critical bottleneck in quantum computing: the limited number of fundamental algorithms, or “primitives,” available to tackle complex problems. Existing methods often rely on variations of established techniques like the quantum Fourier transform, restricting the scope of quantum advantage; however, the QHT offers a structurally distinct approach with the potential to unlock new computational pathways. This new algorithm isn’t simply a theoretical exercise; it’s designed to efficiently translate mathematical operations used in fields like physics and machine learning onto quantum hardware. A key innovation lies in the QHT’s ability to perform transformations with logarithmic overhead, a significant improvement over traditional methods. This means the computational steps required scale proportionally to the logarithm of the problem size, rather than linearly, offering exponential speedups for large quantum states. The team also incorporated a technique, allowing quantum computers to directly compute a system’s future state, bypassing lengthy simulations. Crucially, the QHT is paired with novel methods for the process of configuring qubits in the correct initial configuration. This combination creates a practical, high-precision primitive capable of analyzing and representing data in new ways. According to Bao, “Quantum computers are powerful, but without quantum algorithms, the realm of applicability of this power is very limited.” The development of QHT, originating from a DOE-funded project, underscores the importance of sustained investment in expanding the algorithmic foundations of quantum computing and broadening its potential impact across scientific disciplines. This efficiency is further enhanced by the QHT’s ability to quantum systems, directly computing a system’s future state and drastically reducing preparation time.