Quantum computers have enormous potential, but they're currently limited by a shortage of practical algorithms that can actually use that power. A new collaboration between scientists at the U.S. Department of Energy's Brookhaven National Laboratory, Northeastern University, Google Quantum AI, and the University of Texas at Austin has created what they call the quantum Hermite transform, a fundamental building block that could expand quantum computing's reach into artificial intelligence, materials science, and energy research.

The challenge quantum researchers face is straightforward but urgent: quantum computers lack the algorithmic "primitives," or basic operations, that classical computers take for granted. Most quantum algorithms today rely on variations of the same few techniques, which limits the types of problems they can solve. The quantum Hermite transform changes that by introducing a structurally different approach that could open entirely new problem domains.

What Makes This Algorithm Different?

To understand why this matters, consider how classical computers use Hermite transforms. These mathematical operations are used across engineering and physics to describe energy levels and are fundamental to machine learning systems that rely on Gaussian functions. However, switching a quantum computer into a Hermite-based representation has been slow and computationally expensive, requiring many operations to complete a single transformation.

The research team solved this "slog problem" by constructing an efficient quantum circuit that performs the transform with only logarithmic overhead. In practical terms, this means the quantum computer can complete the transformation in one step instead of many, even when working with extremely large quantum states.

"The quantum Hermite transform is a quantum algorithm that implements the Hermite transform on a quantum state. It is structurally quite distinct from existing quantum primitives, which could lead to more quantum algorithms that solve unique problems," explained Ning Bao, an assistant professor at Northeastern University with a joint appointment in Brookhaven Lab's Computing and Data Sciences Directorate.

Ning Bao, Assistant Professor, Northeastern University and Brookhaven National Laboratory

The algorithm also includes a technique called "fast-forwarding," which allows a quantum computer to jump directly to a quantum system's future state within a few operations. Combined with new methods for preparing quantum states, known as state preparation, the quantum Hermite transform becomes a practical, high-precision tool for analyzing and representing data in ways that classical computers cannot match.

How Does This Expand Quantum Computing's Capabilities?

The real significance of this work lies in what it enables. Quantum computing has been hampered by a limited toolkit of core algorithmic primitives, the building blocks essential for creating more complex quantum algorithms. Most quantum algorithms rely on variations of techniques like the quantum Fourier transform or stabilizer-based methods, which get applied to similar problems repeatedly. This narrow toolkit has confined quantum computing's practical applications to specific domains like physics and engineering research.

By introducing a fundamentally different primitive, the quantum Hermite transform could expand the types of problems quantum computers can tackle. The research team presented their work at the 58th Annual Association for Computing Machinery Symposium on Theory of Computing (STOC 2026) in Salt Lake City in late June 2026.

Steps to Understanding Quantum Algorithm Development

• Identify the bottleneck: Researchers recognized that quantum computers lacked diverse algorithmic primitives, limiting their ability to solve new classes of problems beyond traditional physics and engineering applications.
• Design a novel approach: The team created the quantum Hermite transform as a structurally distinct primitive that could enable new quantum algorithms by offering a different computational pathway than existing techniques.
• Optimize for efficiency: By reducing the computational overhead from many operations to just one logarithmic step, the algorithm became practical for real quantum hardware with limited resources.
• Validate through collaboration: Multi-institutional partnerships between national labs, universities, and industry research teams ensure the algorithm can be tested and refined across different quantum computing platforms.

The potential applications span multiple fields. Beyond artificial intelligence, the quantum Hermite transform could accelerate research in materials science, energy security, and advanced scientific modeling. According to Bao, the algorithm performs these tasks exponentially faster than known classical methods, which is the kind of advantage that could justify the investment in quantum computing infrastructure.

Why Is This Happening Now?

The timing reflects broader momentum in quantum computing. This week alone, multiple research teams reported significant advances in quantum error correction, a critical hurdle for building practical quantum computers. IBM and MIT demonstrated a new method for scalable, fault-tolerant quantum gates in two dimensions, while Google Quantum AI achieved a logical error rate of 7.72 × 10^-4 using the surface code, a key step toward practical quantum computing.

Meanwhile, international efforts are accelerating. India's National Quantum Mission, with a budget of approximately 6 billion rupees (roughly $72 million USD) for 2023 to 2031, aims to develop quantum computers with 50 to 1,000 physical qubits, secure quantum communication infrastructure, and quantum materials for device fabrication. Scientists at BITS Pilani, collaborating with IBM Quantum, recently simulated the behavior of subatomic particles on 120 qubits of an IBM processor, demonstrating quantum advantage in a practical application.

"Quantum computers are powerful, but without quantum algorithms, the realm of applicability of this power is very limited. Having new primitives enables solving broader suites of problems, including those relevant to real-world science. The quantum Hermite transform is a root rather than an endpoint, another staple, reusable operation, like the quantum gate, that empowers quantum computers to realize their advantage over classical systems," noted Bao.

Ning Bao, Assistant Professor, Northeastern University and Brookhaven National Laboratory

The quantum Hermite transform represents a shift in how researchers approach quantum computing development. Rather than focusing solely on building more qubits or reducing error rates, the emphasis is now on expanding the algorithmic toolkit that makes quantum computers useful for real-world problems. This work strengthens a core pillar of the U.S. Department of Energy's mission to advance the algorithmic foundations of quantum computing, ensuring that when quantum hardware matures, there will be algorithms ready to put it to work.