A new quantum algorithm expands the toolkit for AI and science

On July 13, 2026, Brookhaven National Laboratory described a result that sounds abstract but addresses a very practical shortage in quantum computing: the field needs reusable operations from which to build algorithms. A team led by Siddhartha Jain, Vishnu Iyer, Rolando D. Somma, Ning Bao, and Stephen Jordan has proposed one: the Quantum Hermite Transform, or QHT. Their work was presented at the 58th ACM Symposium on Theory of Computing (STOC 2026), held in Salt Lake City from June 22 to 27. The timeline deserves precision: the manuscript has been public on arXiv since October 6, 2025; what is new in July is the conference presentation and the laboratory's public explanation. Affiliations span Brookhaven, the University of Texas at Austin, and Google Quantum AI — where Jordan works — with funding from the U.S. Department of Energy's Advanced Scientific Computing Research program.

This is not a new AI model, nor is it evidence that a quantum computer has already made ChatGPT or a production machine-learning system faster. It is more foundational: an algorithm that, when paired with other methods and capable quantum hardware, could help address a different class of scientific and learning problems.

A missing building block

In quantum computing, a primitive is a broadly useful operation that can be incorporated into more complex algorithms. The quantum Fourier transform is the familiar example: it changes the representation of quantum information and is a central component of several landmark algorithms. The laboratory's release underlines how short today's repertoire is — the Fourier transform and stabilizer-based methods account for much of what is reusable — and quotes Bao with the underlying complaint: "Quantum computers are powerful, but without quantum algorithms, the realm of applicability of this power is very limited."

QHT aims to play a similar role where problems are better described by Gaussian distributions—the familiar bell curves—than by uniform structures. Hermite functions appear in physics and engineering, especially in the quantum harmonic oscillator, a model for predictable vibrations. They also provide useful mathematical machinery for studying data and functions with Gaussian structure, which is common in statistics and machine learning. The connection is not decorative: measurement noise is modeled as Gaussian by default, kernel methods use Gaussians as a standard part, and much of the statistics underpinning machine learning lives in that world of bell curves. A change of basis designed for that structure speaks, from the start, the language of many data problems.

The authors' paper describes a discrete transform that maps computational-basis states to states whose amplitudes are proportional to Hermite functions. In plain terms, it gives a quantum state a different mathematical language, one that may fit particular questions better.

Keeping the cost from growing too quickly

The team's technical result is a quantum circuit whose cost depends logarithmically on both the problem dimension and the desired precision. That matters because many scientific problems become unwieldy as their size grows. To calibrate what "logarithmic" means: doubling the problem's dimension does not double the circuit's cost, it raises it by a nearly constant amount — the difference between a toll that grows with every kilometer and one that barely notices distance, and what separates a mathematical curiosity from a primitive usable at scale. The construction relies on the ability to fast-forward the evolution of a quantum harmonic oscillator: under the algorithm's conditions, it computes a later state directly instead of simulating every intermediate step. Bao defines it in the release: "Fast forwarding a quantum system means to directly compute its state at a specific moment in time." And he places the structural novelty: QHT "is structurally quite distinct from existing quantum primitives, which could lead to more quantum algorithms that solve unique problems."

That does not establish a universal, practical advantage over classical computers. Any advantage depends on how the input state is prepared, what output must be extracted, and whether a quantum device can run the circuit with enough fidelity. Those conditions matter just as much as an asymptotic complexity claim in a paper.

What it shows—and what it does not—about AI

The authors apply QHT to two task families: testing whether a function is close to a low-degree representation in the Hermite basis, and solving a Gaussian analogue of the Goldreich-Levin learning problem. Within that setting, they describe provable query advantages. The first family — deciding whether a function is close to a low-degree polynomial in the Hermite basis — is the Gaussian version of a classic property-testing question: does this signal hide simple structure, without reading it in full? The abstract also adds a route general coverage usually skips: potential uses of the transform for simulating the time dynamics of quantum systems in the continuum, the terrain of chemistry and materials.

Those are algorithm-theory results with a genuine connection to learning, not proof that training large neural networks will automatically become cheaper. AI belongs in the discussion because many statistical techniques use Gaussian distributions and because future quantum tools may broaden the set of learning methods. But moving from a primitive to a useful application requires complete algorithms, accessible data, measurements that preserve the advantage, and sufficiently reliable quantum machines.

Ning Bao, a Northeastern University professor with a joint appointment at Brookhaven, captured the distinction in the laboratory's release: QHT 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." The metaphor is useful. A root is not a finished product; it is a foundation on which others can build.

From theory to a possible ecosystem

The value of this work is that it broadens quantum computing's vocabulary. Materials research, scientific simulation, and some data problems may benefit from operations that are not forced to reuse the same Fourier-transform approach. QHT offers an alternative tailored to Gaussian structure. The laboratory lists materials science, energy security, advanced scientific modeling, and artificial intelligence as the areas where it expects the primitive to take root.

Turning that possibility into an everyday advantage will take time and independent validation. But that is the role of fundamental advances: they do not sell an immediate solution; they make it possible to formulate algorithms that did not previously exist. In a field often measured by qubit counts, this result is a reminder that quantum computers also need better ideas about what to do with them. And it leaves the reader three reusable questions for any headline joining "quantum" and "AI": is it a primitive or a complete application?; does the advantage survive preparing the input and measuring the output, or does it live only in between?; is there hardware able to run it with the fidelity the paper assumes? None requires a doctorate; all three require reading past the headline.