We don't think anyone needs to wait for quantum computers to use what quantum research has already worked out. The math can be put to work today.
We believe AI is one of the biggest levers in business right now. Almost every company is baking AI into what it does. So when we asked ourselves where quantum methods could have the most impact, we kept landing on AI.
GPU-hours are the billYou'd have to be living under a rock to miss the economics. Companies are raising record rounds, and a lot of that money is going toward compute. When we dug into what model training costs, much of it traced back to VRAM, the memory on the GPU. How much a job needs sets how many GPUs you rent and for how long, and GPU-hours are the bill. During a training run everything has to sit in GPU memory at once, and the run is capped by what fits. Teams usually work around it by choosing settings that fit, smaller batches or shorter sequences, and they give up some training quality to do it.
We think it's one problem: the job needs more VRAM than the GPU has.
We also think this problem isn't new. Physicists hit it decades ago simulating quantum systems, and the math they built to get past it is where we start.
Where the memory goes
GPU memory weightsgradientsoptimizer stateactivations Fig. 1 · What has to sit in memory at once. Sketch, not to scale.Take a model with seven billion parameters. Saved to disk it's about 14 gigabytes, small enough to sit on one ordinary GPU. Training it the standard way is another matter. The GPU has to hold the weights, then a gradient for every weight, then the optimizer's running notes on every weight, kept at higher precision. Depending on the setup, that comes to somewhere between 80 and 110 gigabytes before any training data arrives, and before the activations from each batch are added in.
GPUs have plenty of computing power, but they run out of memory first.
The gap is getting wider. In the transformer's first five years, the largest models grew roughly 410 times every two years, while the memory on a single GPU grew about two times.
Buying more hardware helps until the next model arrives, so the question that lasts is: how much training can you extract per byte?
Everyone else sells you cheaper chips. We make each chip do more.
What the physicists did
A single quantum particle takes two numbers to describe. Every particle you add doubles the count, so by fifty particles you need about a million billion numbers, which is more than the largest supercomputer on Earth can store. Physicists wanted to study systems far bigger than fifty.
1,125,899,906,842,624 50 particles Fig. 2 · Every particle you add doubles the numbers.In the early 1980s their work went two ways. One group proposed a new kind of machine, the quantum computer, which is still being built. The other did what people do when the equipment they want doesn't exist — they made do with ordinary computers.
Anyone can shrink a large object by throwing most of it away. What took decades was learning to tell what had been thrown away, and whether it mattered. The answer came from an observation about nature. Real materials turn out to be repetitive. Each particle mostly responds to its neighbors, and that gives the whole system a pattern. If you can find the pattern, you can write the system down in a fraction of the space and lose almost nothing.
The methods that came out of this find the pattern in a large object and store the pattern. They also let you decide in advance how much accuracy you are willing to give up, and then measure how much you actually gave up. That is the part we care most about, because you can plan around a loss you can measure.
All of it was written for ordinary computers, in linear algebra, and while quantum has its own (admittedly smaller) hype cycles, most of what was learned has stayed within physics.
Why we think it carries over
This is the research Akavion started from, and no quantum computer is involved in anything we do.
A method that finds the pattern should fit more into the same VRAMWe should be careful here. A training job is a different thing from a quantum system. But the weights, the gradients and the optimizer's notes are not random, any more than the particles in a material are, and that is what made the physicists' problem solvable. A method that finds the pattern should fit more into the same VRAM, and lose less accuracy, than one that shrinks everything by the same amount. We say "should" on purpose. How much pattern is there is something you measure, and measuring it is the work.
Physics has crossed into machine learning before. The diffusion models behind today's image generators drew on the physics of systems out of equilibrium. In 2024 the Nobel Prize in Physics went to two researchers who used tools from physics to build the foundations of machine learning. We think there is more where that came from.
What we claim, and what could make us wrong
What we claim today is capacity, meaning the same GPU holds a bigger training job. Compression comes at a cost. Our methods are designed to keep that cost low, and to let you choose the trade-off that makes sense for your team. We are working on more than one part of what fills a GPU during training, and we will publish what each one saves, and what it costs, as the measurements come in.
throughputpeak memoryquality Fig. 3 · Throughput, peak memory, held-out quality, against dense precision.Model architectures change every year, and a company built around one of them is betting on it. We work a level below that. However a model is designed, training it today means holding weights, gradients, optimizer statistics and activations. That holds for pretraining, fine-tuning and reinforcement learning alike.
Hardware memory could start growing faster than models, and the problem we are trying to solve would shrink. The pattern we rely on could also turn out to be thin in some kinds of model, and there the math would have little to work with. We don't know yet how far this goes. Our bet is that it goes a long way.
Memory in training is where we've chosen to start. It won't be the only problem in AI we take this math to.
Why this matters to us
If we're right about the math, teams get to try things their hardware had ruled outWhat a team can attempt today is set by what fits on the hardware it can get. We think that's the wrong thing to be limited by, and an expensive thing to have to be good at. If we're right about the math, teams get to try things their hardware had ruled out, and they get to sweat the things that matter, which are the data and the results.
The physicists who worked this out weren't thinking about AI. Most of them were trying to understand magnets and superconductors. Their math sat in journals for thirty years, and it turns out to fit a problem that didn't exist when they wrote it. We find that hard to stop thinking about. It makes us wonder how much more is sitting there.
We're early, and we're excited to be doing this work. It starts with the math.
If you train models and you have been quietly designing around what fits — smaller batches, more shards, experiments that never got run — perhaps the run fits after all. Tell us what you train.