Applications / AI / Quantum for AI
QRC, quantum reservoir computing
Features from a circuit that trains nothing
Reservoir computing puts the data through a fixed nonlinear system and trains only a readout on top of it. The quantum version uses a fixed entangling circuit with no trainable parameters at all: nothing in the circuit learns, and the whole model is the classical readout. That makes it the cheapest quantum model to run, because there are no gradients and therefore no gradient circuits.
It also makes the readout the entire design decision. The same 200 circuits at the same 512 shots were read twice, once as all 16 bitstring probabilities and once as the 10 local observables, and the difference between those two numbers is the choice of arithmetic applied to identical counts.
- Method
- Quantum reservoir computing with a classical readout
- Who runs this
- Time-series and signal processing teams
- Classical baseline
- The raw coordinates, at 0.850
- Structural limit
- A bitstring readout needs 2^n features from a fixed shot budget; local observables need n^2
Run on our engines
Two moons, 200 samples on a 140/60 split, through a fixed four-qubit entangling map with no trainable parameters. Submitted to each kind of compute we offer, on 18 and 25 September 2026. Every figure below is a real job on the service, priced as any customer would be priced.
| Device | Engine | Kind | Qubits | Result | Cost |
|---|---|---|---|---|---|
 | exact.cpu | CPU | 4 | 0.783 test accuracy from the full bitstring distribution, 16 features | $0.0200 |
| exact.cpu | CPU | 4 | 0.817 from local observables on the same counts, 10 features | $0.0200 |
 | exact.gpu | GPU | 4 | 0.767 from the same bitstring readout, one test point of sixty from the CPU run | $0.0200 |
 | exact.tpu | TPU | 4 | 0.783 from the same bitstring readout, matching the CPU run exactly | $0.1799 |
The same problem is yours to run: every instance here is seeded, so it rebuilds exactly. Open the console and a cost estimate is free before anything executes.
The raw two-dimensional coordinates, with no quantum step at all, give 0.850 on the same split.
The naive readout estimates each of 16 features from 512 shots, so each carries about 0.022 of sampling noise, against an exact two-dimensional feature set. The local observables use every shot for every feature, so their noise per feature does not grow with qubit count, which is why the reservoir computing literature reads them out this way.
The same bitstring readout on the GPU engine returns 0.767 against the CPU's 0.783, which is 46 of 60 test points against 47. Everything upstream of the shots is fixed, so that single point is the sampling noise above, and it is what a second CPU run would also produce. The engines agree; the measurement has a resolution of one test point.
What the makers say it is for
Quandela and NVIDIA describe the arrangement this method already uses. The GPU stays at the centre of the workflow and the quantum processor acts as a specialised accelerator for one part of it. A quantum reservoir is precisely that division of labour, since the circuit is never trained and only the classical readout is.
It is also the cheapest version of it, because the reservoir runs once per input rather than once per gradient step.
Where this stops
- A bitstring readout does not scale: the outcome space is 2^n while the shot budget is fixed, so at 10 qubits most of 1,024 outcomes are never observed once and the feature vector becomes absence
- Local observables give n^2 features rather than 2^n, which is the standard readout and the reason it is standard
- Nothing in the circuit trains, so the reservoir cannot adapt to the problem and the map has to be chosen in advance
The structural limit above does not move when a benchmark is re-run. Everything else on this page is a measurement, and a measurement can be repeated.
Run it yourself
Every figure above is from a job billed on the production service. Load the same circuits into the console, change the instance to your own data, and export a certificate for your own run rather than citing ours.
The argument behind these numbers, at length: Quantum machine learning on simulators and real quantum hardware.
Other AI use cases
QCBM and quantum generative models
Sampling from a distribution learned from scratch
QCBM against its own untrained start
QGAN and synthetic data
Adversarial generation against a learning discriminator
QGAN with a classical discriminator
Quantum AI image generation
Writing an image into a circuit and reading it back
Patch GAN and NTQIP, both on Rigetti