Applications / AI / Quantum for AI
QCBM and quantum generative models
Sampling from a distribution learned from scratch
A Born machine is the simplest generative model a quantum computer supports. The circuit's measurement probabilities are the distribution, so sampling it is a single execution rather than a decoding step, and training means moving those probabilities toward a target by adjusting rotation angles. Nothing is fed in: the model has no input, only parameters.
The distance reported throughout is total variation distance (TVD), half the sum of the absolute differences between the learned and target probabilities, so 0 is an exact match and 1 is no overlap. The circuit was trained on exact.cpu, where every gradient evaluation is its own job, and the converged circuit was then submitted once to a Rigetti superconducting QPU.
Run on our engines
A spin Hamiltonian solved on the TPU tier, and the H2 molecule solved on both neural engines for comparison. Submitted to each kind of compute we offer, on 18 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 |
|---|---|---|---|---|---|
 | neural.tpu | TPU | 12 | energy -6.918861, ceiling -6.886729, against an exact ground state of -7.048804 | $0.0395 |
 | neural.cpu | CPU | 2 | H2 at -1.116981 Ha, 0.0203 Ha above exact certificate | $0.0001 |
| neural.tpu | TPU | 2 | the same H2 molecule, -1.116981 Ha certificate | $0.0740 |
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.
Training took 806 circuits across 60 Adam steps and moved the distribution from 0.459 to 0.0117. The same converged circuit on Rigetti returned 0.102 at 1,000 shots, against 0.068 for the noiseless reference at the same shot count.
The learned distribution puts 0.496 on 00 and 0.492 on 11 against a target of 0.5 and 0.5, with the two remaining outcomes at 0.006 each.
Where this stops
- The outcome space is 2^n and the shot budget is fixed, so the number of shots per outcome falls exponentially with width. At 4 qubits, 16 outcomes from 512 shots is already thin
- Every gradient evaluation is a separate job, so a training loop is hundreds of circuits and training on hardware is priced per task
- TVD is measured against a known target, which is available here and is not available for a distribution you are trying to learn from data
The classical baseline for this case is the untrained circuit, at TVD 0.459. The structural limit, which does not move when a benchmark is re-run, is 2^n outcomes against a fixed shot budget: at 20 qubits most outcomes are never sampled once.
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
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
Quantum RL and control policies
Choosing an action from an observed state
Variational quantum policy trained by REINFORCE