Applications / AI / AI for quantum
NNQS tomography
Reconstructing the state a device prepared
Tomography reconstructs the state a device actually prepared from the records of measuring it. The neural version fits a network to those records instead of solving for a density matrix, which is what makes it reach widths a full density matrix cannot. The records come from hardware: run a circuit on a QPU, measure it in several bases, and reconstruct on the neural tier.
What the result can claim is narrower than it looks, and the narrowness is the useful part. A maximum-likelihood fit has no equivalent of the variational principle, so nothing bounds the distance between the reconstruction and the state the device prepared. What is bounded is agreement with records held back from the fit, reported per observable with intervals that hold together after a Bonferroni correction.
Run on our engines
Measurement records from a two-qubit state, measured across all nine two-qubit Pauli bases. 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.cpu | CPU | 2 | 900 records over 9 bases, 720 fitted and 180 held back, agreement reported per observable | $0.0002 |
 | neural.tpu | TPU | — | refused at submission: the fit is seconds of work against minutes of provisioning, so the TPU would be slower and dearer than the CPU tier | — |
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.
A first submission carrying only three of the nine bases was refused before it ran, because those bases cannot determine a state: a fit would converge, and it would converge to whichever state consistent with the data the network happened to prefer. The measured cost of ignoring that check is a Bell state reconstructed at fidelity 0.51 from five bases and 0.98 from all nine, at identical settings.
The result is not eligible for certification and says so in the result body rather than in a footnote, because every certificate this service issues states how wrong an answer can be and a reconstruction carries no such number.
Where this stops
- No fidelity bound exists for the reconstruction itself; only agreement with held-out records is reported
- An under-determined set of bases is refused rather than fitted, which is a refusal you will meet if the records were not planned for tomography
- The reconstruction runs on the CPU tier only: it is refused on neural.tpu, where provisioning would dominate the run
The classical baseline for this case is held-out measurement records the fit never saw. The structural limit, which does not move when a benchmark is re-run, is Refused outright when the measured bases cannot determine a state.
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: Neural network quantum states, with a bound.
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