Applications

Quantum computing use cases

Real world use cases measured with QPUs and classical solvers

Every page here takes one real problem from an industry, runs it on our quantum engines, runs it again on the best classical solver available, and publishes both results side by side, including the many cases where the classical method returns the better answer.

Every benchmark states its method, seeds an instance anyone can regenerate, and carries a certified error bound on every approximate result. You can load the same circuit into the console, change the instance to your own numbers, and export a certificate for your own run rather than citing ours.

Unfamiliar terms are defined in the quantum computing dictionary

Load any of these into the console, or run one from a phone. Get the Android app

One worked example before the sectors below. This is satellite observation tasking, from space and satellites, and it is the same table that page carries.

Run on our engines

Satellite observation tasking at 14 requests, seed 20260902, whose exact optimum is value 32.5128. On 25 September the same instance ran on exact.tpu, a Google TPU, which returned 31.2164 and the smallest gap on the table. Submitted to each kind of compute we offer, on 16 September 2026 at 500 shots. Every figure below is a real job on the service, priced as any customer would be priced.

Engine	Kind	Qubits	Result	Cost
mps.quimb.cpu	CPU	14	25.1546, gap 7.36 certificate	$0.0001
exact.cpu	CPU	14	20.0569, gap 12.46 certificate	$0.0001
exact.gpu	GPU	14	25.1546, gap 7.36 certificate	$0.0001
qpu.iqm.garnet	QPU	14	26.8778, gap 5.64 certificate	$1.025
qpu.rigetti	QPU	14	27.0176, gap 5.49 * certificate	$0.5125
qpu.iqm.emerald	QPU	14	26.9421, gap 5.57 certificate	$1.100
exact.tpu	TPU	14	31.2164, gap 1.30 certificatebest outcome	$0.0776
neural.tpu	TPU	—	the tasking QUBO is diagonal, which is not the shape a neural ansatz is for	—

A note on the hardware certificates: they state Hellinger fidelity against the exact distribution. For an optimisation circuit that distribution is spread across many outcomes rather than concentrated on one, so the figure is low by construction and is not a measure of whether the device found a good answer. The result column above is.

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.

Quantum computing for AI, and AI for quantum computing

Two directions, both measured here: quantum for AI puts a circuit where a model layer would go (QCBM, QGAN, quantum image generation, quantum reinforcement learning, QML kernels and classifiers, quantum reservoir computing), and AI for quantum points the other way, with neural network quantum states and neural network tomography. Eight use cases, each a billed run against the production API, five of them re-run on a quantum processor.

QCBM and quantum generative models: sampling from a distribution learned from scratch
QGAN and synthetic data: adversarial generation against a learning discriminator
Quantum AI image generation: writing an image into a circuit and reading it back
Quantum RL and control policies: choosing an action from an observed state
NNQS for materials and chemistry: ground states where tensor networks stop
QML and classification: labelling data through a quantum feature map
QRC, quantum reservoir computing: features from a circuit that trains nothing
NNQS tomography: reconstructing the state a device prepared

Run on our engines

A spin Hamiltonian solved on the TPU tier, and the H2 molecule solved on both neural engines for comparison. On 25 September the identical spin request ran on neural.gpu, an NVIDIA GPU, reaching energy -6.647038 with a ceiling of -6.630361. Submitted to each kind of compute we offer, on 16, 18 and 25 September 2026. Every figure below is a real job on the service, priced as any customer would be priced.

Engine	Kind	Qubits	Result	Cost
neural.tpu	TPU	6	energy -6.918861, ceiling -6.886729, against an exact ground state of -7.048804	$0.0395
neural.gpu	GPU	6	energy -6.647038, ceiling -6.630361, against an exact ground state of -7.048804 certificate	$0.0253
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.

AI and machine learning

QML, QGAN, QCBM, image generation and neural wavefunctions

QCBM, QGAN and a variational policy on Rigetti, NNQS on a Google TPU

ML research, generative modelling, materials and device teams

Finance and trading

Cardinality-constrained portfolio selection

QAOA against exhaustive enumeration

Quantitative research, treasury, risk

Chemicals and pharmaceuticals

Molecular ground-state energy

VQE against exact diagonalisation

Computational chemistry, materials, drug discovery R&D

Cryptography and digital assets

When current encryption becomes breakable

Quantum resource estimation

Security, compliance, custody

Space and satellites

Satellite observation tasking

QAOA against OR-Tools CP-SAT

Mission planning, earth observation, constellation operators

Traffic and smart cities

Vehicle route assignment to minimise congestion

QUBO / maximum independent set against exhaustive search

Mobility planning, fleet operations, smart city programmes

Scheduling and allocation

Conflict-free task scheduling and channel allocation

Maximum independent set on neutral atoms, against exhaustive search

Operations, spectrum and channel planning, shift rostering

Logistics and transportation

Vehicle routing and delivery planning

Encoding cost against OR-Tools routing

Fleet operations, distribution, supply chain

Manufacturing and production

Job-shop scheduling and makespan

Encoding cost against CP-SAT

Plant operations, industrial engineering

The size at which each classical baseline stops being tractable

Every figure below follows from the problem's own combinatorics or from its encoding, so unlike a timing it does not move when the benchmarks are re-run. Each is the point at which the classical method named beside it stops being computationally tractable, which is a property of the problem rather than of any machine. The measured results sit on each sector page.

Sector	Quantum method	Classical baseline	Where classical runs out
AI and machine learning	QCBM, QGAN and a variational policy on Rigetti, NNQS on a Google TPU	Classical baselines on the identical split, and the untrained circuit	2^n outcomes against a fixed shot budget, and one qubit per pixel
Finance and trading	QAOA	Exhaustive enumeration	5.3 x 10^13 portfolios to enumerate at 60 assets choosing 15
Chemicals and pharmaceuticals	VQE	Exact diagonalisation	About 16 TB of state at 40 qubits, 17 EB at 60
Cryptography and digital assets	Quantum resource estimation	No classical attack	RSA-2048 needs 4,099 logical and 6,894,518 physical qubits
Space and satellites	QAOA	OR-Tools CP-SAT	No wall reached: CP-SAT stays optimal at every size tested
Traffic and smart cities	QUBO / maximum independent set	Exhaustive search	10 cars solved exactly in 0.18s; 50 cars needs 150 qubits to encode
Scheduling and allocation	Maximum independent set on neutral atoms,	Exhaustive search	Unit-disk graphs only: an arbitrary conflict graph needs a layout step first
Logistics and transportation	Encoding cost	OR-Tools routing	10,000 qubits to encode a 100-stop round
Manufacturing and production	Encoding cost	OR-Tools CP-SAT	268,425 qubits to encode a 15 x 15 shop

Cryptography is the outlier and the only row where no classical method competes at all, so the figure is what a quantum attack would itself require. Space is the other: at every size we have tested, the classical solver reaches the proven optimum and quantum does not.

Results are published whichever method performs better

On most of the problems benchmarked here, the classical method returns the better result at the sizes that can currently be tested. Those results are published in full, with the same detail as any other.

Each page answers two questions. At the size that can be tested today, how do the two methods compare on the same instance? And at what size does the classical method stop being tractable? The second is the more durable figure, because it follows from the problem rather than from the state of any hardware.

A benchmark that reports only favourable results carries no information, because a reader cannot know what was discarded. The rules every page follows are stated in advance and written down.

Read the benchmark methodology

Working in a sector not covered here? Most industrial problems reduce to one of three shapes we already run: combinatorial optimisation, quantum chemistry, or cryptographic resource estimation. Tell us the problem and we will benchmark it.