Top Quantum Computing Use Cases
Last updated · 18 min read · ZKSF team
The short version
- Nine sectors, each with a sample run: chemistry and pharmaceuticals, finance and trading, artificial intelligence, scheduling and allocation, space and satellites, logistics and transport, manufacturing, traffic and smart cities, and cryptography
- Every section carries the same three things: the table from that benchmark, the classical baseline it was measured against, and what the run cost
- Quantum machine learning is the largest group, with eight QML and AI cases published separately as 3.a to 3.h
- These are sample runs at small widths. They show the path end to end and are a starting point for your own work rather than the last word on any sector
- Hardware on four processors from four makers, across superconducting, trapped-ion and photonic machines, with the same trained model sent to each one that can take it
- Every sector instance is seeded, so the problems here rebuild exactly through the SDK, the console or the Android app. Where a case trains a model, the seed is stated with it
Everything here is runnable on your own circuit. Try it in the console
Quantum computing use cases are usually presented as a list of industries with a promise attached to each. This page is the same list with a measurement attached instead. Every sector below was posed as a concrete instance, run on our engines and in several cases on real quantum hardware, and scored against the best classical answer available for the same problem.
The runs are samples. They are sized so the true answer is knowable, which is what makes the comparison meaningful, and that also means they sit well inside what the field is working on. Quantum computing is early, the encodings and the parameter-finding methods are both active research, and results at these widths are a baseline to improve on rather than a ceiling. Anyone who wants to push further can run the same problems at their own sizes through our Python SDK, the web console or the Android app, on the same account and the same billing.
1. Chemistry and pharmaceuticals
Molecules are quantum objects, and the cost of describing them exactly on a classical computer grows with the number of electrons, which is the theoretical case for the sector. The instance is the H2 molecule at its equilibrium bond length, small enough to fit every device we offer, which makes it the one problem here that reaches all four kinds of compute. The method is VQE, the variational quantum eigensolver.
Run on our engines
The H2 molecule at its equilibrium bond length, whose exact electronic ground state is -1.857275 Ha. Two qubits, so it fits every device we offer. Submitted to each kind of compute we offer, on 16 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 | 2 | ZZ = -1.0000, the ideal value certificate | $0.0001 |
 | exact.gpu | GPU | 2 | ZZ = -1.0000, the ideal value certificate | $0.0001 |
 | qpu.iqm.garnet | QPU | 2 | ZZ = -0.9326, superconducting, 4,096 shots certificate | $6.239 |
 | qpu.rigetti | QPU | 2 | ZZ = -0.5420, superconducting, 4,096 shots * certificate | $2.041 |
| qpu.rigetti | QPU | 2 | ZZ = -0.5107, the same circuit re-run * certificate | $2.041 |
 | qpu.aqt.ibex | QPU | 2 | ZZ = -0.9200, trapped ion, 100 shots certificate | $2.650 |
| neural.cpu | CPU | 2 | -1.116981 Ha total, 0.0203 Ha above exact certificate | $0.0001 |
 | neural.tpu | TPU | 2 | -1.116981 Ha total, 0.0203 Ha above exact certificate | $0.074 |
* The two Rigetti rows are one circuit run twice, an internal reproduction of the published benchmark notebook. A depolarizing noise model puts both versions at about -0.99, so the shortfall is not the circuit shape, but the identical program has not yet run on both devices. The steps are in the docs.
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.
Given noiseless expectation values the variational method matches exact diagonalisation to six decimal places. With a realistic shot budget it lands about a factor of two from chemical accuracy, which places the current limit in the sampling rather than in the circuit. Shot budgets, error mitigation and better ansatz design are all active work. The full method is on chemicals and pharma.
2. Finance and trading
Portfolio selection under a cardinality constraint, which is the shape most quantum finance work takes: choose exactly four holdings from twelve so the risk-adjusted objective is minimised, with the constraint carried as an energy penalty and solved with QAOA, the quantum approximate optimisation algorithm. At this width the provable optimum is available by enumeration, so every engine can be scored against the right answer.
Run on our engines
A 12-asset portfolio choosing exactly 4 holdings, seed 20260902, whose provable optimum is 0.199796. On 25 September the same instance ran on exact.tpu, a Google TPU, which found that optimum. Submitted to each kind of compute we offer, on 16 and 25 September 2026 at 500 shots. Every figure below is a real job on the service, priced as any customer would be priced.
| Device | Engine | Kind | Qubits | Result | Cost |
|---|---|---|---|---|---|
| mps.quimb.cpu | CPU | 12 | 0.199796, the optimum certificatebest outcome | $0.0001 |
| exact.cpu | CPU | 12 | 0.247259, beats 97.6% certificate | $0.0001 |
| exact.gpu | GPU | 12 | 0.251747, beats 96.4% certificate | $0.0001 |
| qpu.rigetti | QPU | 12 | 0.247730, beats 97.4% * certificate | $0.5125 |
| qpu.iqm.garnet | QPU | 12 | 0.221427, beats 99.2% certificate | $1.025 |
| qpu.iqm.emerald | QPU | 12 | 0.245130, beats 98.0% certificate | $1.100 |
| exact.tpu | TPU | 12 | 0.199796, the optimum certificate | $0.0776 |
| neural.tpu | TPU | — | the penalised QUBO is diagonal, which is not the shape a neural ansatz is for | — |
* The Rigetti row is a separate sample of ours on this same instance, with the QAOA angles re-optimised for it. The steps are in the docs.
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.
A tensor network on CPU found the provable optimum of 0.199796. The quantum processors returned values between 0.221 and 0.252 on a single unoptimised draw. The gap between the CPU and GPU statevector rows, which compute the identical distribution, is about half the spread across the whole table and is a useful scale for reading the rest of it. Deeper QAOA, better angle-finding and error mitigation are the levers here. The instance and its penalty construction are on finance and trading.
3. Artificial intelligence and quantum machine learning
This is the largest group on the page, and it runs in both directions. Quantum machine learning, QML, puts a parameterised quantum circuit where a model layer would sit, which covers quantum circuit Born machines (QCBM), quantum generative adversarial networks (QGAN), quantum image generation, reinforcement-learning policies, quantum kernels and quantum reservoir computing (QRC). AI for quantum points the other way, using neural network quantum states (NNQS) as the wavefunction itself.
Eight cases are published with their results, and five of the eight were re-run on hardware after training on a simulator. Between them those runs reach four processors from four manufacturers across three modalities: superconducting on Rigetti and on IQM Garnet, trapped ion on AQT IBEX Q1, and single photons on Quandela Belenos. Each case is below with its own table, and the same trained model appears on every engine that can take it rather than on whichever one was cheapest.
3.a QCBM and quantum generative models
Sampling from a distribution learned from scratch, approached with QCBM against its own untrained start. The classical baseline is the untrained circuit, at TVD 0.459.
Run on our engines
A quantum circuit Born machine (QCBM) learning a two-qubit target distribution from a random start, then sampled. 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 |
|---|---|---|---|---|---|
| exact.cpu | CPU | 2 | TVD 0.459 untrained, 0.0117 after 60 Adam steps | $0.0806 |
| exact.gpu | GPU | 2 | TVD 0.041, the same converged circuit at 1,000 shots certificate | $0.0001 |
| qpu.rigetti | QPU | 2 | TVD 0.102, the converged circuit re-run at 1,000 shots | $0.7250 |
| qpu.iqm.garnet | QPU | 2 | TVD 0.104, the same circuit and shot count on a second superconducting device certificate | $1.7500 |
| qpu.aqt.ibex | QPU | 2 | 3 of 100 shots outside the target, against 102 of 1,000 on Rigetti and 38 of 1,000 on Garnet certificate | $2.6500 |
| neural.tpu | TPU | — | a Born machine is a circuit, not a Hamiltonian, so it does not reach the neural tier | — |
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.
The method reaches its current limit where 2^n outcomes against a fixed shot budget: at 20 qubits most outcomes are never sampled once. The full write-up, with the criterion fixed before the run, is on QCBM and quantum generative models.
3.b QGAN and synthetic data
Adversarial generation against a learning discriminator, approached with QGAN with a classical discriminator. The classical baseline is the discriminator gap, which starts at 0.0069.
Run on our engines
A two-qubit generator of four rotations against a two-layer classical discriminator, 40 alternating steps, targeting 0.4 / 0.1 / 0.1 / 0.4. 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 |
|---|---|---|---|---|---|
| exact.cpu | CPU | 2 | TVD 0.269 to 0.146, discriminator gap 0.0069 to -0.0006 | $0.0722 |
| exact.gpu | GPU | 2 | TVD 0.278, the same converged generator at 1,000 shots certificate | $0.0001 |
| qpu.rigetti | QPU | 2 | TVD 0.286, the converged generator re-run at 1,000 shots | $0.7250 |
| qpu.iqm.garnet | QPU | 2 | TVD 0.240, the same generator and shot count on a second superconducting device certificate | $1.7500 |
| photonic.slos.cpu | CPU | 3 | generator half, P(target) 1.000, 0.989, 0.932, 0.875 and 0.766 across five seeded starts | $0.1096 |
 | qpu.quandela.belenos | QPU | 3 | 2,686 coincidences in 100,000 attempts, P(target) 0.974 with the two bunched outcomes returning 4 to 1 certificate | $0.4584 |
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.
The method reaches its current limit where mode collapse onto a subset of outcomes, the same failure mode as a classical GAN. The full write-up, with the criterion fixed before the run, is on QGAN and synthetic data.
3.c Quantum AI image generation
Writing an image into a circuit and reading it back, approached with patch GAN and NTQIP, both on Rigetti. The classical baseline is the target image itself, pixel by pixel.
Run on our engines
An 8x8 target for the trained generator, and a 32x32 letterform written one pixel to a qubit. 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 |
|---|---|---|---|---|---|
| exact.cpu | CPU | 4 | patch GAN, TVD 0.828 untrained to 0.2326 trained, 3,224 circuits | $0.3224 |
| qpu.rigetti | QPU | 4 | patch GAN, TVD 0.4129 for the converged generator | $0.7250 |
| qpu.rigetti | QPU | 32 | one qubit per pixel, 32x32 image in 11 circuits, 0.0525 mean error per pixel | $3.4683 |
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 method reaches its current limit where one qubit per pixel: a 108-qubit processor holds about a 10x10 image in a single job. The full write-up, with the criterion fixed before the run, is on Quantum AI image generation.
3.d Quantum RL and control policies
Choosing an action from an observed state, approached with variational quantum policy trained by REINFORCE. The classical baseline is a random policy, at 0.533 mean return.
Run on our engines
A two-qubit policy with four trainable weights, trained by REINFORCE over 60 decisions, then probed at two states on hardware. 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 |
|---|---|---|---|---|---|
| exact.cpu | CPU | 2 | mean return 0.611 over the last three batches, against 0.533 for a random policy | $0.0540 |
| exact.gpu | GPU | 2 | P(action 1) 0.158 and 0.624 at the same two probe states certificate | $0.0002 |
| qpu.rigetti | QPU | 2 | P(action 1) 0.199 and 0.650 at two probe states, against 0.049 and 0.708 noiseless | $1.4500 |
| qpu.iqm.garnet | QPU | 2 | P(action 1) 0.177 and 0.576 at the same two probe states certificate | $3.5000 |
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.
The method reaches its current limit where one circuit per decision: an episode of 1,000 steps is 1,000 jobs. The full write-up, with the criterion fixed before the run, is on Quantum RL and control policies.
3.e NNQS for materials and chemistry
Ground states where tensor networks stop, approached with neural network quantum states on a Google TPU. The classical baseline is exact diagonalisation, where the system still fits in memory.
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.
| Device | 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.
The method reaches its current limit where 40 spins on the neural tier; exact diagonalisation stops near 30. The full write-up, with the criterion fixed before the run, is on NNQS for materials and chemistry.
3.f QML and classification
Labelling data through a quantum feature map, approached with quantum kernel and variational classifier against classical baselines. The classical baseline is logistic regression, k-NN, an MLP and an RBF kernel.
Run on our engines
Two moons drawn by numpy's default_rng for seeds 1 to 3 (noise 0.12), 22 training and 40 test points, features scaled into [0, π] on the training range. Logistic regression, k-NN and an MLP, written out in numpy, and an RBF kernel ran on the identical split. Submitted to each kind of compute we offer, on 17, 24 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 | 2 | variational classifier 0.925 / 0.825 / 0.700 across three seeds, 4,000 circuits a seed | $0.4000 |
| exact.cpu | CPU | 2 | quantum kernel 0.675 / 0.750 / 0.750, 1,111 circuits a seed | $0.1111 |
| exact.gpu | GPU | 2 | quantum kernel 0.675 on seed 1, the CPU's seed-1 figure, 1,111 circuits | $0.1111 |
| exact.tpu | TPU | 2 | quantum kernel 0.675 on seed 1, the same again, 1,111 circuits in 1,540 s | $1.0336 |
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 method reaches its current limit where a kernel needs one circuit per pair: 1,111 circuits for 62 points. The full write-up, with the criterion fixed before the run, is on QML and classification.
3.g QRC, quantum reservoir computing
Features from a circuit that trains nothing, approached with quantum reservoir computing with a classical readout. The classical baseline is the raw coordinates, at 0.850.
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 method reaches its current limit where a bitstring readout needs 2^n features from a fixed shot budget; local observables need n^2. The full write-up, with the criterion fixed before the run, is on QRC, quantum reservoir computing.
3.h NNQS tomography
Reconstructing the state a device prepared, approached with neural network tomography from measurement records. The classical baseline is held-out measurement records the fit never saw.
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.
The method reaches its current limit where refused outright when the measured bases cannot determine a state. The full write-up, with the criterion fixed before the run, is on NNQS tomography.
All eight are indexed on AI quantum computing use cases, and the longer argument behind them is in quantum machine learning on simulators and real quantum hardware.
4. Scheduling and allocation
Maximum independent set is the largest set of tasks with no two in conflict. Shift rostering is this problem, so is channel allocation, and so is siting transmitters that interfere when placed too close together. It is the case on this page where the hardware and the problem fit most directly, because the Rydberg blockade on a neutral-atom machine forbids neighbouring atoms from both being excited, which is the independent-set constraint expressed in physics rather than as a tuned penalty.
Run on our engines
Nine atoms on a 3x3 grid at 6 um spacing, whose blockade graph is the king's graph: 9 vertices, 20 edges, and a maximum independent set of 4 that can be checked by hand. On 25 September the identical sequence ran on analog.pulser.gpu, an NVIDIA GPU, returning the same set with all 500 shots valid. 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 |
|---|---|---|---|---|---|
| analog.pulser.cpu | CPU | 9 | found [0, 2, 6, 8], size 4; 500 of 500 shots valid | $0.0001 |
| analog.pulser.gpu | GPU | 9 | found [0, 2, 6, 8], size 4; 500 of 500 shots valid certificate | $0.0017 |
 | qpu.quera.aquila | QPU | 9 | found [0, 2, 6, 8], size 4; 883 of 947 shots valid, 574 optimalbest outcome | $10.3000 |
 | qpu.pasqal.fresnel | QPU | — | takes the identical Pulser sequence, but is billed as machine time at one shot per four seconds, so a run at this shot count is not comparable in cost | — |
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.
Both rows found the optimum, the four corners of a 3x3 register. They differ in the share of shots that obeyed the constraint, every one on the exact emulator against 883 of 947 on the device, which is the quantity that carries forward to sizes where the answer cannot be checked by hand. The method is on scheduling and allocation.
5. Space and satellites
Observation tasking, where a satellite passes over more requests than it can photograph and the scheduler picks the subset that maximises value. Fourteen requests, whose exact optimum is available by exhaustive search so every row can be scored against it.
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 and 25 September 2026 at 500 shots. Every figure below is a real job on the service, priced as any customer would be priced.
| Device | 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 | — |
* The Rigetti row is a separate sample of ours on this same instance, with the QAOA angles re-optimised for it. The steps are in the docs.
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.
The engines returned values between 20.06 and 27.02 against an optimum of 32.5128, on a single draw at fixed parameters. The quantum processors placed above the exact statevector engines here, which is a property of one unoptimised sample rather than a result about the hardware. The write-up is on space and satellites.
6. Logistics and transport
Vehicle routing as a QUBO, a quadratic unconstrained binary optimisation. The instance is small by design, and the reason is the useful part of this section. A 100-stop delivery round encodes to roughly 10,000 qubits, which is beyond what is available today, so the runnable version is 16 variables. What it shows is how the encoding behaves rather than a routing result to act on.
Run on our engines
A random 16-variable QUBO, seed 20260902, whose exact optimum is -18.7897: the size a machine can hold, with no routing structure in it, generated by small_qubo.py in the public benchmarks folder. It is deliberately small, because the 100-stop round this benchmark is about needs 10,000 qubits and fits nothing. Submitted to each kind of compute we offer, on 16 and 25 September 2026 at 500 shots. Every figure below is a real job on the service, priced as any customer would be priced.
| Device | Engine | Kind | Qubits | Result | Cost |
|---|---|---|---|---|---|
| mps.quimb.cpu | CPU | 16 | -16.3521, gap 2.44 certificate | $0.0001 |
| exact.cpu | CPU | 16 | -14.0904, gap 4.70 certificate | $0.0001 |
| exact.gpu | GPU | 16 | -16.5132, gap 2.28 certificate | $0.0001 |
| qpu.rigetti | QPU | 16 | -216.06, gap 76.30 on the routing instance * certificate | $0.5125 |
| qpu.iqm.garnet | QPU | 16 | -14.7420, gap 4.05 certificate | $1.025 |
| qpu.iqm.emerald | QPU | 16 | -10.5934, gap 8.20 certificate | $1.100 |
| exact.tpu | TPU | 16 | -18.7897, the optimum certificatebest outcome | $0.0776 |
| neural.tpu | TPU | — | a QUBO is diagonal, which is not the shape a neural ansatz is for | — |
* The Rigetti row is not scored against the optimum named above. The run used the 4-vehicle routing instance that sector_instances.py generates instead. Its exhaustive minimum is -292.3588, and the 76.30 gap is measured against that rather than against -18.7897. The IQM rows are our own internal testing. The exact.tpu row, added 25 September, is the only run on this instance to reach the exact optimum of -18.7897. The steps are in the docs.
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.
The GPU statevector engine came closest to the optimum here, for a hundredth of a cent. Bringing the useful sizes into reach is a question of encoding efficiency as much as qubit count, and both are moving. The arithmetic is on logistics and transport.
7. Manufacturing
Job-shop scheduling, the same encoding story in a different industry. A 15x15 shop encodes to roughly 268,425 qubits, so the runnable version is again 16 variables and is published to show the encoding cost rather than a factory result.
Run on our engines
A random 16-variable QUBO, seed 20260903, whose exact optimum is -15.6952: the size a machine can hold, with no scheduling structure in it, generated by small_qubo.py in the public benchmarks folder. It is deliberately small, because the 15x15 shop this benchmark is about needs 268,425 qubits and fits nothing. Submitted to each kind of compute we offer, on 16 and 25 September 2026 at 500 shots. Every figure below is a real job on the service, priced as any customer would be priced.
| Device | Engine | Kind | Qubits | Result | Cost |
|---|---|---|---|---|---|
| mps.quimb.cpu | CPU | 16 | -12.7064, gap 2.99 certificate | $0.0001 |
| exact.cpu | CPU | 16 | -11.7508, gap 3.94 certificate | $0.0001 |
| exact.gpu | GPU | 16 | -12.4192, gap 3.28 certificate | $0.0001 |
| qpu.rigetti | QPU | 16 | -346.31, gap 4.95 on the scheduling instance * certificate | $0.5125 |
| qpu.iqm.garnet | QPU | 16 | -10.6113, gap 5.08 certificate | $1.025 |
| qpu.iqm.emerald | QPU | 16 | -11.3923, gap 4.30 certificate | $1.100 |
| exact.tpu | TPU | 16 | -12.8804, gap 2.81 certificatebest outcome | $0.0776 |
| neural.tpu | TPU | — | a QUBO is diagonal, which is not the shape a neural ansatz is for | — |
* The Rigetti row is not scored against the optimum named above. The run used the 4-job scheduling instance that sector_instances.py generates instead. Its exhaustive minimum is -351.2615, and the 4.95 gap is measured against that rather than against -15.6952. The IQM rows are our own internal testing. The exact.tpu row, added 25 September, is the best of the eight at a gap of 2.81. The steps are in the docs.
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.
A tensor network on CPU returned the closest value here. The encoding arithmetic that decides when this becomes practical is on manufacturing.
8. Traffic and smart cities
Congestion routing for ten vehicles over three candidate routes each, which is 30 qubits and 228 couplings, the largest instance in this survey.
Run on our engines
Route assignment for 10 vehicles over 3 candidate routes each, seed 20260910: 30 qubits, 228 couplings, whose exact optimum is congestion 11. Submitted to each kind of compute we offer, on 16 and 25 September 2026 at 500 shots. Every figure below is a real job on the service, priced as any customer would be priced.
| Device | Engine | Kind | Qubits | Result | Cost |
|---|---|---|---|---|---|
| mps.quimb.cpu | CPU | 30 | 0 of 500 valid assignments | $0.0001 |
| exact.gpu | GPU | 30 | 0 of 500 valid assignments | $0.0001 |
| qpu.rigetti | QPU | 30 | 0 of 500 valid assignments * certificate | $0.5125 |
| qpu.iqm.emerald | QPU | 30 | 0 of 500 valid assignments | $1.100 |
| exact.tpu | TPU | 29 | 0 of 500 valid assignments ** certificate | $0.1607 |
| neural.tpu | TPU | — | the congestion QUBO is diagonal, which is not the shape a neural ansatz is for | — |
* The Rigetti row is this same instance. Thirty qubits is past exact simulation, so its QAOA angles were optimised on the 24-qubit instance of the same family and carried over.
** The exact.tpu row is a 29-qubit variant of the instance, with the last vehicle's third route removed, because that engine holds 29 qubits and this instance is 30. Its exact optimum is congestion 12 rather than 11, so it is not scored against the same number as the rows above it, and an engine with more capacity could return a different result on the full instance. Its angles also come from the 24-qubit optimisation. The steps are in the docs.
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.
At this width and this shot count, none of the 500 shots on any engine satisfied the one-route-per-vehicle constraint. The penalty terms that enforce it grow with the problem, and at 30 qubits they dominate the sampling, so the shots land in the infeasible region. That is a statement about this encoding at this size rather than about the sector, and it is exactly the regime where better penalty weighting, constraint-preserving mixers and deeper QAOA are being researched. The analysis is on traffic and smart cities.
9. Cryptography
The one sector here where the use case is a risk to plan for rather than a capability to buy. We ran Shor's algorithm against real elliptic curves and recovered private keys up to 7 bits, over curves from F5 through F107, using 9 to 21 qubits. The 7-bit key was recovered on the GPU tier as well, in 66 seconds. The two-qubit gate count went from 328 at 3 bits to 235,470 at 7. Width grew by about three qubits per bit, and depth is what grew fastest.
Run on our engines
Shor's discrete logarithm algorithm on real elliptic curves y² = x³ + ax + b over F5 to F107, recovering each private key from its public key at 64 shots. On 25 September the 7-bit recovery ran again on exact.tpu, a Google TPU, recovering the same key from 25 usable shots in 271 seconds. Submitted to each kind of compute we offer, on 10, 24 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 | 9 | 3-bit key recovered, d = 7, in 0.14 s * | $0.0001 |
| exact.cpu | CPU | 12 | 4-bit key recovered, d = 11, in 0.57 s * | $0.0001 |
| exact.cpu | CPU | 15 | 5-bit key recovered, d = 19, in 8.40 s * | $0.0002 |
| exact.cpu | CPU | 18 | 6-bit key recovered, d = 35, in 6.70 s * | $0.0002 |
| exact.cpu | CPU | 21 | 7-bit key recovered, d = 67, in 70.5 s * | $0.0020 |
| exact.gpu | GPU | 21 | 7-bit key recovered, d = 67, in 66 s certificate | $0.1066 |
| exact.tpu | TPU | 21 | 7-bit key recovered, d = 67, in 271 s certificate | $0.4534 |
| neural.tpu | TPU | — | Shor's algorithm is a circuit, not a Hamiltonian, so it does not reach the neural tier | — |
* Run in-process on the exact.cpu engine rather than submitted as billed jobs. Each cost is the measured runtime priced at the rate the service quotes for CPU work, with its $0.0001 minimum. The steps are in the docs.
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.
Bitcoin and Ethereum both sit on secp256k1, which is 256 bits. The textbook construction needs roughly 2,304 logical qubits, and the 2026 physical estimates put a break at somewhere between about 10,000 and 500,000 physical qubits depending on the error rate assumed. The measured gate counts, the resource estimates and the fidelity each key size demands are on cryptography.
What any of this costs
The simulations (CPU rows in these tables) for these sample runs cost on average $0.0001. Switching to QPU hardware changed the cost dynamics. A gate task carries a flat $0.30 fee plus the device's own per-shot rate, so the same 500-shot run is $0.5125 on one processor and several times that on another, and a neutral-atom run at 1,000 shots is $10.30.
The decision of whether a workload belongs on hardware at all is mostly arithmetic, and what it costs to rent a quantum computer works it through on every machine we offer, including the cases where a simulator returns the exact result for a fraction of a cent and no queue.
Before submitting to real hardware, live engine status is worth a look. Several of these devices accept work only during scheduled windows, and the page reports which are open now and how many tasks are queued ahead of you.
Taking any of these further
Everything above is a sample run, and the instances are deliberately small so the true answer is knowable. Running them at sizes where the answer is not knowable is the interesting work, and it is open to anyone on the platform.
- Python SDK.
pip install qsim-sdk, thenclient.estimate()for a free quote andclient.run()to submit. The same call takes any engine name, so a circuit moves from a simulator to a quantum processor by changing one argument - Web console. Build or paste a circuit, pick a program kind, see the price before anything executes, and export a certificate for the run
- Android app. The same account and the same engines from a phone, including job history and certificates
- Qiskit and PennyLane. The engines appear as Qiskit backends and as a PennyLane device, so an existing program runs by naming one
Every instance on this page is seeded, so it rebuilds exactly rather than approximately. The sector pages carry the construction and a notebook for each, the benchmark methodology explains how each criterion was fixed before its run, and all nine are indexed on applications.
Use cases the manufacturers name, that we have not benchmarked
Some of the upcoming benchmarks you can expect in future from ZKSF where we run tests on the different sectors that Quantum Computing is impacting.
- Materials science and condensed-matter physics. Rigetti names it as a primary target for the 108-qubit system, and Quandela lists material simulation among the workloads Belenos is aimed at
- Quantum error correction and logical qubits. Rigetti positions the wider register at experiments needing enough physical qubits to encode a meaningful logical one
- Energy and power systems. IQM names energy alongside finance, pharmaceuticals and logistics as a target sector
- Computational fluid dynamics. IQM cites a 3D advection-diffusion simulation run on Emerald with a substantial reduction in circuit depth against earlier approaches
- Drug discovery beyond ground-state energies. IonQ names drug discovery as an enterprise application and lists pharmaceutical partners
- Telecommunications network optimisation. IonQ cites a network interference optimisation case study run on Forte Enterprise hardware
- Risk analysis. AQT names it alongside chemistry and portfolio optimisation as proof-of-concept work suited to IBEX Q1
- Many-body physics and analog quantum simulation. QuEra describes Aquila as an analog Hamiltonian simulator, and Pasqal positions FRESNEL the same way
- Structural mechanics, engine combustion and electromagnetic simulation. Quandela lists these among the hybrid quantum and HPC workloads it aims Belenos at
- Meteorology and earth observation data. Also named by Quandela, and distinct from the satellite tasking benchmark above, which schedules observations rather than processing what they return
We look forward to running these on our engines and sharing the certified results with our readers.
Pricing every figure below against your own workload: open the per shot cost calculator.
Run your own 100-qubit circuit, with an error bar.
