Quantum algorithms · Applied machine learning

The hard part isn't the qubit. It's proving it was worth it.

Neuraq is a research and engineering studio for quantum algorithms and applied machine learning. We prototype on simulators, run on real hardware, and put the result next to a properly tuned classical baseline — including the times the baseline wins.

See the services How an engagement runs

Simulator before device time
Baseline next to every result
Error bars on everything we publish

Fig. 1 Hardware-efficient ansatz, n = 4, ring entangler, 2n parameters per layer. Transpiled depth and two-qubit count are what decide whether this survives on real hardware — so that is what we report.

§1ServicesSix practices
Simulator → hardware
Fixed-scope phases

Six practices. Each one ends in a number you can check.

We work across the quantum stack and the classical one, because almost every real problem needs both. Engagements are scoped in phases with a stated deliverable, so you are never buying an open-ended research budget.

QML

Quantum machine learning

Variational models, quantum kernels, and hybrid training loops.

We design and train parameterised quantum circuits for classification, regression, and generative tasks on your data — then evaluate them against a tuned classical model on the identical split. The work covers feature-map and data-re-uploading design, quantum kernel estimation, barren-plateau diagnostics, gradient strategy (parameter-shift versus adjoint), and a shot budget costed in money rather than in abstractions.

Methods: VQC · data re-uploading · quantum kernels (QKE) · QCBM
Stack: PennyLane · Qiskit · JAX · scikit-learn
Runs on: statevector → noisy sim → superconducting / trapped ion
You get: Trained model, baseline comparison, shot-cost model
Phase: 8–14 weeks

OPT

Quantum optimisation

QAOA, annealing, and hybrid decomposition for combinatorial problems.

Portfolio construction, vehicle routing, crew and production scheduling, unit commitment: reformulated as QUBO or Ising models and then solved across QAOA, quantum annealing, and a commercial classical solver so the comparison is on one table. Large instances are handled by decomposition — only the hard core goes to the quantum device. We report where the crossover sits, including when it has not arrived.

Methods: QUBO / Ising · QAOA · warm starts · Benders-style decomposition
Stack: Qiskit Optimization · D-Wave Ocean · Gurobi (baseline)
Runs on: annealers · gate-model · CPU/GPU solvers
You get: Formulation, solver bench, scaling projection
Phase: 6–12 weeks

SIM

Quantum simulation for chemistry and materials

Ground-state energies and spectra for molecules and lattice models.

Active-space selection, fermion-to-qubit mapping, and measurement reduction for VQE and phase-estimation workflows — always alongside a DMRG or coupled-cluster reference, so a result has something to be checked against. Applied to catalyst intermediates, battery electrolytes, and correlated-electron models. Where the molecule is beyond today's devices, we say so in logical qubits and T-gate counts rather than in adjectives.

Methods: VQE · ADAPT-VQE · qubit tapering · Jordan–Wigner / Bravyi–Kitaev · QPE estimates
Stack: PySCF · OpenFermion · Qiskit Nature · ITensor
Runs on: GPU statevector · trapped ion · neutral atom
You get: Active-space study, resource estimate, reference comparison
Phase: 10–16 weeks

Applied AI and classical machine learning

The half of the problem that ships this quarter.

Most of the value in a quantum programme is unlocked by classical machine learning first: a clean data pipeline, a strong baseline, and a model actually in production. We build gradient-boosted and deep forecasting models, computer-vision inspection systems, and retrieval-grounded LLM assistants — each with an evaluation harness, so quality is measured rather than asserted, and with the drift monitoring that keeps it true six months later.

Methods: gradient boosting · temporal CNN / transformers · RAG · eval harnesses
Stack: PyTorch · XGBoost · scikit-learn · Claude & open-weight models
Runs on: your cloud · on-prem GPU · edge
You get: Production model, eval suite, monitoring
Phase: 4–10 weeks

Tensor networks and quantum-inspired methods

Algorithms borrowed from quantum physics, running on today's GPUs.

Matrix product states and tree tensor networks compress high-dimensional problems without a quantum computer: simulating circuits well past the hundred-qubit mark at modest entanglement, compressing neural-network layers, and modelling heavy-tailed dependence in risk models. Often the fastest route to an answer — and the honest benchmark any quantum claim has to beat before it means anything.

Methods: MPS / MPO · DMRG · TTN · tensor-train compression
Stack: quimb · ITensor · cuQuantum · cuTensorNet
Runs on: multi-GPU nodes · no quantum hardware required
You get: Simulation harness, compression study, bond-dimension scaling
Phase: 4–8 weeks

CAL

Error mitigation, benchmarking and hardware evaluation

What your circuits will actually return, and on which machine.

Zero-noise extrapolation, probabilistic error cancellation, Pauli twirling, readout unfolding, and dynamical decoupling, applied to your workload rather than to a textbook one — with the sampling overhead each method costs stated up front. For procurement decisions we run randomised benchmarking, mirror circuits, and layer fidelity across vendors on the same circuit family, and publish the full method with the error bars.

Methods: ZNE · PEC · twirling · readout unfolding · RB / mirror circuits · layer fidelity
Stack: Mitiq · Qiskit Experiments · pyGSTi
Runs on: any device with pulse or gate-level access
You get: Device report, mitigation pipeline, vendor recommendation
Phase: 3–6 weeks

Shorter engagements

Technical due diligence

An independent read on a quantum vendor, an acquisition target, or a claim in a paper. We reproduce what can be reproduced and name what cannot.

1–3 weeks / written opinion

Team enablement

A hands-on course for your physicists and engineers: circuit construction, transpilation, noise, and where the real bottlenecks are. Your problems, not toy ones.

2–5 days / on-site or remote

Standing advisory

A monthly retainer for roadmap review, hardware-release triage, and a named person to ask before you sign anything.

Monthly / capped hours

§2EngagementFive stages
Gate after each
Stop whenever

A sequence, with a gate after every stage.

These stages run in order because each one needs the previous one's output. You decide at every gate whether the next stage is worth funding, and the work so far is yours either way.

01
Scoping 1–2 weeks
We take your problem and write down what an advantage would even look like for it: the objective, the instance sizes you actually care about, the current state of the art, and the single metric that settles the question. Most of the value of a quantum programme is decided here, before anything is built.
Output One-page problem statement & go/no-go
02
Classical baseline 2–3 weeks
Before a single qubit is touched, we build the best classical solution we reasonably can and tune it properly. Everything that follows is measured against that number. It is also, often enough, the thing you end up shipping.
Output Tuned baseline + evaluation harness
03
Quantum prototype 4–8 weeks
Circuit design and training on a statevector simulator, then under a device noise model, then on real hardware with mitigation applied. Every run is logged with its calibration snapshot, so a result can be traced back to the machine that produced it.
Output Working circuit + hardware results with error bars
04
Resource estimate 1–2 weeks
How many logical qubits, how many T gates, how many shots, and at what physical error rate the result becomes useful — mapped onto published vendor roadmaps so the answer is a date range, not a feeling. This is the slide your board actually needs.
Output Resource & timeline estimate
05
Integration — or the report that says wait ongoing
Either we ship it into your stack with tests, monitoring, and a handover your own team can maintain, or we write the document explaining why it is not ready and precisely what would have to change. Both are finished work.
Output Production integration + handover, or a written recommendation

§3PlatformsVendor neutral
Simulator first
Your cloud account

Vendor neutral, because the modality should follow the problem.

Different hardware is good at different things: ion traps for depth and all-to-all connectivity, superconducting chips for speed, neutral atoms for width, annealers for a narrow class of optimisation. We pick per problem and run on your own cloud accounts, so access and data stay with you.

Modality	Example systems	What we use it for
Superconducting	IBM Heron · Rigetti Ankaa	Fast sampling, large shot counts, dynamic circuits and mid-circuit measurement.
Trapped ion	Quantinuum H-series · IonQ Forte	Deep circuits and all-to-all connectivity, where transpilation would otherwise dominate the error.
Neutral atom	QuEra Aquila · Pasqal	Wide registers and analogue Hamiltonian simulation of lattice models.
Annealing	D-Wave Advantage	Large QUBO instances and hybrid decomposition on the quadratic core.
GPU simulation	NVIDIA cuQuantum · cuTensorNet	Everything, first. Noise-model studies and tensor-network baselines before any device time is bought.

Frameworks

Qiskit
PennyLane
Cirq
CUDA-Q
Braket SDK
D-Wave Ocean
OpenFermion
Mitiq
quimb
ITensor
PySCF
PyTorch
JAX

Access & deployment

IBM Quantum
Amazon Braket
Azure Quantum
Google Cloud
On-prem GPU cluster
Air-gapped engagement

§4CandourRead before
you brief us

Things we will tell you that are bad for selling quantum.

No quantum computer available today beats a well-tuned classical solver on a production-sized instance of your problem. Anyone who tells you otherwise is selling something.

Some engagements end with a recommendation not to proceed yet. That report is the deliverable, and it is far cheaper than the alternative.

We benchmark against the strongest classical method we can find, not the one that is easiest to beat. A win against a weak baseline is not a win.

A quantum-inspired tensor-network method on a GPU solves a surprising number of problems people arrive here wanting a quantum computer for. We will tell you when yours is one of them.

The work that pays for itself in the next two years is the data pipeline, the baseline, and the resource estimate. The circuit is how you are ready when the hardware arrives.

§5JournalMethod notes
Benchmarks
Readings

What we are working out, in public.

All journal entries

§6 Contact

Bring us the problem, not the technology.

Send a paragraph about what you are trying to compute, how big the real instances are, and what you do today. We will tell you within a week whether there is anything here worth a scoping phase — and if there isn't, we will say that instead.

Send a problem brief Back to services

Enquiries

Email: hello@neuraq.ai
Reply: Within two working days
NDA: Signed before any brief is read
Data: Stays in your cloud tenancy
Minimum: One scoping phase