NxQuantum

Benchmark-backed quantum ML primitives for Elixir teams on BEAM.

NxQuantum is a pure-Elixir quantum ML library for the Nx ecosystem. It keeps estimation, sampling, kernels, and transpilation in the same runtime as your ML training loops, inference services, and production pipelines.

Who It Is For

Teams building ML systems in Elixir/Nx that need deterministic-by-default quantum workflows in the same runtime.
Researchers who want reproducible, typed contracts and BEAM-native integration patterns.
Product teams exploring hybrid quantum-AI workflows where runtime fit and reproducible evidence matter.
Not a primary fit (today) for teams whose top requirement is immediate broad hardware-provider coverage.

Why Teams Choose NxQuantum

Quantum tooling is mostly Python-first today. NxQuantum focuses on the Elixir/Nx/BEAM community by providing:

Fast local workflow execution in the same BEAM runtime (no required cross-language service hop).
Deterministic-by-default behavior with explicit runtime and seed contracts.
Elixir-native primitives (Estimator, Sampler, Kernels, Transpiler) built for production integration.
A practical path from experiments to hybrid quantum-AI production workflows.

See positioning and comparison details:

Performance Value Proposition

Evidence, not hype:

In the reproducible cross-framework benchmark (docs/python-alternatives-benchmark-2026-03-25.md), NxQuantum is faster than Qiskit on all 5 local simulator scenarios in the report (baseline_2q, deep_6q, batch_obs_8q, state_reuse_8q_xy, sampled_counts_sparse_terms).
The same report shows strong wins vs PennyLane and Cirq on the same machine and run configuration.
In the BEAM integration case-study throughput lane, throughput increases from 1333.333 ops/s to 3030.303 ops/s on :cpu_portable, and from 1666.667 ops/s to 3787.879 ops/s on :cpu_compiled as batch size increases (8 -> 32).

Benchmark references:

Caveat: these speed figures are from local simulator/fixture workflows on specific environments; they are not universal claims about remote provider/QPU execution latency.

Determinism Scope (Important)

Deterministic means fixed inputs + fixed seed + fixed runtime profile/options produce stable outputs in simulator and fixture lanes.
Live provider/QPU execution remains physically probabilistic and can vary due to noise, calibration drift, and queue/runtime conditions.
For live lanes, NxQuantum guarantees typed lifecycle/error envelopes and reproducible request metadata; it does not guarantee bit-for-bit identical measured outcomes.

Choose Your Path

Evaluate vs Python-first workflows: docs/python-comparison-workflows.md
Plan migration from Python workflows: docs/migration-python-playbook.md
Use provider-specific migration packs: docs/v0.5-migration-packs.md
Start interactive tutorials: docs/livebook-tutorials.md
Check provider support tiers and limits: docs/v0.5-provider-support-tiers.md
Use standalone and external integration profiles: docs/standalone-integration-profiles.md
Review Quantum AI tool contract strategy (sync + async): docs/v1.0-quantum-ai-tool-contracts.md
Review hybrid benchmark/dataset/API spec (planned Phase 20): docs/v1.0-hybrid-quantum-ai-benchmark.md
Review TurboQuant-inspired rerank compression guide: docs/turboquant-rerank-guide.md
Review reproducible provider benchmark matrix: docs/v0.5-benchmark-matrix.md
Review Python alternatives benchmark run: docs/python-alternatives-benchmark-2026-03-25.md
Review benchmark narrative evidence: docs/case-study-beam-integration.md

Quick Start

mise trust
mise install
mix setup
mix run examples/quantum_kernel_classifier.exs

For full setup and API walkthroughs and usage examples:

docs/getting-started.md

Main Features (Current)

Circuit construction and expectation estimation.
Shot-based sampling with explicit seeds (deterministic in simulator/fixture lanes).
Batched estimator/sampler APIs.
Gradient modes (backprop, parameter_shift, adjoint).
Error mitigation pipeline (readout, zne_linear).
Topology-aware transpilation interface.
Quantum kernel matrix generation.

What Is Still Planned

v0.8 migration-assurance toolkit scope from ADR 0007 (unscheduled).
Additional provider depth and broader provider-native dynamic/non-gate-model paths.
More benchmark-backed case studies across real BEAM deployment patterns.

Track status here: