Built for the Classiq user

Keep Classiq.
Extend what it can prove.

Ampcode orchestrates Wolfram Mathematica, Lean 4, and your existing Classiq infrastructure—from research paper to validated quantum implementation.

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Agenda

How the pieces become one research system.

01The research gapWhat remains before and after circuit synthesis.
02Backend-agnostic designWhy OpenQASM was a demo choice, not a dependency.
03MathematicaSymbolic, numerical, quantum, and reference computation.
04Lean 4Machine-checked proof with an explicit assurance boundary.
05ClassiqHigh-level quantum design, synthesis, optimization, and execution.
06Ampcode + ESLOrchestration, traceability, validation, and a practical pilot.
A clarification about the first presentation

OpenQASM was the demonstration bridge—not the architecture.

We used OpenQASM because it is openly specified, accessible, inspectable, and easy to exchange across tools. The workflow itself is implementation-backend agnostic.

Why QASM then

An open intermediate representation made the first proof of concept easy to reproduce without requiring commercial infrastructure.

What stays stable

The paper-linked specification, proof obligations, reference outputs, constraints, and validation gates do not depend on one circuit format.

Why Classiq now

If Classiq is already available, use its high-level QMOD workflow and synthesis engine as the production implementation backend.

Design rule: swap the quantum implementation backend—Classiq, OpenQASM tooling, Qiskit, or another qualified platform—without replacing the evidence pipeline.

Source: OpenQASM introduction and role as an intermediate representation · official Apache-2.0 repository

The starting point

A Classiq user should not rebuild Classiq.

Classiq already provides the quantum engineering infrastructure. We preserve that investment and strengthen the work before, around, and after synthesis.

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High-level modeling

Express the quantum function without manually assembling every gate.

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Synthesis

Translate the functional model into an executable quantum circuit.

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Optimization

Apply depth, width, gate-set, and hardware constraints.

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Execution

Simulate, estimate resources, and target supported quantum backends.

The opportunity

The difficult work often begins before the Classiq model.

Paper → specification

  • Recover equations and algorithms
  • Expose hidden assumptions
  • Resolve notation and transcription issues

Claim → evidence

  • Reproduce figures and tables
  • Build a numerical reference
  • Test limits and special cases

Result → confidence

  • Prove exact central claims
  • Validate the synthesized behavior
  • Produce traceable audit evidence

This is the layer Ampcode adds—without asking the user to abandon Classiq.

The integrated workflow

One orchestrated path from paper to validated circuit.

01 Research paper Equations, figures, algorithms, datasets
02 Ampcode intake Claims, assumptions, issues, provenance
03 Mathematica Symbolic model and numerical reference
04 Lean 4 Machine-checked exact claims
05 Classiq model High-level quantum function and constraints
06 Synthesis Optimized circuit, resources, execution
07 Validation Comparison, traceability, evidence report

Ampcode orchestrates every transition: generates artifacts, runs tools, checks results, and routes failures back to the responsible stage.

Ampcode is the orchestrator

More than a chat interface.

Ampcode coordinates the actual engineering work across the paper, repositories, Mathematica, Lean 4, and Classiq.

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Maintains traceabilityEvery model, theorem, and circuit requirement links back to a paper claim.
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Executes the workflowWrites adapters, runs builds and tests, and captures generated evidence.
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Closes correction loopsUses failures to identify whether the paper interpretation, model, proof, or circuit specification needs revision.
claim-ledger.json
{
  "claim": "Theorem 2: invariant preserved",
  "paper": "Section 4, Equation 17",
  "mathematica": "CheckInvariant[params]",
  "lean": "PaperProofs.main_invariant",
  "classiq": "build_quantum_model(params)",
  "validation": {
    "reference": "passed",
    "proof": "formally proved",
    "circuit": "agreement checked"
  }
}
Why Mathematica matters to quantum computing

Useful quantum work begins before the circuit.

A circuit encodes an implementation. Research and business teams first need to turn a physical, scientific, or optimization question into a defensible computational model.

1 · Frame

Define the question, data, assumptions, objective, and success measure.

2 · Model

Derive equations, operators, tensors, constraints, and classical baselines.

3 · Explore

Use symbolics, numerics, visualization, simulation, and optimization to test the idea.

4 · Implement

Translate the validated quantum formulation into Classiq for synthesis and execution.

Division of labor: Mathematica is the computational research workbench; Classiq is the high-level quantum implementation and synthesis environment.

Based on Wolfram's 2026 overview: Quantum Computation for Research and Business

Wolfram Mathematica

The independent computational reference.

Before asking whether a synthesized circuit is correct, establish what the paper predicts—symbolically and numerically.

Reconstruct

Encode the paper’s equations, domains, parameters, and limiting cases.

Reproduce

Regenerate the paper’s named figures, tables, and benchmark values.

Explore

Run symbolic reductions, parameter sweeps, and high-precision simulations.

Reference

Export expected states, observables, and distributions for circuit comparison.

Benefit to the Classiq user: the synthesized circuit is tested against an independent scientific model—not only against itself.

The Wolfram stack combines symbolic and numerical computation, visualization, optimization, circuit construction, and hardware analysis in a notebook-centered research environment. Read the Wolfram overview

Wolfram Quantum Framework

One environment for theory, simulation, and experiment.

Wolfram's framework puts finite-dimensional quantum systems inside the same language used for symbolics, optimized numerics, data, and visualization.

Represent

States, gates, operators, channels, measurements, and parameterized circuits.

Compute

Symbolic or numerical evolution, distances, entanglement, and quantum optimization.

Visualize

Circuit diagrams, state views, Bloch spheres, measurement results, and research plots.

Connect

Interoperate with external quantum platforms, simulators, and quantum processing units.

Design circuits, simulate behavior, compare theory with data, and connect to hardware—while preserving the notebook as an executable research record.

Official sources: Wolfram Quantum Framework · framework guide

The tools are complementary by design

Mathematica + Classiq is already an official direction.

Wolfram and Classiq announced an integration that brings Classiq's engine into Mathematica, combining classical algorithm development with QMOD-based quantum algorithm development in one environment.

01 Develop Build the mathematical and classical algorithm in Mathematica.
02 Analyze Explore models, parameters, baselines, and expected outputs.
03 Describe Express the quantum algorithm at a high level with QMOD.
04 Synthesize Compile under hardware, depth, width, and gate constraints.
05 Execute Run across supported simulators and quantum backends.
06 Assess Bring results back for analysis and evidence capture.
07 Orchestrate Ampcode keeps artifacts, proofs, tests, and provenance aligned.

Official announcement, 23 April 2024: Wolfram and Classiq integrate advanced quantum software tools into Mathematica

Lean 4 formal verification

Turn central claims into machine-checked theorems.

Paper claim

“For all valid parameters, the transformation preserves normalization and the stated invariant.”

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Lean theorem

Explicit types, domains, assumptions, definitions, and a proof accepted by the Lean kernel.

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Usable guarantee

The exact algorithmic claim is proved—not inferred from selected simulations.

Honest proof boundary: Lean proves the formalized algorithm and assumptions. A Classiq-generated circuit is separately checked for agreement unless circuit-level equivalence is also formally proved.
Classiq remains the quantum backend

Give Classiq a better-defined input.

Ampcode converts the verified research specification into the existing Classiq integration, including algorithm parameters and engineering constraints.

1
Functional modelDerived from a versioned, paper-linked algorithm specification.
2
Synthesis constraintsDepth, width, gate set, approximation, and target-backend requirements.
3
Execution artifactsCircuit, resource estimates, simulation results, and QASM when required.
CLASSIQ IN THE COMBINED SYSTEM
Receive validated specification

Algorithm intent and constraints are explicit.

Amp → Classiq
Synthesize and optimize

Classiq performs its core quantum-engineering role.

Classiq
Run or export

Simulator, hardware backend, resource report, or QASM.

Classiq
Return evidence

Results flow back into cross-validation.

Classiq → Amp
The confidence layer

Ampcode closes the loop after synthesis.

Mathematica referenceExpected states, observables, distributions, figures, and edge cases.
Lean guaranteesExact claims and the assumptions under which each theorem applies.
Agreement gateCompare behavior, verify assumptions, and check constraints.
Classiq evidenceSynthesized circuit, resources, simulation, and backend output.
Traceable reportPass, mismatch, limitation, proof status, and source claim.
If results disagree: Ampcode routes the issue to the paper interpretation, Mathematica model, Lean assumptions, Classiq specification, or synthesis constraints—rather than hiding the mismatch.
A concrete research day

From “interesting paper” to reviewable evidence.

Researcher provides the paper and target experiment

No need to manually transcribe every equation before useful work begins.

Researcher
Ampcode builds the claim and assumption ledger

Each important result receives a source, implementation, proof, and validation target.

Ampcode
Mathematica reproduces the reference result

Figures, special cases, and expected measurements are exported as evidence.

Mathematica
Lean proves the exact core claim

Missing assumptions become explicit; numerical-only claims remain clearly labeled.

Lean 4
Classiq synthesizes and executes the implementation

The user retains the established Classiq workflow and backend options.

Classiq
Ampcode delivers the reproducibility package

Models, proofs, circuit evidence, resource reports, and traceability arrive together.

Ampcode
What improves for the Classiq user

Not another circuit generator—an evidence multiplier.

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Manual translation

Reduce repetitive work between papers, mathematical models, proof obligations, and Classiq inputs.

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Scientific confidence

Combine an independent numerical reference with formal proof of selected exact claims.

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Faster correction

Identify which layer caused a disagreement and rerun the affected workflow automatically.

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Reproducibility

Preserve provenance from paper equation to model, theorem, synthesized circuit, and result.

Classiq optimizes the quantum implementation. Ampcode orchestrates and verifies the journey from scientific claim to that implementation.

A practical pilot

Prove the value on one real paper.

Step 1 · Reproduce

Select a Classiq-relevant paper

Choose one central equation, one published figure or table, and one circuit-level outcome.

Step 2 · Integrate

Connect the existing Classiq option

Generate the high-level model and constraints through a narrow, versioned adapter.

Step 3 · Measure

Compare the complete workflow

Evaluate time, manual steps, result agreement, proof coverage, resources, and reproducibility.

Success criterion: an independent reviewer can trace a paper claim through Mathematica evidence and Lean proof status to the Classiq-generated implementation and its validated output.
ESL Engineering Software Lab logo
Engineering Software Lab

ESL—AI SDLC consultants.

We design and integrate agentic engineering workflows across research, formal methods, computational modeling, quantum platforms, testing, security, and delivery.

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Workflow architectureTurn disconnected tools into one governed, traceable engineering process.
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Assurance by designCombine executable models, formal proof, tests, security checks, and review evidence.
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Integration without replacementExtend the platforms you already trust—including Classiq, Mathematica, Lean 4, and Ampcode.
Visit ESL ↗ Explore Amp ↗ Contact ESL ↗
The combined proposition

Keep the platform you trust.
Add the evidence you need.

For a Classiq user, Ampcode is not a competing quantum SDK. It is the orchestration layer that makes research interpretation, mathematical reproduction, formal proof, synthesis, and validation operate as one system.

Ampcode orchestrates · Mathematica computes · Lean 4 proves · Classiq synthesizes
Research-to-implementation Formal verification Independent validation Existing Classiq infrastructure
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