Verified simulation concepts distributed across the six public modules.
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Hardware-constrained learning for quantum computing and artificial intelligence
Simulation program
This public page now hosts the March 2026 QC+AI simulation library as a live browser surface: sixteen verified simulations, inline corrections, runnable teaching prototypes, and the architecture notes needed to harden them into fully persisted product features.
This page now includes browser-playable educational prototypes for all sixteen verified simulation concepts. They run live in the browser today, while session persistence, analytics, and lesson-embedded progression remain the next implementation layer.
Verified simulation concepts distributed across the six public modules.
Concepts with explicit scientific or implementation corrections carried into the public design.
UX and pedagogy rules that keep the labs source-grounded and study-oriented.
Sequential implementation phases from foundation work to public demo polish.
Public framing
The simulation program is now public, inspectable, and runnable in the browser. That still does not mean the deeper platform layer is complete: simulation sessions are not yet persisted into learner history, and analytics or arena variants are still future engineering work. The value of this page is that the interaction layer and the remaining implementation boundaries are both explicit.
Current status
Prototype anchor
It is the simplest complete public demo, the most directly tied to the course thesis, and the fastest way to change the first impression of the platform from brochure to learn-by-doing studio.
SIM-01A remains the clearest thesis statement for the simulation layer because it is mathematically compact, easy to explain, and directly tied to why NISQ realism matters.
Interaction model
The program is intentionally mixed. Some simulations teach classification and architecture framing, some teach constrained behavior, and some expose quantitative physics or optimization tradeoffs. Every one of them should still move through explore, challenge, and explain states.
Learning tier
Visual and classification-first simulations that make the idea legible before the learner reads the deeper explanation.
Learning tier
Hands-on parameter and workflow manipulation where tradeoffs become visible through guided interaction and constrained goals.
Learning tier
Formula-backed, systems-level simulations that expose convergence, fidelity, energy, or solver behavior with quantitative outputs.
Explore
Build intuition through play and visible cause-and-effect.
Challenge
Force applied reasoning under realistic tradeoffs and time pressure.
Explain
Close the loop so the learner understands not only what worked but why.
Concept library
The catalog is organized by module so evaluators can see exactly how the simulation layer reinforces the current lesson path. Concepts marked corrected include explicit change notes, not silent edits, and each card now opens a browser-playable lab.
Module 1
Module 1 simulations make the NISQ-era constraints visible and clarify where the quantum subroutine actually sits inside a hybrid workflow.
Learners adjust circuit depth, gate error rate, qubit count, and backend assumptions while a live fidelity curve collapses from 1.0 toward 0.0.
Controls include circuit depth, epsilon, qubit count, and backend options for IBM Heron, IonQ Forte, and a simulated ideal baseline.
F(G, epsilon) = (1 - epsilon)^G
Corrected as a conservative upper-bound model that uses total gate count G rather than depth times qubits. The 0.85 threshold is labeled as an illustrative teaching threshold, not a universal literature standard.
Recommended first build because it is the fastest high-value public demo and the clearest expression of the course thesis.
Browser-playable lab
Conservative upper-bound model with total noisy gate count G per layer, not depth times qubits.
Controls
Outputs
Maximum gate density per layer assumption.
Backend-adjusted epsilon.
Illustrative teaching threshold at 0.85 fidelity.
Final modeled fidelity is 0.3248 after 140 total noisy gates on IBM Heron.
Ten real abstracts from the 2025 and 2026 proceedings are sorted into QAI or AI4QC with immediate reasoning feedback.
Drag each abstract into the correct bucket, then inspect why the classification is right or wrong after every move.
A hybrid pipeline is split into classical preprocessing, quantum subroutine, and classical post-processing zones.
Task cards such as normalization, gate compilation, parameter optimization, measurement averaging, and output decoding are dragged into the most plausible stage, then scored against cost and orchestration tradeoffs.
Module 2
Module 2 simulations focus on the classical support machinery that keeps near-term quantum workflows tractable under sparse hardware and small qubit budgets.
A logical circuit is mapped onto a sparse coupling graph that mimics IBM Heron heavy-hex topology or a generic sparse backend.
Learners manually insert SWAP operations, watch routing overhead accumulate, and compare their path with an AI-assisted router.
Corrected hardware reference from IBM Eagle to IBM Heron.
A naive QUBO encoding starts above the available qubit budget and must be reduced through reformulation choices.
Variable merging, penalty absorption, and subgraph factoring move the learner across a quality-versus-qubit scatter chart with a goal of staying under 10 qubits at greater than 90 percent quality.
An industrial scheduling problem exposes primal and dual residual behavior under RL-tuned, fixed, and human-tuned penalty strategies.
Learners adjust lambda, RL learning rate, and ADMM iteration count, then inspect convergence curves and compare policy quality across strategies.
Module 3
Module 3 simulations focus on application architecture decisions, kernel behavior, and how hybrid models should be decomposed and evaluated.
Five paper-derived pipelines are decomposed into input, classical encoder, quantum layer, classical decoder, and output stages.
Learners inspect each layer, compare architectures side by side, and see how the quantum layer changes the end-to-end design rather than replacing it.
A synthetic biomedical dataset shows how an RBF SVM and a quantum-kernel SVM behave as dimensionality scales upward.
Decision boundaries update live while the learner increases dimensionality and compares where quantum feature maps plausibly help or collapse back to parity.
Few-shot episodes expose how support-set size, embedding depth, and classical-head choice affect accuracy.
Accuracy-versus-K curves update in real time, revealing where quantum embedding helps at K=1 and where classical parity returns by K=10.
Module 4
Module 4 simulations make representational tradeoffs visible, especially where quantum structure is used for compression or explanation acceleration.
A full-resolution image or signal is compressed with both a classical INR and a quINR so the learner can compare compression ratio and PSNR.
Quantum parameter count changes the quality-compression frontier while a residual viewer reveals which spectral components are captured more efficiently.
A GNN over a molecular graph compares classical SHAP evaluation cost with a QGSHAP path that uses amplitude amplification.
Matching explanation quality is held fixed while the learner watches computational cost fall from exhaustive or sampled classical evaluation toward a quantum-assisted square-root sample regime.
Classical exact cost O(2^N), sampled cost O(M), QGSHAP cost O(sqrt(M))
Module 5
Module 5 simulations translate the course into deployment realism: solver tradeoffs, migration strategy, vertical prioritization, and time-horizon judgment.
Three solvers attack the same logistics-style optimization problem while cost and runtime update every 500 milliseconds.
Problem size reveals crossover behavior across brute force, simulated annealing, and a D-Wave-style QUBO path, with a hardware cost panel included for business realism.
A twelve-service infrastructure is triaged under escalating quantum threat, forcing the learner to decide which cryptographic assets actually require migration.
Services using RSA-2048, ECC-256, AES-128, and AES-256 are examined under time pressure so the learner separates urgent migration from good operational hygiene.
Critical correction applied: AES-256 does not require PQC migration. AES-128 is upgraded to AES-256 as hygiene, while RSA-2048 maps to ML-KEM, ECC-256 to ML-DSA, and signature systems to SLH-DSA under the relevant FIPS standards.
A Sankey-style map connects industry verticals to QC+AI application types, maturity levels, and deployment horizons.
Each connection can be filtered and opened against the source passage in the industry-use-case document so commercial narratives stay tied to evidence.
Module 6
Module 6 simulations turn the closing roadmap material into measurable tradeoff surfaces instead of abstract future-state claims.
A hybrid scheduling or optimization agent exposes energy cost, memory cost, and solution quality as coupled live outputs.
Learners vary classical compute allocation, quantum QPU shots, and memory architecture while searching for a Pareto frontier against the Landauer limit reference line.
Landauer limit E_min = kT ln(2) per bit erasure, about 4 x 10^-21 J at 300K
Claims from the 2026 synthesis are sorted across time horizon and evidence strength rather than being accepted at face value.
Learners drag thirty claims onto a canvas with axes for time horizon and evidence strength, then compare their placements with the source authors' reasoning.
Teaching rules
The design is not only about visual polish. These principles keep the simulations aligned with the source-grounded character of the platform and prevent them from becoming detached toy widgets.
Principle
The intended sequence is simulation first, then source-grounded explanation, then flashcards and quiz work. The learner should encounter the phenomenon before reading the abstract account of it.
Principle
Every simulation should support an intuitive progression from open play to constrained task execution and then to explanation.
Principle
Every simulation state should resolve back to the corpus passage that justifies it so the product stays trustworthy instead of drifting into generic illustration.
Principle
Session state should be saveable, reloadable, annotatable, comparable, and eligible for project submission so the labs tie into notes, analytics, and portfolio work.
Principle
Basic mode should stay public and legible, advanced mode should unlock after related quiz completion, and expert mode should expose model-level controls only after deeper work.
Principle
When a configuration fails, the UI should explain what parameter caused the failure, suggest one concrete adjustment, and preserve the failed state because it is pedagogically valuable.
Principle
Each simulation should have a competitive variant so the existing Arena surface can host substantive technical tasks instead of recall-only prompts.
Implementation architecture
The existing product already has a credible foundation, but a real simulation layer needs state persistence, citation resolution, event analytics, and a disciplined browser-side rendering strategy.
Architecture note
Architecture note
Architecture note
Recommended stack choices
React + Canvas API + targeted D3.js visualizations
Fits the existing web product and keeps public guest demos easy to load and share.
D3.js v7 or equivalent lightweight charting primitives
Good fit for animated SVG or canvas-based explanatory charts without pushing the app into a heavyweight graphics stack.
Force-directed or custom D3 graph layouts
Well suited to routing maps, coupling graphs, and QUBO reduction workflows.
Custom TypeScript statevector utilities
Enough for education-scale simulations without introducing opaque black-box libraries.
Existing WebSocket and arena surfaces with Redis-style pub/sub if needed
Aligns with the current Arena model and supports ranked or timed challenges.
API surface
Save simulation state, parameters, outcome, and timestamp.
New simulation route group
Reload a saved simulation state for continued study or review.
New simulation route group
Compare two saved runs side by side.
New simulation route group
Resolve simulation state to the corpus passage that supports the output.
Extends search and citation surfaces
Create a competitive simulation challenge session.
Extends Arena
Fetch rankings for a specific simulation challenge.
Extends Arena
Log learner interaction events for dashboards and skill-gap reporting.
Extends analytics
Phase 0 checklist
Roadmap
The rollout sequence is intentionally staged. Phase 0 unlocks everything else. After that, the emphasis shifts from the clearest public demo to the strongest technical differentiators and then to full curriculum coverage.
Implementation phase
Simulation shell component, state store, TypeScript simulator utilities, seven API endpoints, analytics wiring, and a source-citation resolver.
Blocker for every later phase.
Implementation phase
SIM-01A and SIM-01C embedded in the NISQ lesson flow, with simulation completion unlocking advanced study prompts.
Highest immediate learner impact.
Implementation phase
SIM-02A and SIM-02B, plus an Arena variant of the routing sandbox.
Highest technical differentiation.
Implementation phase
SIM-05A and SIM-05B, with corrected post-quantum migration logic and project integration.
Highest commercial and portfolio relevance.
Implementation phase
SIM-04B, SIM-06A, SIM-06B, and additional Arena variants for the most demonstrable labs.
Completes coverage across the course path.
Implementation phase
Comparison mode, export and share flows, mobile-optimized layouts, and a guest-access teaser set of simulations.
Raises the platform credibility ceiling.
Most important next step
It is the simplest complete public demo, the most directly tied to the course thesis, and the fastest way to change the first impression of the platform from brochure to learn-by-doing studio.
Confirmed clean
Explore next
The simulations page now exposes both the product direction and a working browser layer. The next useful step is to read the relevant module, inspect the existing lesson path, and decide which labs should be embedded directly into lessons with persistence, citations, and analytics.