Quantum Algorithm Catalog¶

The Quantum room of Franklin teaches the operator nineteen quantum algorithms across seven families, and the seven combination stacks where those algorithms compose into outcomes at the scale of human problems. This page is the operator-facing reference for what each algorithm does in plain terms, what CALORIE value it produces, and what CURE deficit it heals.

Every claim on this page is warranted by a substrate row. Atom IDs are listed alongside each entry; the same content renders into the chat narration in the operator's locale via FranklinMeaningRenderer. The same content is the body of the corresponding franklin_ontology_facts row that the chat oracle reads when the operator asks "what is Shor for".

The 19 algorithms in plain terms¶

Quantum Circuit Family¶

QC-001 Shor — factoring large numbers Substrate atom: narration_quantum_qc001_shor_teaching · FOF-100

What it does: Takes a huge number that two big prime numbers were multiplied to make, and finds those two primes.

CALORIE: Forces the world to upgrade to post-quantum encryption before bad actors steal everyone's banking, medical records, and national secrets. Real value: protected savings accounts, protected medical privacy, protected infrastructure.

CURE: Heals the looming deficit where current encryption (RSA) protects trillions of dollars of assets and will fail once quantum machines mature. Without Shor running first in controlled hands, criminals run it first in the wild.

QC-002 Grover — searching faster Substrate atom: narration_quantum_qc002_grover_teaching · FOF-101

What it does: Finds a needle in a haystack in roughly the square root of the time normal search takes. If a normal search takes a million tries, Grover takes about a thousand.

CALORIE: Drug discovery search across millions of molecular configurations. Pattern matching in fraud detection. Database searches at unprecedented speed.

CURE: When a child has a rare disease and the molecular match for treatment is buried in a database of 10 million candidates, Grover finds it in 3,000 tries instead of 5 million.

QC-003 QFT — quantum Fourier transform Substrate atom: narration_quantum_qc003_qft_teaching · FOF-102

What it does: Detects rhythms and patterns inside data the way an ear separates a song into individual instruments.

CALORIE: Foundation for image processing, signal analysis, communication systems. Almost every other quantum algorithm uses it.

CURE: Without QFT, MRI machines, radar systems, audio processing all lose their fastest path. Heals the deficit of slow signal analysis in medical imaging where a clearer scan in less time means catching a tumor earlier.

QC-004 QPE — quantum phase estimation Substrate atom: narration_quantum_qc004_qpe_teaching · FOF-103

What it does: Measures the exact "frequency" of a quantum system, the way a tuner measures the exact pitch of a guitar string.

CALORIE: How chemists determine molecule energy levels for drug design. How materials scientists understand new battery chemistries.

CURE: Heals the slow-drug-discovery deficit. A medicine that takes 10 years to discover the traditional way might take 2 with QPE-guided molecular simulation.

QC-005 Amplitude Amplification — boosting good answers Substrate atom: narration_quantum_qc005_ampamp_teaching · FOF-104

What it does: Out of many possible answers, pushes the good ones to the top so you see them first.

CALORIE: Faster routing for delivery trucks, faster machine learning training, faster optimization in any system with many possible solutions.

CURE: When emergency services must route ambulances through a city in real time, this gets the best route faster, saving lives in the difference between 12 minutes and 7 minutes.

Quantum Variational Family¶

QC-006 VQE — Variational Quantum Eigensolver Substrate atom: narration_quantum_qc006_vqe_teaching · FOF-105

What it does: Finds the lowest-energy shape of a molecule, which tells you how it will behave.

CALORIE: Discovery of new drugs, new fertilizers, new battery materials, new catalysts that capture carbon.

CURE: The big one — solving how to fix nitrogen from air into fertilizer at room temperature (currently requires huge energy and produces 2% of global CO₂). This is the FeMo-co nitrogenase mimic. Solving it heals world hunger and climate at the same time.

QC-007 QAOA — Quantum Approximate Optimization Substrate atom: narration_quantum_qc007_qaoa_teaching · FOF-106

What it does: Finds the best arrangement when many things compete for limited resources.

CALORIE: Airline scheduling, supply chain logistics, financial portfolio optimization, electrical grid balancing.

CURE: When the grid has to decide moment-to-moment which power source supplies which neighborhood as solar comes and goes and demand changes, this prevents blackouts. Heals the brittleness deficit of aging power infrastructure.

QC-008 Quantum Classifier (VQC) — quantum machine learning Substrate atom: narration_quantum_qc008_vqc_teaching · FOF-107

What it does: Learns to recognize patterns the way regular AI does, but on quantum hardware that can sometimes find patterns classical AI misses.

CALORIE: Medical image classification (cancer in scans), fraud detection in financial systems, anomaly detection in network security.

CURE: When a radiologist must look at 200 mammograms per day, this is the second opinion that catches what fatigue missed. Heals the human-attention-limit deficit in diagnostic medicine.

QC-009 QUBO — Quadratic Unconstrained Binary Optimization Substrate atom: narration_quantum_qc009_qubo_teaching · FOF-108

What it does: Solves "yes or no" decisions across many variables that all affect each other.

CALORIE: Job scheduling, traffic light coordination, vaccine distribution planning, workforce assignment.

CURE: When 50,000 doses of vaccine must reach 200 clinics across a region during an outbreak, QUBO solves the routing better than human planners can. Heals the distribution-bottleneck deficit during epidemics.

Quantum Linear Algebra Family¶

QC-010 HHL — Quantum Linear Solver Substrate atom: narration_quantum_qc010_hhl_teaching · FOF-109

What it does: Solves giant systems of equations that describe how thousands of things relate to each other.

CALORIE: Climate modeling, fluid dynamics for aircraft and wind turbines, financial risk modeling, fusion plasma simulation.

CURE: Foundational for post-quantum cryptography. When the world transitions away from RSA, HHL is one of the tools verifying the new encryption is actually secure. Heals the future-of-encryption deficit.

QC-011 QSVT — Quantum Singular Value Transformation Substrate atom: narration_quantum_qc011_qsvt_teaching · FOF-110

What it does: A general-purpose mathematical tool that makes many quantum algorithms easier and faster.

CALORIE: Improves the efficiency of nearly every algorithm in this list. The "better engine" that other algorithms use.

CURE: Heals the gate-count deficit — it lets quantum algorithms run on smaller, more reliable machines, which means useful quantum computing arrives years sooner than otherwise.

QC-012 qPCA — Quantum Principal Component Analysis Substrate atom: narration_quantum_qc012_qpca_teaching · FOF-111

What it does: Finds the most important patterns hidden in massive datasets.

CALORIE: Image compression, recommendation systems, scientific data analysis, anomaly detection.

CURE: When astronomers have terabytes of telescope data and need to find the few signals that matter, qPCA finds them. Heals the data-overwhelm deficit where important discoveries get lost in too much information.

Quantum Simulation Family¶

QC-013 CTQW — Continuous-Time Quantum Walk Substrate atom: narration_quantum_qc013_ctqw_teaching · FOF-112

What it does: Lets a quantum system explore a network the way a person explores a city, but in multiple paths at once.

CALORIE: Network analysis (social networks, supply chains, electrical grids), drug-target interaction prediction, transportation optimization.

CURE: Tracing contact networks during an outbreak to find super-spreaders fast enough to contain transmission. Heals the contact-tracing deficit during pandemics.

QC-014 Hamiltonian Simulation (Trotter) — simulating physical systems Substrate atom: narration_quantum_qc014_hamsim_teaching · FOF-113

What it does: Models how a real-world quantum system evolves over time. Atoms moving, plasma flowing, magnetic fields changing.

CALORIE: Fusion plasma stability simulation, superconductor design, new material discovery.

CURE: The fusion big one. Simulating tokamak plasma instabilities classically takes weeks of supercomputer time. Hamiltonian simulation on quantum hardware does it in hours. Heals the fusion-energy deficit by making the next generation of fusion plant designs actually verifiable before they are built.

Quantum Bosonic Family¶

QC-015 Boson Sampling — photonic quantum supremacy Substrate atom: narration_quantum_qc015_boson_sampling_teaching · FOF-114

What it does: Shows that photonic quantum computers can do specific tasks no classical computer can match.

CALORIE: Demonstrates quantum advantage on photonic hardware, opens the door to room-temperature quantum computing (no liquid helium required).

CURE: Heals the cost-and-cooling deficit. If photonic quantum computers reach commercial scale, quantum capability becomes affordable for hospitals, research universities, and mid-sized companies — not just government labs.

QC-016 Gaussian Boson Sampling (GBS) — photonic drug discovery Substrate atom: narration_quantum_qc016_gbs_teaching · FOF-115

What it does: Uses photonic quantum hardware to evaluate which drug molecules bind to which protein targets.

CALORIE: Faster drug screening, especially for cancer therapies where the molecular target is well-known but the binding-molecule search space is huge.

CURE: Estradiol-and-ERα binding analysis for breast cancer. Targeted protein-drug interaction screening for personalized medicine. Heals the one-size-fits-all deficit in cancer treatment.

Quantum Error Correction Family¶

QC-017 Steane Code — small fault-tolerant quantum Substrate atom: narration_quantum_qc017_steane_teaching · FOF-116

What it does: Encodes one trustworthy quantum bit using seven physical quantum bits, protected against errors.

CALORIE: The foundation for any quantum computation that needs to run longer than a few microseconds before quantum noise destroys it.

CURE: Without error correction, every other quantum algorithm above fails at scale. Steane heals the noise-destroys-the-answer deficit.

QC-018 Surface Code — large fault-tolerant quantum Substrate atom: narration_quantum_qc018_surface_teaching · FOF-117

What it does: Encodes one trustworthy quantum bit using hundreds or thousands of physical qubits, the architecture Google and IBM are pursuing.

CALORIE: The path to actually useful quantum computers (millions of physical qubits encoding thousands of logical qubits).

CURE: Heals the "quantum is just demos" deficit. Surface code is what gets quantum to deployment in medicine, materials, and cryptography at production scale.

QC-019 Topological Quantum Computing — anyons and braiding Substrate atom: narration_quantum_qc019_topological_teaching · FOF-118

What it does: Uses exotic particles whose physics naturally protects against errors, removing the need for the massive overhead of surface code.

CALORIE: The long-term path to compact, reliable quantum machines. Microsoft's quantum bet is here.

CURE: If topological quantum works, it heals the scaling deficit completely. Quantum computers become small enough and reliable enough to deploy widely.

How they combine into higher-level C⁴ teachings¶

The real power is not in any single algorithm. The real C⁴ value comes when several algorithms combine to produce CALORIE or CURE at a scale no single algorithm could reach.

Combination 1: The Drug Discovery Stack¶

Substrate atom: narration_quantum_combo_drug_discovery · FOF-200

VQE + qPCA + GBS + Grover + Surface Code

VQE finds the molecular energy landscape. qPCA reduces the millions of candidate molecules to the most promising patterns. GBS evaluates protein-drug binding on photonic hardware. Grover searches the resulting candidate set for the best matches. Surface Code keeps the whole computation reliable long enough to finish.

Combined CURE: A new cancer drug discovered, validated, and ready for clinical trials in 18 months instead of 10 years. Pancreatic cancer survival, currently 12% at five years, becomes treatable. Personalized medicine becomes affordable.

Combined CALORIE: Pharmaceutical R&D productivity rises 5-10x. The cost of developing one new drug, currently $2.6B average, drops to a few hundred million. New treatments reach patients faster and cheaper.

Combination 2: The Climate-and-Food Stack¶

Substrate atom: narration_quantum_combo_climate_food · FOF-201

VQE + Hamiltonian Simulation + QAOA + HHL

VQE models the FeMo-co nitrogenase enzyme that fixes nitrogen at room temperature. Hamiltonian Simulation watches it work over time. QAOA optimizes how to deploy synthetic-nitrogenase fertilizer production across a continent. HHL solves the climate-impact equations to verify the deployment actually reduces emissions.

Combined CURE: Nitrogen fertilizer produced at room temperature instead of by the Haber-Bosch process (which uses 2% of global energy and produces 1.4% of global CO₂). World food production becomes carbon-negative. Hunger and climate solved at the same load-bearing point.

Combined CALORIE: Agricultural input costs drop globally. Small farmers in developing nations gain access to fertilizer that was previously priced out of reach. Crop yields increase. Rural poverty decreases.

Combination 3: The Energy Infrastructure Stack¶

Substrate atom: narration_quantum_combo_energy · FOF-202

Hamiltonian Simulation + QAOA + QUBO + HHL

Hamiltonian Simulation models fusion plasma stability. QAOA optimizes the magnetic confinement field configuration in real time. QUBO schedules grid distribution across competing demands. HHL solves the giant systems of equations that connect plasma physics to grid output.

Combined CURE: Working commercial fusion power plants delivering baseload electricity by mid-2030s instead of mid-2050s. Fossil fuel dependency for electricity ends within one generation instead of three.

Combined CALORIE: Electricity becomes too cheap to meter for most applications. Desalination becomes affordable for water-stressed regions. Heavy industry decarbonizes economically. Standard of living rises globally without climate cost.

Combination 4: The Security and Privacy Stack¶

Substrate atom: narration_quantum_combo_security · FOF-203

Shor + HHL + Surface Code + QPE

Shor forces the world to upgrade encryption before bad actors do. HHL verifies the new post-quantum encryption is actually secure. Surface Code keeps the cryptographic computations reliable. QPE provides the underlying measurement precision.

Combined CURE: A controlled transition from RSA to post-quantum cryptography across banking, healthcare, government, infrastructure. Trillions of dollars of assets and billions of patient records remain protected through the quantum transition.

Combined CALORIE: Digital trust infrastructure survives the quantum era. International commerce continues. Privacy protections hold. The internet's economic value is preserved.

Combination 5: The Medical Diagnosis Stack¶

Substrate atom: narration_quantum_combo_medical · FOF-204

QFT + Quantum Classifier + Grover + Surface Code

QFT analyzes the rhythms in medical signals (EKG, EEG, blood biomarkers over time). Quantum Classifier learns to recognize disease patterns. Grover searches reference databases for matches. Surface Code keeps the diagnostic chain reliable enough for clinical decisions.

Combined CURE: Early detection of cancer, heart disease, neurological decline at stages where intervention works. Diagnostic accuracy improves 30-50% over human-only or classical-AI-only approaches.

Combined CALORIE: Healthcare cost per outcome drops dramatically. Specialist time is freed from routine pattern-matching. Rural and underserved populations gain access to specialist-quality diagnosis.

Combination 6: The Materials Discovery Stack¶

Substrate atom: narration_quantum_combo_materials · FOF-205

VQE + Hamiltonian Simulation + qPCA + Surface Code

VQE finds new material energy landscapes. Hamiltonian Simulation watches them behave under temperature, pressure, magnetic field. qPCA identifies which materials have the most useful properties. Surface Code keeps the whole search reliable.

Combined CURE: Room-temperature superconductors (eliminating ~10% of global electricity loss in transmission). Cheap, dense batteries (enabling electric aviation and grid-scale renewable storage). Catalysts that pull CO₂ from air at industrial scale.

Combined CALORIE: Energy infrastructure transformation. Transportation electrification at full scale. Climate remediation becomes economically practical.

Combination 7: The Logistics-and-Distribution Stack¶

Substrate atom: narration_quantum_combo_logistics · FOF-206

QAOA + QUBO + CTQW + Grover

QAOA optimizes routing. QUBO assigns resources. CTQW analyzes the network for bottlenecks. Grover finds optimal substitutions when supply disruptions hit.

Combined CURE: Vaccine and medical supply distribution during pandemics. Food distribution in famine zones. Disaster relief routing during natural catastrophes. Each of these has historically failed at the coordination layer; quantum optimization at scale closes the coordination gap.

Combined CALORIE: Global supply chain resilience. Lower waste in food distribution (currently 30% of food spoils before reaching consumers). Lower costs across logistics-dependent industries.

What this means for normal people understanding¶

Math by itself does not feed anyone. The 19 algorithms in isolation are interesting puzzles. The combinations produce CALORIE and CURE at scales that match the actual scope of human problems.

The breakthrough is not "quantum is fast." The breakthrough is that these algorithms, combined with measurement closure (the vQbit substrate), let humans tackle problems that classical computation, classical chemistry, classical optimization, and classical AI cannot reach on a timeline that matters:

Cancer treatment within a generation
Fusion energy within a generation
Climate remediation within a generation
Food security within a generation
Privacy preservation through the quantum transition
New materials that change physical infrastructure
Coordination of global systems at the scale humanity actually needs

Each of these is a CURE at planetary scale. Each is CALORIE-generating for billions of people. None of them are accessible through math alone, classical computing alone, or LLMs alone. All of them become accessible when the right algorithms combine on a substrate that produces auditable receipts every step of the way.

That is what C⁴ Constitutional Consequence means in plain terms. Not math. Real outcomes for real people on a timeline that matters. The substrate that closes the c₃ Measurement Closure gap is the one that lets these combinations run in regulated, life-safety, audit-defensible deployments. The substrate is yours. The combinations are what the patent protects making possible. The CALORIE and CURE are what normal people get when the work lands.

That is the bridge from quantum math to human meaning.

The autonomous improvement loop — visible numbers¶

Teaching alone does not prove that an algorithm is operational right now. The 19 algorithms and 7 stacks are each walked continuously by the sentinel, and the cell improves itself without operator prompting. See The Quantum C4 Autonomous Improvement Loop for the full architecture.

Headline behaviour:

19 QC-NNN-WALK sovereign_scenarios + 7 QC-COMBO-* sovereign_scenarios are seeded by v38; the existing SentinelReflectionLoop walks them on its 30s cadence.
v39 fixes the per-algorithm warrant to point at the algorithm's substrate-resident teaching atom, so each algorithm has a stable, per-algorithm CALORIE warrant rather than the v38 fuzzy LIKE.
QuantumC4MetricsAggregator refreshes per-scenario aggregates every 30s into quantum_c4_metrics.
ContinuousImprovementLoop picks the worst-performing or oldest scenario every 60s, bumps it to the front of the walk queue, and records the prior→post health delta in improvement_loop_audit.
The HUD strip visible in the Quantum room reads ALGORITHMS N/19 · STACKS M/7 · CALORIE RATE XX% · LAST IMPROVED QC-NNN ▲ +Δ and refreshes every 5s.

Substrate references¶

Layer	Where the truth lives
Per-algorithm semantic predicate	`meaning_atoms.atom_id` for each `narration_quantum_qcXXX_teaching`
Per-algorithm en-US rendering	`meaning_renderings.rendered_text` keyed by `(atom_id, locale='en-US')`
Per-algorithm operator-facing ontology fact	`franklin_ontology_facts.body` for FOF-100..118
Combination-stack semantic predicate	`meaning_atoms.atom_id` for each `narration_quantum_combo_*`
Combination-stack ontology fact	`franklin_ontology_facts.body` for FOF-200..206
Per-algorithm walk scenario	`sovereign_scenarios` rows where `domain='quantum_algorithm'` (QC-001-WALK..QC-019-WALK)
Combination walk scenario	`sovereign_scenarios` rows where `domain='quantum_combination'` (QC-COMBO-*)
Walk receipts	`sentinel_walk_receipts` rows where `scenario_id LIKE 'QC-%'`
Per-scenario live metrics	`quantum_c4_metrics` (refreshed every 30s)
Improvement-loop audit	`improvement_loop_audit` (one row per autonomous action)
Render audit (every speak event)	`meaning_render_audit`
Migration that seeded teaching	`cells/xcode/Sources/GaiaFTCLCore/NarratorSchemaV36.swift`
Migration that seeded walk scenarios	`cells/xcode/Sources/GaiaFTCLCore/NarratorSchemaV38.swift`
Migration that fixed warrant queries	`cells/xcode/Sources/GaiaFTCLCore/NarratorSchemaV39.swift`

When the chat oracle answers "what is Shor for", it reads FOF-100. When the Quantum room narration cycle reaches the Shor beat, FranklinMeaningRenderer resolves narration_quantum_qc001_shor_teaching to the operator's locale via meaning_renderings. The same content; one substrate truth; multiple operator-facing projections — Franklin's chat narration, the NOW SHOWING label, this wiki page.

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