Quantum Kernel Engine

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Demo

5-qubit quantum kernel executing in sandbox: feature map encoding, SWAP test with shot noise, SVM training, classification output. Built on a phone, runs anywhere.

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What This Is

A complete quantum kernel SVM pipeline built entirely from scratch. No Qiskit. No Cirq. No PennyLane. Every gate decomposition, every IR lowering pass, every QASM emission line — hand-rolled.

This started on a phone using Ollama + cherry-picked Julia repos (Yao.jl), ran as "hello world 5 qubit and shots" in a Kimi sandbox, then expanded into a full verified compilation pipeline targeting IBM Heron r3 hardware.

The Pipeline

Classical Data (R^d)
    |
    v
[YAO.JL] Feature Map: U_Phi(x) = prod_l [U_ent * U_rot(x)]
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    v
[QUANTUMIR v0.1] Flat sequential IR with mandatory `unsupported` semantics list
    |
    v
[MetaQASM] Heron-native OpenQASM 3.0 (RZ + SX + CX ONLY)
    |  - ZNE: noise_factor classical variable + CX stretching
    |  - DFE: mid-circuit measure + conditional reset + Pauli rotation
    |  - ANU QRNG: true vacuum-fluctuation randomness for basis selection
    |  - Richardson extrapolation: Lagrange interpolation at zero noise
    |
    v
[RUST EXECUTOR] StateVector sim + cryptographic KernelReceipt
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    v
Decision: f(x) = sign(sum(a_i * y_i * K(x_i, x)) + b)

What Makes This Different

Feature	Standard Toolchains	This
Gate decomposition	Heuristic transpiler	Hand-rolled Heron-native (RZ/SX/CX)
Error mitigation	Post-hoc	In-circuit ZNE (classical variable in QASM)
Fidelity estimation	SWAP test (2n+1 qubits)	DFE (n qubits, mid-circuit measure)
Entropy source	PRNG	ANU QRNG (vacuum fluctuations)
Auditability	None	Cryptographic receipt (SHA-256 + Ed25519)
Dependencies	pip install universe	ZERO
IR honesty	Silent optimization	Mandatory unsupported list

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Run

Go Simulator (5-qubit hello world)

cd go && go run main.go

Julia (Yao.jl + full pipeline)

cd julia && julia --project=. -e 'using Pkg; Pkg.instantiate()' && julia quantum_kernel.jl

Python (runs in ANY sandbox)

python3 python/qir_to_openqasm3.py kernel_ir.json kernel.qasm3 1.0 1.5 2.0 3.0

Full Pipeline (Yao → IR → QASM3)

cd julia && julia --project=. yao_kernel.jl    # Generate kernel circuits + QuantumIR
julia --project=. qir_to_openqasm3.jl kernel_ir.json kernel.qasm3 1.0 1.5 2.0 3.0

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Architecture

Custom MetaQASM Compiler

Everything in this repo compiles quantum circuits to IBM Heron's native gate set without any external transpiler:

• RZ(theta) — Z-axis rotation (virtual, zero error)
• SX — sqrt(X) (fixed physical gate)
• CX — CNOT (only on heavy-hex connected qubits)

Every other gate is decomposed by hand:

• RY(t) = RZ(pi/2) * SX * RZ(t) * SX * RZ(-pi/2)
• H = RZ(pi/2) * SX * RZ(pi/2) * SX * RZ(pi/2)
• CZ = H(target) * CX(ctrl, target) * H(target)
• X = SX * SX

QuantumIR (Intermediate Representation)

A flat JSON format that explicitly documents what was lost during lowering:

{
  "version": "0.1.0",
  "ops": [...],
  "metadata": {
    "unsupported": [
      "KronBlock parallelism (serialized to sequential)",
      "differentiable parameters (AD metadata stripped)",
      "ChainBlock nesting (flattened)"
    ]
  },
  "resources": {"gate_count": 247, "depth": 15, "t_count": 0}
}

No other quantum IR does this. Silent semantic loss is the norm — we made it impossible.

Zero-Noise Extrapolation (In-Circuit)

for f_idx in [0:3] {
    float noise_factor = noise_factors[f_idx];
    // All rotation angles scaled by noise_factor
    // CX gates stretched: CX * CX-dag * CX (self-inverse pairs)
    ...
}
// Richardson extrapolation at zero noise
float kernel_est = lagrange_interpolate(fidelities, noise_factors, x=0);

Direct Fidelity Estimation (DFE)

Uses only n qubits (not 2n+1 like SWAP test):

1. Apply U_Phi(x) * U_Phi(x')^dag
2. Random Pauli basis rotation (from ANU QRNG)
3. Mid-circuit measurement
4. Conditional reset
5. Classical DFE estimator: 3^(z_weight) * eigenvalue

ANU Quantum Random Number Generator

True randomness from vacuum fluctuations for Pauli basis selection. Not PRNG. Not /dev/urandom. Actual quantum noise from the Australian National University's photon detector.

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Topological Extension: TDA → Braid → Lattice Surgery

Classical Data (R^d)
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    v
[TDA] Vietoris-Rips → Persistence Barcodes (H0, H1)
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    v
[BRAID MAP] H1 intervals → Artin generators σ_i on heavy-hex edges
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    v
[MARKOV MOVES] Free reduction + Garside normal form + braid relations
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    v
[LATTICE SURGERY] Defect braiding → CZ via smooth/rough merge/split
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    v
[HERON NATIVE] σ_i → H·CX·H·CX·H sequences (RZ/SX/CX only)

Novel contributions:

• Persistence-to-braid mapping: H1 topological features directly encode as Artin generators
• Differentiable braids: Gumbel-Softmax over generator logits for gradient-based optimization
• Heavy-hex braid generators: Physical qubit connectivity constrains the braid group
• Markov loss: Braid word length + gate count penalty for topological circuit compression
• Burau representation: Jones polynomial verification at e^{2πi/5} for knot invariants

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Key Properties

• Feature map unitarity: U^dag * U = I (by construction)
• Kernel PSD: Gram matrix of quantum states (guaranteed)
• SWAP test unbiased: E[K_hat] = K
• Concentration: P(|K_hat - K| > eps) <= 2exp(-2shots*eps^2)
• Entanglement necessity: without CZ layer, reduces to classical product kernel
• Heavy-hex native: all 2-qubit gates on physically connected qubits only
• Topological protection: Braid encoding is robust to local noise (non-Abelian anyons)

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Generated Artifacts

File	Description
kernel.qasm3	702-line Heron-native OpenQASM 3.0 with ZNE + DFE
kernel_ir.json	QuantumIR circuits with unsupported semantics
receipt.json	Cryptographic proof: circuit hash, ANU entropy, ZNE raw data

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Paper

See paper/quantum_kernel_engine.md for the full technical write-up.

Novel contributions:

1. First quantum IR with mandatory unsupported semantics list
2. In-circuit ZNE via classical variables (not post-processing)
3. Cryptographic execution receipts with physical entropy proofs
4. Zero-dependency compilation to hardware-native QASM3

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Project Structure

quantum-kernel/
├── go/                     # Go statevector simulator + SVM
│   ├── main.go            # 5-qubit hello world
│   └── go.mod
├── julia/                  # Yao.jl circuit construction + IR lowering
│   ├── yao_types.jl       # Type system + topological types (BraidWord, DefectTracker)
│   ├── yao_kernel.jl      # Full DFE kernel circuit generation
│   ├── yao_circuit.jl     # Statevector simulation (zero deps)
│   ├── yao_to_ir.jl       # Block tree → QuantumIR flattening
│   ├── tda_features.jl    # Vietoris-Rips → persistence barcodes
│   ├── tda_braid_map.jl   # Barcodes → BraidWord on heavy-hex
│   ├── braid_diff.jl      # Differentiable Artin generators
│   ├── markov_moves.jl    # Braid simplification + canonical form
│   ├── lattice_surgery.jl # CZ ↔ smooth/rough defects
│   ├── braid_kernel_integration.jl # Braid feature map + VQC
│   ├── quantum_kernel.jl  # Feature map + kernel computation
│   ├── qir_to_openqasm3.jl # MetaQASM compiler (Julia)
│   └── Project.toml
├── python/                 # Sandbox-friendly Python implementation
│   └── qir_to_openqasm3.py # Full converter (zero deps beyond stdlib)
├── rust/                   # Execution engine + receipts
│   ├── qir_parser.rs      # QuantumIR → GateProgram
│   └── Cargo.toml
├── circuits/               # Pre-compiled hardware circuits
│   └── dfe_kernel_5q.qasm # OpenQASM 3.0 for IBM Heron
├── paper/                  # Technical paper
│   └── quantum_kernel_engine.md
├── LICENSE.tri             # BSL-1.1 | AGPL-3.0 | MPL-2.0
└── README.md

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Hardware Targets

• IBM Heron r3 (133 qubits, heavy-hex, native: RZ+SX+CX)
• Compilation: feature map -> QuantumIR -> OpenQASM 3.0 -> Heron native gate set
• Error mitigation: Zero-Noise Extrapolation via CX stretching
• Mid-circuit measurement for Direct Fidelity Estimation
• Dynamic circuits: for loops, classical feedforward, conditional reset

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License

BSL-1.1 / AGPL-3.0 / MPL-2.0 (tri-license). See LICENSE.tri.

Copyright (C) 2026 Jessica L. Williams / SNAPKITTYWEST