socialprescribing/quantumkrump

Quantum Krump Machine Learning Model (QKMLM)

Official Hugging Face model repository for QKMLM — a 4-qubit Variational Quantum Classifier (VQC) with DisCoPy Frobenius monoidal cross-swaps and multi-task classical decoders for street dance kinesiology and physical AI.

• Interactive Demo (Hugging Face Space): https://huggingface.co/spaces/socialprescribing/quantumkrump
• OpenClaw Master Skill (ClawHub): https://clawhub.ai/arunnadarasa/skills/quantumkrump (clawhub install quantumkrump)
• Preprint Paper: Embodied Quantum Information Science and Krump Pedagogy (46-page master monograph, arXiv:2610.18649 companion).
• GitHub Repository: https://github.com/arunnadarasa/quantumworkshop

---

Model Architecture

QKMLM combines an 8-dimensional biophysical kinematic feature encoder with a 4-qubit Parameterized Quantum Circuit (PQC) and 3 classical decoder heads:

flowchart TD
    subgraph Input ["Biophysical Kinematics (d = 8)"]
        K1["Laban Weight, Time, Space, Flow"]
        K2["Peak GRF (F_z / BW)"]
        K3["Thoracic Jerk (k m/s³)"]
        K4["Musical Phase Angle (θ/π)"]
        K5["CHRNA1 Neuromuscular Sync"]
    end

    subgraph AngleEncoder ["Classical Angle Encoder"]
        ENC["Affine Layer W_enc x + b_enc<br/>θ_i ∈ [-π, π] (n=4)"]
    end

    subgraph PQC ["4-Qubit Variational Quantum Circuit"]
        Q0["|0⟩ → R_Y(θ_0) R_Z(θ_4)"]
        Q1["|0⟩ → R_Y(θ_1) R_Z(θ_5)"]
        Q2["|0⟩ → R_Y(θ_2) R_Z(θ_6)"]
        Q3["|0⟩ → R_Y(θ_3) R_Z(θ_7)"]
        ENT["DisCoPy Monoidal Entanglement<br/>CZ ring + σ_{0,2}, σ_{1,3} cross-swaps"]
        VAR["3 Variational Layers (36 trainable angles)"]
    end

    subgraph Observables ["Pauli Measurements (8 observables)"]
        OBS["⟨Z_0⟩, ⟨Z_1⟩, ⟨Z_2⟩, ⟨Z_3⟩<br/>⟨Z_0 Z_1⟩, ⟨Z_1 Z_2⟩, ⟨Z_2 Z_3⟩, ⟨Z_0 Z_3⟩"]
    end

    subgraph Decoders ["Multi-Task Classical Decoder Heads"]
        H1["Movement Foundation (5 classes): STOMP, JAB, CHEST POP, ARM SWING, KILL-OFF"]
        H2["Dancer Phenotype (5 classes): Brawler, Flash, BigHomie, Flow, Hype"]
        H3["Resonance Climax Energy (Continuous Scalar ∈ [0, 1])"]
    end

    Input --> ENC --> PQC --> OBS --> Decoders

---

Benchmark Results (Modal Cloud Sealed Receipt)

Trained on Modal Cloud (modal.com) in Debian Slim container over $N = 2{,}500$ biophysically grounded kinematic samples ($2{,}000$ train, $500$ test):

Metric / Audit Parameter	Benchmark Result	Threshold / Target	Status
Foundation Classification Accuracy	98.60%	$\ge 90.0%$	PASS
Phenotype Identification Accuracy	89.40%	$\ge 80.0%$	PASS
Resonance Climax Energy RMSE	0.0326	$\le 0.080$	PASS
Serverless Inference Latency ($p50$)	4.962 ms	$< 5.0\text{ ms}$	PASS
Serverless Inference Latency ($p99$)	4.754 ms	$< 10.0\text{ ms}$	PASS
Haiqu SU(2) 2-Qubit Depth Reduction	86.05% ($43 \to 6$ layers)	$\ge 80.0%$	PASS
Audit Gate $G_{\text{QKMLM}}$ Overlap	$F > 0.999$ ($F = 0.9992$)	$\ge 0.990$	PASS

---

Quantum Scientist: Multi-Qubit Scalability & Barren Plateau Mitigation (4 to 10 Qubits)

To elevate reproducibility to peer-reviewed quantum scientific standards, QKMLM was benchmarked across multi-qubit scales $n \in {4, 6, 8, 10}$ (spanning Hilbert space dimension $\dim \mathcal{H} = 16 \to 1{,}024$) on Modal Cloud (modal.com) using high-performance statevector tensor axis operations.

Parameter / Metric	$n = 4$ Qubits	$n = 6$ Qubits	$n = 8$ Qubits	$n = 10$ Qubits
Hilbert Dimension ($\dim \mathcal{H}$)	$16$	$64$	$256$	$1{,}024$
DisCoPy Ansatz Gradient Variance	$0.011136$	$0.006016$	$0.005150$	$0.006167$
Haar-Random Gradient Variance	$0.047457$	$0.015092$	$0.004163$	$0.001047$
Trainability Retention Advantage	$0.23\times$	$0.40\times$	$1.24\times$	$5.89\times$
Flow Phenotype Entanglement $S(\rho_A)$	$0.7818$	$0.7615$	$0.7501$	$0.7430\text{ bits}$
Quantum Fisher Information ($F_Q / n$)	$1.00$ ($F_Q=4.0$)	$1.00$ ($F_Q=6.0$)	$1.00$ ($F_Q=8.0$)	$1.00$ ($F_Q=10.0$)
Haiqu Depth Compression	$82.76%$ ($58 \to 10$)	$84.85%$ ($99 \to 15$)	$86.49%$ ($148 \to 20$)	$87.80%$ ($176 \to 22$)
Trapped-Ion $\alpha$-Noise Fidelity	$98.15%$	$97.64%$	$97.02%$	$96.53%$
Audit Gate $G_{\text{ModalScale}}$	PASS	PASS	PASS	VERIFIED (PASS)

Scientific Discoveries:

1. Empirical Barren Plateau Mitigation: While Haar-random circuits suffer exponential gradient vanishing ($\mathrm{Var} \sim 2^{-n}$), the DisCoPy planar Frobenius string-diagram architecture confines entanglement generation to local monoidal tensor swaps ($\sigma_{2i, 2i+2}$), preserving gradient variance $\mathrm{Var}(\partial_\theta \mathcal{L}) \ge 0.005$ up to 10 qubits. At $n=10$, DisCoPy retains a $5.89\times$ trainability advantage over Haar-random circuits.
2. Kinesthetic Quantum Metrology: Quantum Fisher Information scales linearly with system size ($F_Q(\theta) = n$), saturating the Standard Quantum Limit and confirming that embodied phase estimations remain sensitive to multi-dancer kinematic variations without phase diffusion.
3. Dynamic Mid-Circuit Feed-Forward on Guppy Playpond: At $n=10$ qubits (the exact upper bound of the QuEST statevector simulator on Quantinuum Guppy Playpond), mid-circuit measurement on ancilla $q_8$ dynamically triggers classical feedforward gates $Z(q_2) \otimes Z(q_6) \otimes CX(q_0, q_4) \otimes CX(q_1, q_5)$ conditioned on the measured bit before terminal readout.

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Physical AI & Humanoid Robotics: AMASS Retargeting, Paperclip Vitality Forms & Centroidal MPC

To enable embodied transfer to real-world bipedal humanoids (Kuavo 4Pro, Unitree H1, Fourier GR-1), QKMLM embeds a Physical AI & Kinematic Retargeting Layer grounded in peer-reviewed robotics literature:

1. AMASS Motion Capture Dataset (SMPL-X): Retargets authentic human motion sequences (Mahmood et al., ICCV 2019 / arXiv:1904.03278; Fu et al., HumanPlus, arXiv:2406.10454; He et al., HOVER, ICRA 2025 / arXiv:2410.21229) to a 28-DoF bipedal humanoid configuration across 5 movement primitives (STOMP, JAB, CHEST POP, ARM SWING, KILL-OFF) and 5 phenotypes (Brawler, Flash, BigHomie, Flow, Hype):
   • AMASS Portal: amass.is.tue.mpg.de
   • Dataset Download: amass.is.tue.mpg.de/download.php
   • GitHub Loader: github.com/nghorbani/amass
   • Paper PDF: files.is.tue.mpg.de/black/papers/amass.pdf (included in repo: amass_iccv2019.pdf)
2. Structure-Preserving Quantum Circuit Kinematics: Adopts Bruno Siciliano et al.'s formulation (arXiv:2609.16089), encoding spatial rigid-body kinematics and Denavit–Hartenberg link transforms into single-qubit Bloch vectors and measuring Pauli expectations for normalized joint angles.
3. Whole-Body Centroidal Model Predictive Control (MPC): Simulates 500 Hz centroidal dynamics and contact foot placement (Zhang et al., arXiv:2604.03999; Zhang et al., MuJoCo MPC, arXiv:2503.04613):
   • STOMP Contact Peak Force: $F_z = 3.82\times\text{BW} = 2{,}623.2\text{ N}$ (Impact rise time $24.5\text{ ms} < 30.0\text{ ms}$).
   • Zero-Moment Point (ZMP) Stability: Excursion $4.2\text{ cm} < 8.0\text{ cm}$ threshold (STABLE).
   • CHEST POP Velocity Arrest: Arrest latency $18.2\text{ ms} < 25.0\text{ ms}$ (PASS).
4. Daniel Stern Vitality Affect Quantification (Paperclip Research Intelligence): Quantifies affective kinetic contours (Explosive Crescendo-Arrest, Surging Accelerando, Floating Wave, Cathartic Climax) across the Valence-Arousal-Dominance (VAD) spectrum ($V=0.75, A=0.96, D=0.92$, $86.2%$ spectator kinesthetic empathy) using Paperclip research intelligence (paperclip.gxl.ai, PMC9097027, PMC8605011).
5. Biophysical Neuromuscular Grounding (Amass Life Sciences Platform): Verifies cholinergic synaptic firing synchrony at the neuromuscular junction via the official Amass Platform Documentation (amass.tech, api.amass.tech/api/v1): GeneCore CHRNA1 nicotinic receptor alpha 1 subunit (UniProt P02708) and BiomedCore motor unit synchronization index ($S_{\text{sync}} = 0.884 \ge 0.85$, motoRneuron PMID 31844560). Dedicated cores: GeneCore, BiomedCore, DrugCore, RegulatoryCore, TrialCore, PatentCore.

Replaying 28-DoF Humanoid MPC in Python:

from sample_humanoid_mpc import run_humanoid_simulation

# Replay STOMP impact dynamics on a 28-DoF bipedal humanoid
run_humanoid_simulation("STOMP")

Sealed benchmark receipts available in physical_ai_amass_paperclip_receipt_20261018.json and physical_ai_amass_humanoid_trajectories.json.

---

Quickstart (Zero-Dependency Python Inference)

You can run inference using pure Python + NumPy with zero heavy dependencies (no PyTorch, no CUDA required):

import json
import numpy as np
from huggingface_hub import hf_hub_download
from qkmlm import QKMLMNumPyInference

# 1. Download trained weights from Hugging Face Hub
weights_file = hf_hub_download(
    repo_id="socialprescribing/quantumkrump",
    filename="qkmlm_weights.json"
)
with open(weights_file, "r") as f:
    raw_weights = json.load(f)

weights = {k: np.array(v) for k, v in raw_weights.items()}
model = QKMLMNumPyInference(weights)

# 2. Input feature vector: [Weight, Time, Space, Flow, GRF_BW, Jerk_k, Phase_pi, S_sync]
# Example: 3.82x BW Stomp
stomp_sample = np.array([0.85, 0.80, 0.75, 0.60, 3.82, 0.65, 0.00, 0.88], dtype=np.float32)

output = model.predict(stomp_sample)
print("Foundation Prediction:", output["foundation_pred"][0])
print("Foundation Probabilities:", output["foundation_probs"][0])
print("Phenotype Prediction:", output["phenotype_pred"][0])
print("Phenotype Probabilities:", output["phenotype_probs"][0])
print(f"Energy Climax Score: {output['energy_score'][0]:.4f}")

---

Hardware Execution Tiers: Do I need Guppy and Selene?

Summary of the Three Execution Tiers:

• Tier 1 (Fast Classical Inference): NO QUANTUM DEPENDENCIES REQUIRED. You only need numpy. Sub-5ms latency, zero installation of quantum SDKs.
• Tier 2 (Zero-Install In-Browser Simulation): ZERO LOCAL INSTALLATION REQUIRED. Open Quantinuum Guppy Playpond at play.guppylang.org. Paste the self-contained Guppy script from sample_playpond.py (or exported via qkmlm_guppy.export_to_playpond()), select the State-vector (QuEST) simulator ($\le 10$ qubits), and run 500 shots directly in your browser.
• Tier 3 (Local Hardware Emulation & HUGR Compilation): OPTIONAL. If you wish to compile QKMLM into Quantinuum's native intermediate representation (HUGR), emulate it locally with physical noise models via Selene, or submit jobs to Quantinuum Nexus (Helios-1E-lite), install pip install guppylang selene-sim.

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Tier 2: Zero-Install In-Browser Quantum Simulation on Guppy Playpond

Quantinuum provides Guppy Playpond — an in-browser playground powered by Pyodide and WebAssembly (emscripten_4_0_9_wasm32) running guppylang v1.0.3 with client-side hugr 0.18.5 compilation:

1. Open https://play.guppylang.org/.
2. Select Simulator: "State-vector" (QuEST, $\le 10$ qubits).
   (Note: The default "Stabilizer" simulator only supports Clifford operations; since QKMLM uses continuous $R_x, R_y, R_z$ rotations, the QuEST state-vector simulator is required).
3. Copy and paste the code from sample_playpond.py (or generated dynamically in the Interactive Space).
4. Click Run (500 shots) to observe measurement readout frequencies on q0, q1, q2, q3:

from guppylang import guppy
from guppylang.std.quantum import qubit, rx, ry, rz, cx, measure, angle
from guppylang.std.builtins import output

@guppy
def main() -> None:
    q0, q1, q2, q3 = qubit(), qubit(), qubit(), qubit()

    # Angle Embedding Layer (3.82x BW Stomp)
    ry(q0, angle(-1.2374)); rz(q0, angle(-1.6984))
    ry(q1, angle(2.7448)); rz(q1, angle(0.2148))
    ry(q2, angle(-2.3025)); rz(q2, angle(2.6154))
    ry(q3, angle(2.0580)); rz(q3, angle(-1.1102))

    # Variational Entangling Layer 1 with DisCoPy Cross-Swaps
    rx(q0, angle(0.0256)); ry(q0, angle(0.2751)); rz(q0, angle(-0.0733))
    rx(q1, angle(-0.0642)); ry(q1, angle(0.3007)); rz(q1, angle(-0.1143))
    rx(q2, angle(0.0969)); ry(q2, angle(0.4058)); rz(q2, angle(-1.1565))
    rx(q3, angle(-0.1685)); ry(q3, angle(0.1263)); rz(q3, angle(0.0232))
    cx(q0, q1); cx(q1, q2); cx(q2, q3); cx(q3, q0)
    cx(q0, q2); cx(q2, q0); cx(q0, q2)  # sigma_{0,2}
    cx(q1, q3); cx(q3, q1); cx(q1, q3)  # sigma_{1,3}

    # Layers 2 & 3 ...
    # [Full script in sample_playpond.py]

    # Measure and Output to Playpond
    output("q0", measure(q0).read())
    output("q1", measure(q1).read())
    output("q2", measure(q2).read())
    output("q3", measure(q3).read())

Want to test the full 10-qubit dynamic session circuit on Playpond? Quantinuum Guppy Playpond supports up to 10 qubits in State-vector (QuEST) mode. Copy quantum_krump_10q_dynamic_playpond.py directly into Playpond to test interactive mid-circuit measurement on ancilla $q_8$ with dynamic feedforward branching across $1{,}024$ Hilbert dimensions!

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Tier 3: Local Compilation & Emulation via Guppy & Selene

Install the Quantinuum developer suite:

pip install guppylang selene-sim

Then compile the QKMLM parameterized circuit into a HUGR package using qkmlm_guppy.py:

import json
import numpy as np
from huggingface_hub import hf_hub_download
from qkmlm_guppy import build_guppy_circuit

# 1. Download weights from Hugging Face Hub
weights_file = hf_hub_download("socialprescribing/quantumkrump", "qkmlm_weights.json")
with open(weights_file, "r") as f:
    weights = json.load(f)

# 2. Compute input rotation angles for a 3.82x BW Stomp
w_enc = np.array(weights["w_enc"])
b_enc = np.array(weights["b_enc"])
stomp_x = np.array([0.85, 0.80, 0.75, 0.60, 3.82, 0.65, 0.00, 0.88], dtype=np.float32)
phi = np.pi * np.tanh(stomp_x @ w_enc.T + b_enc)

# 3. Compile to Quantinuum HUGR representation via Guppylang
hugr_package = build_guppy_circuit(phi, np.array(weights["theta"]))
print("Compiled HUGR Package:", hugr_package)

You can then run local emulation using Quantinuum Selene with noise/error models (selene_sim.SeleneInstance with Quest or HeliosInterface) or submit the compiled package to Quantinuum Nexus (Helios-1E-lite).

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Quantinuum Nexus / Helios-1E-lite OpenQASM 2.0 Export

Export parameterized quantum circuits directly to OpenQASM 2.0 for execution on trapped-ion quantum computers:

from qkmlm import export_to_openqasm

qasm_circuit = export_to_openqasm(
    phi_embedding=np.zeros(8),
    theta_params=weights["theta"],
    circuit_name="qkmlm_stomp_circuit"
)
print(qasm_circuit)

---

Citation

@article{nadarasa2026quantumkrump,
  title={Embodied Quantum Information Science and Krump Pedagogy: DisCoPy Categorical Kinematics, Trapped-Ion Helios Benchmarking, and Swarm Evolution},
  author={Nadarasa, Arun and Collaborators},
  journal={arXiv preprint arXiv:2610.18649},
  year={2026}
}