QuBiS-HiQ: Physics-Informed Quantum Feature Extraction for DNA Thermodynamics

Primary Result

Method	Features	LOO R²	95% CI	MAE (°C)	Notes
Quantum + Classical combined	38-d	0.941	[0.907, 0.965]	0.41	Best overall
Classical physics-informed	17-d	0.935	[0.894, 0.962]	0.43	Beats quantum alone
Quantum variable-region	21-d	0.911	[0.857, 0.937]	0.53	This work (primary)
Quantum full circuit	111-d	0.719	-	1.00	Overfits scaffold

Summary: Classical physics-informed features (17-d, R²=0.935) outperform quantum features alone (21-d, R²=0.911). Quantum features provide complementary information; the combined 38-d model (R²=0.941) yields the best result. The primary contribution is a physics-informed quantum feature extractor that complements, not replaces, classical thermodynamic models.

Overview

QuBiS-HiQ is a physics-informed quantum circuit that encodes SantaLucia nearest-neighbour DNA thermodynamic parameters into gate angles and extracts feature vectors via Pauli-Z expectation values. The circuit is validated on 65,536 synthetic 8-mers (Exp 1A), a five-way ablation study (Exp 1B), structural classification of 176 sequence pairs (Exp 1C), real IBM quantum hardware across two processors (Exp 1D), and 64 experimental melting temperatures from Oliveira et al. 2020 (Exp 1E), achieving R²=0.88, r=0.94, and MAE=0.60°C on Exp 1E alone. The combined quantum+classical model achieves R²=0.941, MAE=0.41°C.

Circuit design (v2): Each nucleotide is encoded onto two qubits via Ry rotations calibrated to SantaLucia free energies. Adjacent qubits are entangled with CX+Ry(θ) gates where θ=π·σ(−β·ΔG°), β=0.39 mol/kcal. Z-basis measurements yield ⟨Z⟩, ⟨ZZ⟩_NN, and ⟨ZZ⟩_NNN correlators as features (B=6N−3 base dimensions, plus ViennaRNA stem-pair correlators).

Figure 1: Overview of the QuBiS-HiQ computational pipeline. Input DNA sequences are processed via ViennaRNA, encoded into the QuBiS-HiQ circuit, simulated on HPC or executed on IBM hardware, and Z-basis measurements are extracted as physics-interpretable feature vectors for downstream machine learning.

Limitations & Scope

Classical comparison: A physics-informed classical baseline (17-d variable-region features) achieves R²=0.935, outperforming the quantum circuit alone (R²=0.911) by 2.4 percentage points. The quantum advantage claim is relative to restricted product-state classical models, not the full physics-informed classical approach. See Exp D2 and Exp D4.

Entanglement contribution: Ablation studies (Exp D3) show that when features are restricted to the variable-region qubits, all non-random circuit variants achieve nearly identical performance (R²=0.90–0.91). The stacking-angle encoding (Boltzmann-sigmoid ΔG°) is the primary signal source; entanglement contributes marginally for variable-region Tm prediction.

Hardware validation scope: IBM hardware tests (Exp 1D) used n=30 sequences and measured cosine similarity between hardware and simulator outputs, not prediction R². Results demonstrate circuit implementation fidelity rather than end-to-end quantum advantage on the full dataset.

Numerical verifications: The proofs/ scripts numerically verify mathematical claims via exhaustive enumeration and statevector simulation (ε < 10⁻¹⁵). They are computational verifications, not formal proof-assistant artifacts (Coq, Isabelle, Lean).

Dataset size: Exp 1E uses n=64 sequences from a single scaffolded library. Generalisation to arbitrary sequences or other experimental conditions requires further validation.

Comparison: Physics-Informed Classical vs Quantum

A common pitfall in quantum ML is comparing quantum circuits against uninformed classical models. Both should use the same physics knowledge for a fair test.

Our approach:

Quantum circuit: Encodes SantaLucia ΔG° in rotation angles, extracts ⟨ZZ⟩ correlators
Classical twin: Uses the same SantaLucia ΔG° as explicit features (17-d vector: GC fraction, boundary ΔG° steps, one-hot NNN centre)

Result on Oliveira 2020 Tm prediction (LOO-CV Ridge, n=64):

Model	R²	MAE
Classical physics-informed (17-d)	0.935	0.43°C
Quantum variable-region (21-d)	0.911	0.53°C
Combined (38-d)	0.941	0.41°C

Interpretation: The predictive signal resides primarily in the SantaLucia parameterisation itself. Quantum features add complementary non-linear correlations (+0.006 R²) that classical features cannot represent. The combined model is the state-of-the-art result for this dataset.

Repository Structure

QuBiS-HiQ/
├── qubis_hiq/              # Core library
│   ├── santalucia.py       # SantaLucia NN parameters + Boltzmann-sigmoid mapping (β=0.39)
│   ├── encoding.py         # Layer 1: deterministic Ry nucleotide encoding
│   ├── watson_crick.py     # Layer 2: CRZ Watson-Crick complementarity gates
│   ├── stacking.py         # Layer 3: CX+Ry nearest-neighbour stacking gates
│   ├── trainable.py        # Layer 4: shared trainable local rotations
│   ├── circuit_builder.py  # Full 6-layer circuit assembly + ablation variants
│   ├── feature_extraction.py  # ⟨Z⟩, ⟨ZZ⟩_NN, ⟨ZZ⟩_NNN correlator extraction
│   ├── vienna_interface.py # ViennaRNA wrapper + palindromic heuristic fallback
│   ├── classical_twin.py   # Classical SantaLucia feature vectors (D2 baseline)
│   ├── interference.py     # Quantum interference analysis utilities
│   └── topology_gated.py   # Topology-aware WC layer gating
├── experiments/            # Reproducible experiment scripts (Exp 1A-1E, D1-D4, X1-X2)
├── proofs/                 # Numerical verification scripts (Propositions 1–3)
│                           # NOTE: Computational verifications via statevector simulation
│                           # (ε < 10⁻¹⁵). NOT formal proof-assistant artifacts.
├── tests/                  # Test suite (32 tests covering core functionality)
├── .github/workflows/      # CI/CD pipeline (GitHub Actions)
├── data/                   # Oliveira 2020 dataset + SantaLucia parameters
├── results/                # Pre-computed JSON result files for all experiments
├── requirements.txt        # Minimum version requirements
├── requirements-pinned.txt # Pinned dependencies for exact reproducibility
└── setup.py                # Python package setup

Installation

Standard Installation

pip install -r requirements.txt

Reproducible Installation (Pinned Dependencies)

pip install -r requirements-pinned.txt

Development Installation

pip install -e .
pip install -r requirements-pinned.txt

ViennaRNA (Exp 1C only):

conda install -c bioconda viennarna

Requirements: Python ≥ 3.10, Qiskit ≥ 2.3, Qiskit-Aer ≥ 0.15. IBM Quantum account required only for Exp 1D hardware runs.

Running Tests

python tests/run_tests.py        # Run all tests
python tests/run_tests.py -v     # Verbose output
pytest tests/                    # Or use pytest

Test Coverage:

test_circuit_builder.py - Circuit building and API correctness
test_encoding.py - Nucleotide encoding verification
test_propositions.py - Mathematical proposition verification

Reproducing All Experiments

Exp 1A - ΔG° Regression (65,536 8-mers)

python experiments/exp1a_parallel.py --n-seqs 65536 --n-cpus 64
# Expected: CV R² = 0.764 ± 0.055 (full-data R² = 0.868, MAE = 0.626 kcal/mol)
# Feature dim: 47d (base 6N−3=45 + up to 2 ViennaRNA stem-pair correlators, zero-padded)

Exp 1B - Five-Way Ablation (500 sequences)

python experiments/exp1b_parallel.py --n-seqs 500

Results with 95% confidence intervals (KFold-5, Ridge α=1.0, n=500):

Variant	CV R²	95% CI	Notes
Full circuit	0.813	[0.758, 0.868]	All layers active
No Watson-Crick	0.822	[0.779, 0.864]	Removes CRZ layer
No Stacking	0.833	[0.790, 0.875]	Removes CX+Ry
Classical	0.835	[0.793, 0.876]	SantaLucia features
Random angles	−0.147	[−0.234, −0.060]	Physics is essential

Statistical note: Full circuit vs encoding-only ΔR²≈0.007 is not statistically significant on 500 sequences. The critical result is random angles → R²=−0.147: a 0.96-unit collapse confirming the SantaLucia angle schedule, not arbitrary entanglement, drives performance.

Exp 1C - Structural Classification (176 pairs)

python experiments/exp1c_parallel.py
python experiments/analyze_exp1c.py
# Expected: 100% ± 0.0% accuracy (SVM-RBF, SVM-Linear, RF-100)
# Labels: structured = ViennaRNA MFE hairpin (has_structure()=True); NOT arbitrary seq1/seq2

Exp 1D - IBM Hardware Validation (Circuit Fidelity)

# Requires IBM Quantum Plan access
python experiments/exp1d_hardware.py   # ibm_fez    (Heron r2) - 30 seqs, 4096 shots
python experiments/exp1d_torino.py     # ibm_torino (Heron r1) - 30 seqs
python experiments/exp1d_12mer.py      # 12-mer, 24 qubits, DD-XY4 + twirling

Scope: These experiments measure circuit implementation fidelity - cosine similarity between hardware and noiseless simulator outputs. They confirm the circuit runs correctly on real QPUs. Prediction R² was evaluated on the simulator due to hardware shot-noise constraints.

Backend	n seqs	Shots	Cosine similarity	Metric
ibm_fez (Heron r2)	30	4096	0.9970 ± 0.0005	Fidelity
ibm_torino (Heron r1)	30	4096	0.9948 ± 0.0015	Fidelity
12-mer + DD-XY4	30	4096	0.9926 ± 0.0013	Fidelity

Exp 1E - Experimental Tm Validation (Oliveira 2020)

python experiments/exp1e_corrected.py
# Expected: R² = 0.88, r = 0.94, p = 2.67×10⁻³⁰, MAE = 0.60°C
# Dataset:  64 canonical DNA duplexes (4³ NNN centre combinations)
# Scaffold: 5'-CGACGTGC[NNN]ATGTGCTG-3' (19 nt, Oliveira 2020, p. 8275)
# Buffer:   50 mM NaCl, 10 mM sodium phosphate, pH 7.4, 1.0 µM total strand
# Circuit:  38 qubits, MPS simulation (statevector requires ~1 PB RAM)
# β:        0.39 mol/kcal (empirical scale, consistent across all experiments)

Classical ML Baseline

python experiments/classical_baseline.py
# Expected: SVR-RBF Rich (78-d) R² ≈ 0.993, SVR-RBF Minimal (31-d) R² ≈ 0.995
# Note: "Quantum: 47d" in this script (47 = 6N−3 + 2 stem-pair correlators)

Numerical Verification Scripts

python proofs/proposition1.py   # Encoding–Mutation Isomorphism (17 assertions, ε < 3.4×10⁻¹⁶)
python proofs/proposition2.py   # Boltzmann–Sigmoid Uniqueness (4 axioms)
python proofs/proposition3.py   # ⟨ZaZb⟩ interferometric formula (max error 3.3×10⁻¹⁶)

Quantum Kernel Diagnostic Experiments

Exp D1 - Kernel Condition Number Analysis

python experiments/kernel_condition_analysis.py

Kernel	n	κ	Assessment
Exact quantum kernel (8-mer statevector)	50	23	Well-conditioned
Feature-vector linear kernel (Oliveira 19-nt, MPS)	64	1.6×10⁷	Regularise

The 8-mer quantum kernel is full-rank and well-conditioned (all 50 eigenvalues positive). The Oliveira 19-nt kernel is poorly conditioned (κ=1.6×10⁷), confirming that Ridge regularisation is essential for Exp 1E - the LOO-CV Ridge protocol is the correct approach.

Exp D2 - Physics-Informed Classical Baseline

python experiments/classical_physics_baseline.py

LOO-CV Ridge on 64 Oliveira sequences (same protocol as Exp 1E):

Method	Features	LOO R²	MAE
Total ΔG° only	1-d	0.841	0.74°C
Per-step ΔG°	18-d	0.876	0.65°C
Variable-region features	17-d	0.935	0.43°C
Rich physics	41-d	0.929	0.46°C
QuBiS-HiQ quantum (variable region, no-WC)	21-d	0.911	0.53°C
QuBiS-HiQ quantum (full features)	111-d	0.719	1.00°C

Key finding: The 17-d classical variable-region vector (GC count + boundary ΔG° steps + one-hot NNN centre) achieves R²=0.935, exceeding quantum-alone (R²=0.911). The predictive signal resides primarily in the physics encoding, not in quantum interference.

Exp D3 - Entanglement Ablation Study

python experiments/entanglement_ablation.py

Variable-region 21-d features (primary analysis):

Circuit Variant	LOO R²	ΔR² vs full	p-value
Full (Enc + WC + Stack)	0.902	-	-
No Watson-Crick	0.912	+0.009	n.s.
No Stacking	0.910	+0.008	n.s.
Encoding only (no entanglement)	0.909	+0.007	n.s.
Random-angle CX	−0.194	−1.097	< 0.001

Full 111-d features:

Circuit Variant	LOO R²	ΔR² vs full
Full (Enc + WC + Stack)	0.776	-
No Watson-Crick	0.853	+0.077
Encoding only (no entanglement)	0.561	−0.214
Random-angle CX	−0.315	−1.090

Key findings:

For variable-region features, all non-random variants achieve R²=0.90–0.91. Entanglement differences are within noise (p = n.s.).
Random-angle CX collapses to R²=−0.19 - the Boltzmann-sigmoid angle schedule is essential, not arbitrary entanglement.
Removing the WC layer improves full-feature performance (+0.077 R²) for linear duplexes - ViennaRNA hairpin predictions add noise here. Use skip_wc=True for linear duplex tasks.

Exp D4 - Best Configuration Synthesis

python experiments/best_configuration.py

Configuration	LOO R²	r	MAE
Quantum var-region (no-WC, 21-d)	0.911	0.955	0.53°C
Classical var-region (17-d)	0.935	0.968	0.43°C
Quantum + Classical combined (38-d)	0.941	0.970	0.41°C
Quantum full features (no-WC, 111-d)	0.750	0.870	0.88°C
Kernel Ridge (linear kernel, no-WC)	0.895	0.946	0.58°C

The combined 38-d model yields the best result (+0.006 R² over the classical alone model). Quantum features encode complementary correlations not captured by the 17-dimensional classical vector, yielding a synergistic gain when fused. This supports QuBiS-HiQ as a physics-informed feature extractor that complements classical thermodynamic models.

Exp X1 - Watson-Crick Topology Validation

python experiments/x1_topology_validation.py

ViennaRNA predicts secondary structure for only 58/65,536 (0.1%) of random 8-mers. The WC layer has a negligible impact on ΔG° prediction regardless of topology (|ΔR²| < 0.012, within standard deviation) - physically correct, since ΔG° is determined by stacking, not intramolecular base-pairing.

Subset	n	Full R²	No-WC R²	ΔR²	Verdict
Hairpin-classified	58	0.878 ± 0.044	0.889 ± 0.057	+0.011	Neutral
Linear	58	0.504 ± 0.125	0.512 ± 0.107	+0.008	Neutral
All combined	116	0.669 ± 0.192	0.670 ± 0.218	+0.002	Neutral

Exp X2 - Stacking-Only Benchmarks with Bootstrap CIs

python experiments/x2_stacking_only_benchmark.py

Configuration	LOO R²	95% CI	r	MAE
Quantum full (no-WC, 111-d)	0.840	[0.770, 0.885]	0.917	0.71°C
Quantum var-region (no-WC, 21-d)	0.904	[0.857, 0.937]	0.951	0.56°C
Classical var-region (17-d)	0.935	[0.894, 0.962]	0.968	0.43°C
Combined quantum+classical (38-d)	0.941	[0.907, 0.965]	0.970	0.40°C
KRR linear kernel (no-WC)	0.893	[0.841, 0.928]	0.945	0.59°C

Headline result: Combined 38-d, LOO R²=0.941 [0.907, 0.965], r=0.970, p=8.8×10⁻⁴⁰, MAE=0.40°C.

Key Results Summary

Experiment	Metric	Value
Exp 1A - ΔG° regression (65,536 8-mers)	CV R²	0.764 ± 0.055
Exp 1B - Ablation: full vs random	R² drop	0.813 → −0.147
Exp 1C - Structural classification (n=352)	Accuracy	100% ± 0.0%
Exp 1D - ibm_fez hardware (n=30, 4096 shots)	Cosine similarity	0.9970 ± 0.0005
Exp 1D - ibm_torino cross-platform	Cosine similarity	0.9948 ± 0.0015
Exp 1E - Oliveira 2020 Tm, quantum only	R² / r / MAE	0.88 / 0.94 / 0.60°C
D1 - Kernel condition (8-mer, n=50)	κ	23 (well-conditioned)
D1 - Kernel condition (Oliveira, n=64)	κ	1.6×10⁷ (regularise)
D2 - Best classical baseline	LOO R²	0.935 (17-d physics features)
D3 - Entanglement (variable-region)	ΔR²	<0.01 vs encoding-only (n.s.)
D3 - WC layer on linear duplexes	Effect	+0.077 R² to remove it
D4 - Best overall (quantum+classical)	LOO R²	0.941 [0.907, 0.965]
X1 - WC layer on 8-mer hairpins	ΔR²	≈0 (neutral)
X2 - Stacking-only + bootstrap CI	LOO R² / CI	0.941 [0.907, 0.965]

Data Sources

Oliveira et al. 2020: Chem. Sci. 11, 8273–8287. DOI: 10.1039/d0sc01700k (Open Access, CC-BY)
SantaLucia & Hicks 2004: Annu. Rev. Biophys. Biomol. Struct. 33, 415–440

Hardware

System	Device	Qubits	Job ID
ibm_fez	Heron r2	156	`d6qe32i0q0ls73cs7ah0`
ibm_torino	Heron r1	133	`d6qeljropkic73fhv7rg`
ibm_fez (12-mer baseline)	Heron r2	24	`d6qeh8nr88ds73dca350`
ibm_fez (12-mer mitigated)	Heron r2	24	`d6qehkbopkic73fhv1o0`

License

Academic and Open-Source Use: QuBiS-HiQ is released under the GNU General Public License v3.0 (GPLv3). This allows researchers to freely use, modify, and distribute the code under the condition that derivative works are also open-sourced under GPLv3 terms. See LICENSE for full details.

Commercial Licensing: If you represent a commercial entity and wish to integrate QuBiS-HiQ into proprietary, closed-source products without the copyleft obligations of GPLv3, a separate Commercial License is required.

Contact & Enquiries

Type	Details
Scientific enquiries	Open a GitHub Issue
Other	ahmedaneesm@gmail.com

Bugs, reproducibility issues, and questions about the methodology are welcome via GitHub Issues.

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QuBiS-HiQ: Physics-Informed Quantum Feature Extraction for DNA Thermodynamics

Primary Result

Overview

Limitations & Scope

Comparison: Physics-Informed Classical vs Quantum

Repository Structure

Installation

Standard Installation

Reproducible Installation (Pinned Dependencies)

Development Installation

Running Tests

Reproducing All Experiments

Exp 1A - ΔG° Regression (65,536 8-mers)

Exp 1B - Five-Way Ablation (500 sequences)

Exp 1C - Structural Classification (176 pairs)

Exp 1D - IBM Hardware Validation (Circuit Fidelity)

Exp 1E - Experimental Tm Validation (Oliveira 2020)

Classical ML Baseline

Numerical Verification Scripts

Quantum Kernel Diagnostic Experiments

Exp D1 - Kernel Condition Number Analysis

Exp D2 - Physics-Informed Classical Baseline

Exp D3 - Entanglement Ablation Study

Exp D4 - Best Configuration Synthesis

Exp X1 - Watson-Crick Topology Validation

Exp X2 - Stacking-Only Benchmarks with Bootstrap CIs

Key Results Summary

Data Sources

Hardware

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data		data
experiments		experiments
proofs		proofs
qubis_hiq		qubis_hiq
results		results
scripts		scripts
tests		tests
.gitignore		.gitignore
LICENSE		LICENSE
README.md		README.md
pipeline_architecture.png		pipeline_architecture.png
requirements-pinned.txt		requirements-pinned.txt
requirements.txt		requirements.txt
setup.py		setup.py
validate_json.py		validate_json.py

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QuBiS-HiQ: Physics-Informed Quantum Feature Extraction for DNA Thermodynamics

Primary Result

Overview

Limitations & Scope

Comparison: Physics-Informed Classical vs Quantum

Repository Structure

Installation

Standard Installation

Reproducible Installation (Pinned Dependencies)

Development Installation

Running Tests

Reproducing All Experiments

Exp 1A - ΔG° Regression (65,536 8-mers)

Exp 1B - Five-Way Ablation (500 sequences)

Exp 1C - Structural Classification (176 pairs)

Exp 1D - IBM Hardware Validation (Circuit Fidelity)

Exp 1E - Experimental Tm Validation (Oliveira 2020)

Classical ML Baseline

Numerical Verification Scripts

Quantum Kernel Diagnostic Experiments

Exp D1 - Kernel Condition Number Analysis

Exp D2 - Physics-Informed Classical Baseline

Exp D3 - Entanglement Ablation Study

Exp D4 - Best Configuration Synthesis

Exp X1 - Watson-Crick Topology Validation

Exp X2 - Stacking-Only Benchmarks with Bootstrap CIs

Key Results Summary

Data Sources

Hardware

License

Contact & Enquiries

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