Solve binary classification task with Quantum Support Vector MachineTransparent, Reproducible Results
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Binary classification Solution
We use a classical SVM pipeline to solve binary classification problem. The model seeks a set of separating hyperplanes in feature space, \mathbf{w}^\top \phi(\mathbf{x}) + b = 0 , maximizing the geometric margin between classes. When linear separation is difficult, we map data to a higher-dimensional space and apply the kernel trick: instead of building \phi(\cdot) explicitly, we compute inner products k(\mathbf{x},\mathbf{x}')=\langle \phi(\mathbf{x}), \phi(\mathbf{x}')\rangle , which lets the SVM operate implicitly in a Hilbert space \mathcal{H}.
- • End‑to‑end quantum support vector machine executed on simulator
- • Results: QSVM reached 96% accuracy with strong class balance (Balanced Accuracy 95%, Macro F1 0.95, ROC‑AUC 0.99)
- • Downloadable, citable report (method, experiments, results)
- • Executable Python code with deterministic, reproducible outputs
- • Hardware details: encoding, circuit depth/qubits, backend/cost guidance
- • Baseline comparisons with metrics and plots
Quantum Support Vector Machine
Quantum SVM is implemented using a quantum kernel, where input \mathbf{x} is encoded into a quantum state |\phi(\mathbf{x})\rangle=U(\mathbf{x})|0\rangle^{\otimes n} and using the state overlap (inner product or fidelity) as k(\mathbf{x},\mathbf{x}'). The circuit induces a (potentially very high-dimensional) nonlinear embedding through data-dependent single-qubit rotations and entangling gates; the choice of encoding and entanglement pattern governs which higher-order interactions are represented. These overlaps are estimated by running U(\mathbf{x}')^\dagger U(\mathbf{x}) on quantum hardware; the resulting Gram matrix feeds directly into the standard SVM pipeline.
Before encoding, the 30 FNA features are reduced to a lower-dimensional representation with PCA — near-term devices only expose a handful of qubits, so the circuit needs a compact input. The same preprocessing routine feeds the LS-QSVM with HHL variant described below; only the number of qubits and the downstream solver differ.
Strengths
- Quantum kernels embed data into high-dimensional Hilbert spaces, increasing the chance of linear separability and improving classification quality.
- Shallow, hardware-efficient circuits keep depth, noise, and runtime low enough for practical kernel evaluation on NISQ devices.
- On fault-tolerant quantum hardware, kernel entries over exponentially large state spaces can be estimated in polynomial quantum time for specific problem families.
Weaknesses
- Contemporary quantum devices exhibit non-negligible noise and gate/measurement error rates, which can degrade model or task-level accuracy.
- Performance improvements over classical baselines are not guaranteed and typically depend on the dataset, problem structure, and parameter regime.
- Classical simulation of quantum circuits can avoid hardware noise but incurs additional computational cost compared to purely classical approaches.
Proof-of-Concept Simulation Results
Task: A supervised binary-classification benchmark with continuous features derived from digitized fine-needle aspirate images of breast masses. The dataset consists of 569 samples, each with 30 features, and the labels are benign or malignant. Min-Max scaling to [0, π] is used.
Execution
Simulator
Number of qubits
4
Number of layers
2
Key Outcomes
96%
Accuracy
95%
Balanced Accuracy
0.95
Macro F1
0.99
Macro ROC‑AUC
LS-QSVM with HHL: The Linear-System Variant
Standard QSVM above still trains like a classical support vector machine: the quantum kernel replaces the feature map, but the dual optimization is solved the usual way. LS-QSVM with HHL changes the second half of that pipeline. It restates training as a least-squares SVM, which turns the quadratic-programming dual into a single linear system (K+\lambda I)\boldsymbol{\alpha}=\mathbf{y} , where K is the same quantum kernel Gram matrix and \lambda regularizes the fit. Instead of solving that system classically, this variant runs it through the HHL algorithm — a quantum linear solver that prepares a state proportional to the solution of any system A\mathbf{x}=\mathbf{b}.
HHL's appeal is asymptotic: under strong assumptions — a sparse coefficient matrix, a moderate condition number, and efficient state preparation or oracle access — its cost can scale only polylogarithmically in the system size, instead of the roughly linear scaling a classical sparse iterative solver needs once that size gets large. Those assumptions rarely hold for a dense kernel matrix built from real patient features, and state-preparation and read-out overhead eat into the advantage at any size we can currently run. Our own engineering notes flag this combination as impractical for production and a proof of concept rather than a production path, which is why the run below uses a reduced 25-sample subset with 35 features rather than the full 569-sample, 30-feature dataset QSVM trains on above.
On that reduced set, LS-QSVM with HHL reaches 90% accuracy; standard QSVM's 96% accuracy on the full dataset is not a fair head-to-head — different sample size, different feature count — but both runs share the same reproducibility guarantees: fixed seeds, a downloadable report, and executable Python code. See how QSVM itself compares with classical SVM in our QSVM vs. classical SVM comparison, or read more about the general-purpose HHL algorithm and the standalone QSVM algorithm.
QSVM vs. LS-QSVM with HHL: Side by Side
| Metric | QSVM | LS-QSVM + HHL |
|---|---|---|
| Training samples | 569 | 25 |
| Features | 30 | 35 |
| Qubits | 4 | 6 |
| Circuit layers | 2 | 1 |
| Accuracy | 96% | 90% |
| Balanced accuracy | 95% | 88% |
| Macro F1 | 0.95 | 0.89 |
| Macro ROC-AUC | 0.99 | 0.96 |
Why bother with HHL
Solving the least-squares system is, in principle, the part of QSVM training most likely to gain a genuine quantum speed-up as datasets and qubit counts grow — the same reason HHL underlies quantum approaches to other linear-algebra-heavy problems, from portfolio optimization to differential equations.
Why we still recommend QSVM today
Given present hardware constraints, it's prudent to run HHL-based approaches only on small datasets — the reason this benchmark is capped at 25 samples rather than the full 569. Until state preparation and read-out overhead come down, QSVM's classical dual solve remains the dependable default for a real diagnostic workload.
Both variants ship with the same deliverables regardless of which one you run: a downloadable, citable report, deterministic Python code, and baseline comparisons with metrics and plots, so you can audit either result independently of our claims here.
Use standard QSVM when you want a diagnostic pipeline validated on the full dataset today. Use LS-QSVM with HHL when you want to see the linear-system route to the same problem — useful for research and roadmap planning, not yet for clinical throughput.Business Impact
The QSVM diagnosis model potentially delivers clinic-ready decision support with 96% accuracy, cutting average review time per FNA case and expanding throughput without adding more employees to the task. The LS-QSVM with HHL variant below trades that full-dataset accuracy for a look at the linear-system route to the same diagnosis — a research path today, not a throughput play.
Cost Savings
Annual projected savings from reduced reviews/scrap and faster throughput.
ROI
Return on investment based on value add vs. TCO.
Time Saved
Efficiency gains vs. baseline review/inspection workflows.
How it works
Simple and transparent: from your brief to quantum results, code, and a paper. The same five steps run whether you choose standard QSVM or the LS-QSVM with HHL linear-system variant below — only the algorithm and dataset size change.
Describe
Map your problem to the right quantum use case
Confirm
Confirm the quantum-classical hybrid approach and key assumptions
Run
Download ready-to-run code; execute on simulator with a fized seed
Review
Review reproducible results, iterate as needed
Benchmark
Compare against classical baseline; prepare for quantum hardware
FAQs
What is QSVM used for in breast cancer diagnosis?
Quantum Support Vector Machine (QSVM) classifies breast masses as benign or malignant from digitized fine-needle aspirate (FNA) features. It works like a classical SVM but replaces the kernel with a quantum circuit, embedding the 30 FNA features into a higher-dimensional quantum feature space before the usual margin-maximizing classifier runs on top. The report and code we deliver document every step of that pipeline, from PCA preprocessing to the final Gram matrix.
How accurate is quantum SVM compared to classical SVM?
In our reproducible run on the 569-sample Wisconsin-style FNA dataset, QSVM reached 96% accuracy (Balanced Accuracy 95%, Macro F1 0.95, Macro ROC-AUC 0.99). Whether that beats a classical kernel SVM on your data isn't guaranteed by default — improvements depend on the dataset, problem structure, and parameter regime — so see our QSVM vs. classical SVM comparison for a direct, same-dataset benchmark before assuming a quantum advantage.
What is the difference between QSVM and LS-QSVM with HHL?
Standard QSVM solves the usual SVM dual problem with a quantum kernel, then hands the result to a classical solver. LS-QSVM with HHL instead reformulates training as a least-squares linear system and solves that system with the HHL quantum linear-solver algorithm. It's a proof of concept today, not a production path — our benchmark run used only 25 samples with 35 features and reached 90% accuracy, against QSVM's 96% on the full 569-sample, 30-feature set.
Do I need access to real quantum hardware to run this?
No. Every result on this page runs on a simulator with a fixed seed for reproducibility, on both the QSVM and LS-QSVM with HHL variants. The delivered report and code include hardware notes — circuit depth, qubit count, and backend guidance — for teams that want to move a run onto quantum hardware later.
What dataset is used to benchmark QSVM for breast cancer classification?
A supervised binary-classification set of 569 samples with 30 continuous features derived from digitized FNA images of breast masses, labeled benign or malignant. Features are reduced with PCA and Min-Max scaled to [0, π] before quantum encoding; the HHL variant benchmarks on a 25-sample subset of the same data instead of the full set.
Is LS-QSVM with HHL ready for production use?
Not yet. HHL's polylogarithmic scaling only holds under strong assumptions — a sparse, well-conditioned coefficient matrix and efficient state preparation — that a dense clinical kernel matrix doesn't meet at today's hardware sizes, and present hardware constraints make it prudent to run this combination on small datasets only. We flag it as a research proof of concept; standard QSVM is the path we recommend for a diagnostic pipeline today.
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