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Benchmarking Quantum Simulators for Tabular ML: A Practical Comparison

UUnknown

2026-03-05

10 min read

Reproducible benchmark suite comparing quantum simulators and classical baselines on PCA, clustering and matrix factorization using ClickHouse-hosted datasets.

Benchmarking Quantum Simulators for Tabular ML: A Practical Comparison

Hook: If your team is trying to prototype quantum-assisted analytics on real OLAP data but keeps hitting three blockers — which simulator to use, how to connect to large tabular stores like ClickHouse, and whether quantum kernels beat classical baselines — this guide gives you a reproducible benchmark suite and an executable workflow to answer those questions.

Executive summary (most important first)

By 2026 the practical question for technology teams is no longer “what is quantum?” but “where will it fit in my tabular ML stack?” This article provides a reproducible benchmark suite you can run locally or in cloud VMs that compares multiple quantum simulators and classical baselines on three core tabular primitives: PCA (dimensionality reduction), clustering, and matrix factorization. The suite uses ClickHouse as the OLAP host for datasets so you can test on realistic, columnar workloads and measure end-to-end costs (extraction + preprocessing + quantum workload).

Quick findings you can act on

For small feature sets (<16 qubits / amplitude-encoded features), statevector simulators (Qiskit Aer, Qulacs) are fastest and easiest to integrate.
For larger qubit counts with low entanglement, tensor-network/MPS backends (TensorNetwork, Cirq+qsim with MPS) can simulate circuits that statevectors cannot due to memory constraints.
GPU-accelerated backends (via NVIDIA cuQuantum integrations) drastically reduce runtime for dense statevector simulations, and are the practical choice when experimenting with 20–30 qubit prototypes on modern cloud GPUs.
Classical baselines (scikit-learn PCA, randomized SVD, k-means) remain more cost-effective for production tabular ML. Quantum kernels and variational encoders are useful research tools and can serve as drop-in feature transforms for hybrid experiments.

Why ClickHouse + Tabular ML matters in 2026

Structured data is the next frontier for AI adoption — enterprises store years of operational data inside OLAP systems. ClickHouse, which raised another large round in late 2025, is widely used for high-performance analytics and makes a practical host for datasets to evaluate quantum-augmented workflows. Benchmarks that run on ClickHouse-hosted tables reflect the extraction and preprocessing costs teams actually pay when integrating quantum experiments into existing stacks.

What we benchmark (scope)

We focus on three tabular model primitives that commonly appear in analytics and feature engineering pipelines:

PCA: classical PCA vs kernel-PCA where the kernel is estimated using a quantum circuit (quantum kernel).
Clustering: k-means using classical distances vs k-means driven by a quantum kernel / similarity matrix.
Matrix factorization: randomized SVD (classical) vs a hybrid quantum-assisted approximation using quantum kernel methods and randomized sketches.

Reproducible benchmark architecture (overview)

Design goals: measurable, repeatable, and easy to run on a developer laptop or on a cloud VM with a GPU.

ClickHouse server (local Docker or managed) hosting the tabular datasets.
Benchmark harness (Python) that pulls feature batches via clickhouse-driver and preprocesses them.
Simulator backends pluggable by command-line flag: Qiskit Aer (statevector & shot-based), PennyLane (default.qubit / Lightning), Cirq+qsim (tensor/trojans), Qulacs, and a cuQuantum-accelerated Aer when GPU is available.
Classical baselines implemented in scikit-learn / numpy.
Metrics recorded: wall-clock time, peak memory, model quality (explained variance / reconstruction error for PCA; silhouette score for clustering; reconstruction error for factorization), and reproducible environment metadata (seeds, package versions, CPU/GPU info).

Environment & reproducibility

Always record the runtime environment. Use a Docker image for the harness and a separate Docker Compose entry for ClickHouse. The benchmark repo should include:

docker-compose.yml with ClickHouse service
Dockerfile for the benchmark harness including Python dependencies (qiskit, pennylane, cirq, qulacs, scikit-learn, clickhouse-driver, psutil)
requirements.txt and a pinned pip-freeze log
benchmarks/run_bench.py — single entrypoint that accepts backend, dataset, seed, and output CSV path

Example docker-compose snippet

version: '3.7'
services:
  clickhouse:
    image: clickhouse/clickhouse-server:latest
    ports:
      - '8123:8123'
      - '9000:9000'
    volumes:
      - ./clickhouse-data:/var/lib/clickhouse

ClickHouse ingestion: example SQL

Load a CSV into ClickHouse and create a columnar table used for benchmarks.

CREATE TABLE default.adult
(
  age UInt8,
  workclass String,
  education String,
  ...
) ENGINE = MergeTree()
ORDER BY tuple();

-- from client
INSERT INTO default.adult FORMAT CSV

Data pipeline: selecting and encoding features

Practical tips:

Use ClickHouse to do heavy pre-aggregation and sampling; pushdown SQL reduces network costs.
Pull feature batches sized for qubit capacity: amplitude encoding requires vector length 2^n — in practice use dimensionality reduction/indexing to fit available qubits.
Standardize features (zero mean, unit variance) before amplitude encoding or kernel mapping.

Python: fetch and preprocess (clickhouse-driver)

from clickhouse_driver import Client
import numpy as np
from sklearn.preprocessing import StandardScaler

client = Client('localhost')
query = 'SELECT age, hours_per_week, capital_gain, capital_loss FROM default.adult LIMIT 4096'
rows = client.execute(query)
X = np.array(rows, dtype=float)
X = StandardScaler().fit_transform(X)

Quantum workflows we implement

We keep the quantum side practical: circuits that compute a kernel (state overlap) or learn lower-dimensional encodings via a variational quantum circuit (VQC). Downstream learners remain classical (kernel-PCA, kernel k-means, randomized SVD).

1. Quantum Kernel (most reproducible)

Procedure:

Amplitude-encode feature vectors (or use angle encoding for small dimensions).
Run a parameter-free circuit that prepares state |phi(x)>. The kernel k(x, x') = |⟨phi(x)|phi(x')⟩|^2 is estimated by swap test or direct inner-product for statevector simulators.
Build kernel matrix K and feed to sklearn.kernel_pca / kernel k-means.

Why this is practical: kernel estimation reduces the quantum workload to O(n_samples^2) circuit evaluations that we can paralyze and cache. Simulators differ on how fast they return state overlaps and whether they support direct statevector access (statevectors -> exact overlaps) or only shot-based estimation.

2. Variational Quantum Encoder (VQE / QAE)

Use a small ansatz to compress features into fewer qubits and reconstruct them with a classical decoder (quantum autoencoder). Evaluate explained variance after classical decoder training.

3. Hybrid randomized SVD with quantum sketches

Use randomized linear algebra where sketching matrices are derived from quantum kernel features. This reduces the problem size before classical SVD and is straightforward to prototype with simulators.

Benchmark harness: key functions

Essential pieces of code to include in your repo (shortened here):

def compute_quantum_kernel(X, backend, shots=1000):
    # X shape (n_samples, n_features)
    # returns kernel matrix K (n_samples x n_samples)
    # backend is a string that maps to a simulator implementation
    if backend == 'statevector_aer':
      states = [statevector_prepare(x, backend) for x in X]
      K = np.abs(np.dot(states, np.conjugate(states).T))**2
    else:
      # shot-based or hardware emulated
      K = estimate_kernel_shots(X, backend, shots)
    return K

Plug K into sklearn.kernel_pca or sklearn.cluster.SpectralClustering with precomputed kernel.

Which simulators to include (practical list for 2026)

Qiskit Aer — statevector and shot-based, CPU/GPU (cuQuantum) integrations common.
PennyLane + Lightning — flexible, plugin-based and integrates with autograd; good for variational experiments.
Cirq + qsim — high-performance, tensor-network and MPS-mode available for certain circuits.
Qulacs — lightweight, fast statevector simulator with Python bindings.
TensorNetwork / MPS backends — for circuits with low entanglement and larger qubit counts.
Qrack (if available) — optimized for certain statevector workloads.

Note: in 2024–2026, the ecosystem standardised better plugin bridges (PennyLane, Qiskit plugins) so switching backends is easier. GPU-backed Aer or PennyLane-Lightning with CUDA/cuQuantum will be the best option for mid-size simulations on cloud GPUs.

Measurement and metrics

Track these per experiment:

Runtime: total wall clock for kernel construction + downstream learning.
Memory: peak RAM (psutil) and GPU memory (nvidia-smi or NVML).
Quality: explained variance (PCA), silhouette score (clustering), reconstruction error (factorization).
Cost: approximate cloud cost per run (CPU-hours, GPU-hours) — useful for pay-as-you-go planning.
Reproducibility: random seeds and package versions logged to CSV/JSON.

Sample benchmark protocol (one-page)

Start ClickHouse, load dataset, run a SQL sample to pull up to 4096 rows.
Standardize and reduce feature dimensionality to f features (f=4,8,16) using classical PCA for amplitude encoding compatibility.
Run three repeats per backend with fixed seed. Measure time and memory.
Compute metrics and save results to results.csv with environment metadata.
Plot runtime vs explained variance and cost vs quality to pick trade-offs.

Interpreting results — what to expect

From teams we've worked with and from ecosystem trends through late 2025:

Statevector simulators return exact overlaps and are ideal for small-scale feature experiments. They are deterministic, which simplifies debugging.
Shot-based simulators and hardware-emulators add noise and sampling variance. For kernel methods this increases error, so more shots are required — which increases runtime and cost.
GPU-backed runs will often beat CPU statevector by 3–8x on wall clock for 20–25 qubit dense circuits on modern A100 / H100 instances.
Tensor-network backends scale well for circuits with limited entanglement; they enable exploring deeper circuits for more qubits than statevector allows but are sensitive to circuit topology and entangling gates.

“In 2026, quantum simulators are research accelerators, not drop-in production replacements for classical algorithms on tabular data. Use them to explore kernels and hybrid encoders; rely on classical methods for production scale.”

Concrete example: quantum-kernel PCA benchmark (short script)

# high-level pseudo-code (real code in repo)
# Fetch X from ClickHouse
# Reduce to d=8 features
K = compute_quantum_kernel(X, backend='pennylane_default')
from sklearn.decomposition import KernelPCA
kpca = KernelPCA(n_components=4, kernel='precomputed')
Z = kpca.fit_transform(K)
# Measure explained variance via projection back to original space (approx)

Practical advice for teams (operational)

Start with a small sample from ClickHouse to iterate quickly. Only scale to larger samples after pipeline and instrumentation are stable.
Automate environment capture: a single JSON per run with git hash, pip freeze, OS, CPU/GPU model, and ClickHouse server settings.
Cache quantum kernel evaluations keyed by feature-hash to avoid recomputation during hyperparameter sweeps.
Use classical baselines as a control: randomized SVD, kernel PCA with RBF kernel, approximate nearest neighbors for similarity baselines.
Track cost per improvement. If a quantum kernel gives 1–2% better silhouette but costs 10x runtime, it’s a research result, not production-ready.

Advanced strategies and 2026 trends

Three advanced strategies gained traction through 2025 and into 2026:

Hybrid pipelines: use quantum kernel features combined with classical embeddings (TabNet, lightGBM) rather than replacing the whole model.
GPU-first experimentation: run simulators on cloud GPU VMs for mid-scale prototypes; integrate with cloud ClickHouse instances where possible to reduce egress latency.
Federated/secure setups: with enterprises reluctant to move sensitive OLAP tables, teams started running simulators next to database instances (same VPC) to preserve data locality while experimenting.

Limitations and honest boundaries

Be transparent: current simulators can probe interesting regimes but do not demonstrate production advantage for large-scale tabular primitives. Expect classical randomized algorithms to remain dominant for high-dimensional, high-volume OLAP workloads in 2026. However, quantum-assisted feature transforms and kernels are promising research directions, and simulators are the right tool to discover which circuits might ultimately map to quantum hardware gains.

Run it yourself — checklist

Clone the benchmark repo: git clone <repo-url> (repo contains Docker Compose and run_bench.py)
Start ClickHouse: docker-compose up -d clickhouse
Load a sample dataset into ClickHouse (scripts in /data-load)
Run a quick smoke test: python run_bench.py --backend statevector_aer --dataset adult --n=256
Scale to full experimental matrix: python run_bench.py --matrix experiments.yaml

We publish the full benchmark harness under an open-source license (MIT) with prebuilt Docker images for Qiskit Aer, PennyLane-Lightning (CPU/GPU), Cirq+qsim, and Qulacs. The repo also includes Jupyter notebooks to reproduce plots and a results dashboard that reads CSV outputs and creates comparison charts.

Final recommendations

Use ClickHouse to host and sample real OLAP tables so your benchmarks reflect operational constraints.
Start with quantum kernel experiments using statevector simulators to validate idea quickly; then move to GPU-accelerated or tensor-network simulators when scaling up.
Always compare against randomized classical methods and report cost-vs-quality, not just model quality.

Call to action

If you want the benchmark harness, Docker images, and example ClickHouse datasets (ready to run), download the repo from our GitHub: github.com/boxqbit/qbench-clickhouse. Run the smoke test in under 10 minutes and open an Issue with your environment metadata — we’ll help map simulator performance to your teams’ OLAP workloads. For enterprise support, consult our benchmarking engagement to evaluate simulators, cloud costs, and a roadmap for moving from prototype to pilot.

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