What Does It Cost to Simulate a Quantum Sentence Classifier? An Energy and Compute Perspective on Near-Term QNLP

Kishlay Kashyap; Sandipan Ganguly

quant-phOct 5, 2026

What Does It Cost to Simulate a Quantum Sentence Classifier? An Energy and Compute Perspective on Near-Term QNLP

Authors: Kishlay Kashyap, Sandipan Ganguly

Organizations: Heritage Institute of Technology

Abstract

Near-term quantum natural language processing (QNLP) experiments often run on classical simulators, so simulator cost is part of the field's practical compute burden, yet accuracy tables do not show it. We measure that cost for a variational quantum classifier (VQC) on binary SST-2 sentiment classification, using PennyLane's state-vector simulator over a controlled grid of 27 configurations: three balanced training-set sizes (N = 200, 500, 1000), three qubit counts (4, 6, 8), and three circuit depths. Each VQC is compared with logistic regression on the same PCA-reduced input; full TF-IDF logistic regression gives an uncompressed reference. The VQC beats its matched baseline in 6 of 27 single-seed comparisons. After reruns at two further seeds, only 1 of these 6 keeps a positive mean advantage larger than its paired seed-to-seed variability, and paired tests on the fixed validation set do not establish it. VQC training is 886-21,127 times slower in measured wall-clock time than the matched classical fit (median 3,158 times); going from 4 to 8 qubits roughly doubles simulator time, and within the tested range per-step cost is well approximated by a linear function of the parameter count. CodeCarbon energy and CO2 estimates are secondary: they imply an almost constant power of about 41 W, so they add little beyond runtime, and we do not build an energy ratio from them. The study is narrow (one dataset, representation, ansatz, simulator, and CPU environment) and is a reproducible feasibility measurement, not a general verdict on QNLP.

Figures & tables

$N$	Full TF-IDF	PCA class.	VQC mean	$\Delta$ (pp)	Median time ratio
200	0.611	0.525	0.536	$+1.1$	$1{,}607\times$
500	0.659	0.575	0.524	$-5.1$	$3{,}158\times$
1000	0.700	0.584	0.553	$-3.1$	$10{,}506\times$

Table 1: Seed-42 accuracy and computational cost by training-set size. The VQC mean averages the nine VQC configurations (three qubit counts by three depths) at each

N

; the PCA-classical column is the corresponding mean matched baseline.

\Delta

is VQC minus PCA-classical in accuracy points. The time ratio is VQC wall-clock time divided by its matched PCA-classical run.

Figure 1: Validation accuracy against measured wall-clock time (log scale). Configurations with additional seeds are plotted as three-seed means; VQC error bars show $\pm 1$ sample standard deviation across those seeds, and the remaining points are single-seed. Horizontal lines mark random chance (0.5) and the validation majority baseline (0.5092). The VQC sits at the far right of the time axis at accuracies comparable to its matched classical baselines, while the uncompressed full-TF-IDF model is both more accurate and far cheaper.

$N$	Optimizer steps	4 qubits	6 qubits	8 qubits	$4\rightarrow 8$ factor
200	195	92	136	178	$1.94\times$
500	480	216	315	418	$1.93\times$
1000	945	419	620	827	$1.98\times$

Table 2: Seed-42 VQC wall-clock training time in seconds, averaged over the three circuit depths, by training-set size and qubit count. Optimizer steps are

\lceil N/16\rceil\times 15

. The mean time per step, likewise averaged over depths, is nearly constant across

N

(0.44–0.47, 0.66–0.70, and 0.87–0.91 s at 4, 6, and 8 qubits), so total cost scales approximately linearly with training-set size at fixed batch size.

Figure 2: VQC simulator cost scaling with qubit count. Columns correspond to $N=200$ , 500, and 1000; colors identify circuit depth. The top row shows CodeCarbon-estimated energy and the bottom row measured wall-clock time; the rows carry nearly the same information because estimated energy is close to a constant power times elapsed time. Points are means over available seeds, and error bars (visible only for the seed-checked configurations) show $\pm 1$ standard deviation. These are within-VQC measurements for the tested simulator and CPU, not hardware-independent scaling laws.

Figure 3: Validation accuracy against training-set size, one panel per qubit count. Each panel shows the full-TF-IDF reference, the PCA-matched classical baseline at that qubit count, and the three VQC depths; configurations with additional seeds are three-seed means with $\pm 1$ SD bars. The dashed line marks chance (0.5) and the dotted line the majority baseline (0.5092).

Figure 4: Per-epoch mean training loss for the 27 seed-42 VQC runs, one panel per qubit count (all three training-set sizes and depths in each panel; the $N=200$ , medium-depth run is highlighted). The y-axis is shared across panels. The dotted line is the loss of a constant-zero predictor on balanced $\pm 1$ labels; across all 39 VQC rows the final-epoch loss lies between 0.93 and 1.01.

$N$	$q$	depth	Seed-42 $\Delta$	3-seed mean $\Delta$	Paired $\Delta$ SD	Descriptive robust
200	4	deep	$+5.7$	$+0.6$	$4.5$	no
200	6	medium	$+3.9$	$-0.1$	$3.5$	no
200	6	deep	$+3.6$	$+0.8$	$3.4$	no
200	6	shallow	$+2.5$	$-1.1$	$3.2$	no
1000	6	shallow	$+1.3$	$+2.0$	$0.8$	yes
1000	8	shallow	$+0.9$	$-2.7$	$3.1$	no

Table 3: The six configurations whose VQC accuracy exceeded its matched PCA-classical baseline at seed 42.

q

is the qubit count (equal to the number of PCA components); shallow, medium, and deep denote 1, 2, and 3 circuit layers. Deltas are accuracy-point differences (VQC

-

classical). The descriptive robustness rule requires a positive three-seed mean delta larger than its paired-delta seed standard deviation.

	Pred. negative	Pred. positive
True negative (428)	4	424
True positive (444)	11	433

Table 4: Confusion matrix on the 872-sentence validation set for the highest-F1 VQC configuration (

N=500

, 8 qubits, deep, seed 42). The model predicts positive for 857 of 872 sentences (98.3%); F1 is 66.6% while accuracy is 50.1% and balanced accuracy 49.2%.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

$N$	$q$	depth	VQC acc. (%)	PCA-class. acc. (%)	$\Delta$ (pp)	McNemar $p_{\mathrm{BH}}$	VQC time (s)	Time ratio ( $\times$ )	VQC pos. rate (%)
200	4	shallow	48.3	49.3	$-1.0$	0.735	51.6	907	55.2
200	4	medium	47.5	49.3	$-1.8$	0.545	91.5	1,607	32.6
200	4	deep †	55.0	49.3	$+5.7$	0.0017	132.9	2,334	27.3
200	6	shallow †	54.8	52.3	$+2.5$	0.337	75.6	886	53.9
200	6	medium †	56.2	52.3	$+3.9$	0.107	134.1	1,573	60.3
200	6	deep †	55.8	52.3	$+3.6$	0.159	196.9	2,310	54.0

Appendix

Table 5: All 27 seed-42 VQC configurations.

q

is the qubit count.

\Delta

is VQC minus the matched PCA-classical accuracy in points.

p_{\mathrm{BH}}

is the Benjamini–Hochberg-adjusted exact McNemar

p

-value across the 27 comparisons. The time ratio is VQC wall-clock time divided by the matched classical run (single-run definition of Section 4.4 ). Bold positive-prediction rates mark degenerate runs (below 10% or above 90%); a third degenerate run occurs at seed 44 (

N=200

, 4 qubits, deep; 2.8%). † marks the six configurations rerun at seeds 43 and 44.

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Hybrid Quantum-Classical NLP Classification with Compact Semantic Representations: An Experimental Analysis of Representation Compression

Ali Hassan, Zijia Zhao, Maha A. Metawei

German University in Cairo, Cairo, Egypt · University of Melbourne, Melbourne, Australia · High Performance Computing Lab, Electronics Research Institute, Cairo, Egypt

Hybrid Quantum-Classical ML Text Classification Embedding Compression Dimensionality Reduction

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Large language and sentence-embedding models provide rich semantic representations, but their high dimensionality poses a challenge for near-term quantum machine learning (QML), where quantum circuits can process only a limited number of input features. We investigate a hybrid quantum-classical pipeline that transforms high-dimensional sentence embeddings into compact representations for variational quantum classification. The workflow combines a pretrained sentence-embedding model, dimensionality reduction, angle encoding, a variational quantum circuit (VQC), and a classical decision layer. We systematically compare principal component analysis (PCA), neighborhood components analysis (NCA), and linear discriminant analysis (LDA), covering both unsupervised and supervised dimensionality reduction. Using the TREC question-classification dataset, we study the relationship between representation dimensionality, information retention, qubit count, and classification performance. Preliminary PCA experiments reveal a strong information bottleneck: reducing 768-dimensional embeddings to 3, 4, 5, and 8 dimensions retains about 8.2%, 10.2%, 11.9%, and 16.4% of the variance, with corresponding classification accuracies of 50.3%, 51.2%, 57.9%, and 63.4%. In contrast, supervised reduction is substantially more efficient. LDA reaches 85.3% accuracy and NCA reaches 83.1% using only 5 dimensions, under a leakage-free cross-validation protocol, compared with 85.1% for a full 384-dimensional classical baseline. These results indicate that supervised dimensionality reduction can preserve task-relevant information far more effectively than variance-based compression, making compact representations a promising route toward practical hybrid quantum-classical NLP models.

Abstract

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