Quantum U-Net with Uncertainty Quantification for Brain Tumor Segmentation: A Hybrid Quantum-Classical Approach

Keval Shah; Rajat Masanagi; Maaz Saboowala; Namita Pulgam; Nilesh Marathe

doi:10.2478/ijssis-2026-0063

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Quantum U-Net with Uncertainty Quantification for Brain Tumor Segmentation: A Hybrid Quantum-Classical Approach

International Journal on Smart Sensing and Intelligent Systems

Volume 19 (2026): Issue 1 (January 2026)

By: Keval Shah, Rajat Masanagi, Maaz Saboowala, Namita Pulgam and Nilesh Marathe

Open Access

|Sep 2026

Figures & Tables

BraTS 2020 dataset structure showing the multi-modal MRI sequences (T1, T1ce, T2, FLAIR) and ground truth segmentation labels for brain tumor cases. BraTS, brain tumor segmentation; MRI, magnetic resonance imaging.

Class distribution in the BraTS 2020 dataset illustrating the severe imbalance between background and tumor sub-regions. BraTS, brain tumor segmentation.

Table 1:

Validation ECE for different MC dropout weights in the combined uncertainty map.

α	0.5	0.6	0.7	0.8	0.9	1.0
ECE	0.0741	0.0703	0.0661	0.0679	0.0697	0.0718

[i] Note: Bold text indicates the optimal (lowest) validation Expected Calibration Error (ECE = 0.0661 at α = 0.7), establishing the selected weighting factor for the combined-uncertainty formulation in Eq. (14).

[ii] ECE, expected calibration error; MC, Monte Carlo.

Table 2:

Loss-weighting sensitivity for L = λL_Dice + (1 − λ)L_Focal.

λ	Mean DSC↑	NCR↑	ET↑	ECE↓
0.3	0.7691	0.6984	0.7801	0.0712
0.4	0.7754	0.7101	0.7912	0.0688
0.5	0.7812	0.7223	0.7987	0.0655
0.6	0.7798	0.7189	0.7941	0.0669
0.7	0.7761	0.7142	0.7889	0.0701
1.0	0.7703	0.7031	0.7812	0.0731

[i] Note: Bold text denotes the optimal configuration (λ = 0.5), which simultaneously achieves the highest Mean DSC, NCR Dice, and ET Dice, as well as the lowest ECE, confirming the equal-weight Dice/Focal loss retained for reported results (Eq. 17).

[ii] DSC, dice similarity coefficient; ECE, expected calibration error; ET, enhancing tumor; NCR, necrotic/non-enhancing core.

Hybrid quantum-classical U-net architecture. The quantum SE module at the bottleneck recalibrates channel responses via a six-qubit VQC before the decoder reconstructs the segmentation map and uncertainty overlay. GAP, global average pooling; SE, squeeze-and-excitation; VQC, variational quantum circuit.

VQC: layered RY/RZ rotations and CNOT entangling gates across six qubits over two variational layers. CNOT, controlled-NOT; RY/RZ, rotation gates about the Y-axis and Z-axis of the Bloch sphere; VQC, variational quantum circuit.

Table 3:

Single forward-pass runtime breakdown for one input volume, averaged over 100 runs.

Component	Time (ms)	Share (%)
Classical encoder and bottleneck conv	38.2	57.0
Quantum VQC simulation	12.4	18.5
CPU to GPU attention transfer	4.1	6.1
Classical decoder	10.8	16.1
Output projection and softmax	1.5	2.2
Total single pass	67.0	100
Classical SE block only	0.3	–

[i] GPU, graphics processing unit; SE, squeeze-and-excitation; VQC, variational quantum circuit.

Table 4:

Training-time overhead compared with classical baselines.

Model	Time/epoch (min)	Total time (hr)
Classical 3D U-Net	14.2	16.6
Classical SE block	14.4	16.8
Hybrid quantum U-Net	21.3	24.9

[i] SE, squeeze-and-excitation.

Table 5:

Qubit-count ablation on the validation split.

Qubits	Params	Val DSC↑	Val ECE↓	Time/pass (ms)
4	24	0.7701	0.0748	8.1
6	36	0.7812	0.0655	12.4
8	48	0.7839	0.0641	17.3
10	60	0.7831	0.0638	25.9

[i] Note: Bold text highlights column-best values (Val DSC = 0.7839, Val ECE = 0.0638 at 8 qubits). The 6-qubit setup was selected for the final model as it represents the optimal performance-versus-simulation-cost trade-off, avoiding the ~40% per-pass runtime increase of 8 qubits. ↑ indicates higher is better; ↓ indicates lower is better.

[ii] DSC, dice similarity coefficient; ECE, expected calibration error.

Table 6:

Parameter-matched attention comparison.

Model	Mean DSC↑	NCR↑	ECE↓
Classical 3D U-Net	0.7589	0.6890	0.0877
Minimal linear attention (36 params)	0.7601	0.6912	0.0862
Classical SE block (3,334 params)	0.7768	0.6985	0.0831
Hybrid quantum U-Net (36 params)	0.7812	0.7223	0.0655

[i] Note: Bold text indicates the superior model (Hybrid Quantum U-Net, Mean DSC = 0.7812, NCR = 0.7223) among parameter-matched attention mechanisms, demonstrating that the quantum transformation drives the observed performance gains. ↑ indicates higher is better; ↓ indicates lower is better.

[ii] DSC, dice similarity coefficient; ECE, expected calibration error; NCR, necrotic/non-enhancing core; SE, squeeze-and-excitation.

Table 7:

Internal comparison of all nine model variants on the held-out brats 2020 test split (with TTA and adaptive thresholding)

Model	Arch	Mean↑	NCR↑	ED↑	ET↑	HD95 NCR↓	HD95 ET↓	ECE↓
Hybrid quantum U-Net (proposed)	HybridQ	0.7812	0.7233	0.8210	0.7987	23.87	10.47	0.0655
Classical attention U-Net + deep supervision	AttUNet	0.7812	0.6942	0.8244	0.8249	44.1	16.7	0.0818
Classical UNet++	UNet++	0.7748	0.7187	0.8137	0.7921	24.1	17.3	0.0850
Hybrid quantum U-Net, 1283 CosineWarmRestarts	HybridQ	0.7745	0.7297	0.8022	0.7916	18.1	17.8	0.0728
Hybrid quantum U-Net, 963 CosineWarmRestarts Run 2	HybridQ	0.7723	0.7141	0.8137	0.7890	18.2	17.7	0.0716
Hybrid quantum U-Net, 963 CosineWarmRestarts Run 1	HybridQ	0.7705	0.7224	0.8137	0.7754	24.2	24.9	0.0775
Classical 3D U-Net Baseline	PlainUNet	0.7589	0.6890	0.8127	0.7750	44.3	25.3	0.0877
Hybrid quantum U-Net, MONAI augmentation	HybridQ	0.7132	0.5975	0.7714	0.7705	71.7	18.1	0.1547
Hybrid quantum U-Net, LR decay	HybridQ	0.6845	0.5627	0.7401	0.7508	59.4	19.2	0.2352

[i] ↑ = higher is better; ↓ = lower is better.

[ii] BOLD, best per column; ECE, expected calibration error; ED, peritumoral edema; ET, enhancing tumor; LR, learning rate; MONAI, medical open network for AI; NCR, necrotic/non-enhancing core; TTA, test-time augmentation.

Table 8:

Architecture comparison across methods and datasets

Method	Dataset	Mean↑	NCR↑	ED↑	ET↑
ME-Net [17]^†	BraTS 2020	0.7746	0.7025	0.8827	0.7386
HybridCSF [18]	BraTS 2020	0.7700	0.8100	0.8700	0.6300
nnU-Net [21]^‡	BraTS-PEDs	0.7767	0.6600	0.9000	0.7700
Ensemble (nnU-Net + SwinUNETR) [19]	BraTS 2023 PED	0.7627	0.8090	0.8260	0.6530
SegResNet + Attn [20]^‡	BraTS-PEDs 2023	0.7133	0.6900	0.8500	0.6000
Hybrid quantum U-Net (proposed)	BraTS 2020	0.7812	0.7233	0.8210	0.7987

Note: ↑ indicates higher is better; ↓ indicates lower is better.

SwinUNETR, swin UNEt TRansformer.

Mean = (NCR + ED + ET)/3. BOLD = best.

† Brats 2020 validation set.

‡ Internal pediatric cohort. HD95 and ECE are not reported by any comparison method.

BraTS, brain tumor segmentation; ECE, expected calibration error; ED, edema; ET, enhancing tumor; ME-Net, multi-encoder net; NCR, necrotic core; nnU-Net, “no-new-Net” U-Net; PEDs, pediatrics;

Outcomes from segmentation in four validation cases. Columns: FLAIR image (input), ground truth, prediction, and uncertainty (combined) on both MC dropout and quantum variance. Tumor margins having highest level of uncertainty, where the model is most uncertain. MC, Monte Carlo.

Table 9:

Individual and combined uncertainty-source performance

Source	Val ECE↓	Boundary AUC↑
MC dropout only	0.0718	0.762
Quantum variance only	0.1031	0.694
Combined uncertainty	0.0655	0.801

[i] Note: Bold text marks the best calibration and boundary-error detection (Combined Uncertainty, Val ECE = 0.0655, Boundary AUC = 0.801), verifying that fusing MC-Dropout entropy with quantum measurement variance outperforms individual uncertainty sources. ↑ indicates higher is better; ↓ indicates lower is better.

[ii] AUC, area under the curve; ECE, expected calibration error; MC, Monte Carlo.

Table 10:

Per-sub-region ECE comparison

Model	NCR	ED	ET	Mean
Classical 3D U-Net	0.1041	0.0732	0.0858	0.0877
Attention U-Net	0.0971	0.0691	0.0792	0.0818
UNet++	0.1003	0.0712	0.0835	0.0850
Hybrid quantum U-Net	0.0748	0.0623	0.0594	0.0655

[i] ECE, expected calibration error; ET, enhancing tumor; NCR, necrotic core.

Table 11:

Voxel-level uncertainty as an error detector

Uncertainty source	AUROC	AUPRC
MC dropout entropy	0.784	0.612
Quantum variance	0.693	0.541
Combined uncertainty	0.821	0.653

[i] AUPRC, area under the precision–recall curve; AUROC, area under the receiver operating characteristic curve; MC, Monte Carlo.

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DOI: https://doi.org/10.2478/ijssis-2026-0063 | Journal eISSN: 1178-5608

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Language: English

Submitted on: Apr 1, 2026

Published on: Sep 3, 2026

Published by: International Journal on Smart Sensing and Intelligent Systems

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

hybrid quantum-classical networks,

U-net,

brain tumor segmentation,

VQC (variational quantum circuits),

medical imaging,

NISQ standard computing,

multi-modal MRI

Related subjects:

Engineering,

Introductions and overviews,

Engineering, other

© 2026 Keval Shah, Rajat Masanagi, Maaz Saboowala, Namita Pulgam, Nilesh Marathe, published by International Journal on Smart Sensing and Intelligent Systems
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 19 (2026): Issue 1 (January 2026)

Quantum U-Net with Uncertainty Quantification for Brain Tumor Segmentation: A Hybrid Quantum-Classical Approach

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