Magnitude Is All You Need? Rethinking Phase in Quantum Encoding of Complex SAR Data

Sakthi Prabhu Gunasekar; Prasanna Kumar Rangarajan

quant-phApr 14, 2026

Magnitude Is All You Need? Rethinking Phase in Quantum Encoding of Complex SAR Data

Authors: Sakthi Prabhu Gunasekar, Prasanna Kumar Rangarajan

Organizations: Dept. of Computer Science & Engineering, Amrita School of Computing, Amrita Vishwa Vidyapeetham, India

Abstract

Synthetic Aperture Radar (SAR) data is inherently complex-valued, while quantum machine learning (QML) models operate in complex Hilbert spaces. This similarity suggests that using both the magnitude and phase of SAR data in quantum encoding should help automatic target recognition in SAR images. In this study, we test this assumption by comparing five encoding strategies for quantum models: magnitude-only encoding, joint magnitude-phase encoding, in-phase and quadrature encoding, preprocessed phase encoding, and a purely quantum architecture. All approaches are evaluated under a unified experimental setup on the MSTAR benchmark dataset. Surprisingly, we find that magnitude-only encoding performs better than phase-inclusive encodings in hybrid quantum-classical models. It achieves 99.57 percent accuracy on the 3-class task and 71.19 percent accuracy on the 8-class task, outperforming complex-valued alternatives under the same framework. Adding phase information provides little or no improvement and can sometimes degrade performance. However, in purely quantum models with only 184 to 224 trainable parameters and no classical neural-network layers, phase information becomes much more important, improving accuracy by up to 21.65 percentage points. These findings show that the usefulness of phase information depends not only on the data, but also on the architecture used to process it. Hybrid models can compensate for missing phase information through their classical components, while pure quantum models rely more strongly on phase information for class discrimination. The results provide practical guidance for encoding complex-valued data in quantum machine learning and highlight the importance of jointly designing encoding strategies and model architectures for current quantum systems.

Figures & tables

Panel of Figure 1 — Fig. 1: Quantum circuit diagrams for key encoding strategies. (a) S1: Magnitude-only with $R_{y}$ rotations on 6 qubits with data reuploading. (b) S3: I/Q encoding with $R_{y}(I)$ and $R_{z}(Q)$ on the same qubit. (c) S5: Phase VQC with full data reuploading across 8 sub-layers per variational layer.

Hybrid Architecture — MagQT (S1)
Component	Qubits	Layers	Q. Params	C. Params	Total
Patch encoder	6	2	12	3,676	3,688
Transformer	–	1	–	50,112	50,112
Classifier	–	–	–	4,355	4,355
Total	6		12	$\sim$ 58K	$\sim$ 58K
Dual-Path Architecture (S4)

TABLE I: Quantum resource and parameter comparison across architectures.

Panel of Figure 3 — Fig. 2: Unified architecture overview. (a) Hybrid quantum-classical architecture (MagQT) supporting S1–S3 via swappable encoding. (b) Dual-path architecture (S4) with separate magnitude and phase quantum pathways. (c) Pure quantum architecture (S5) with zero classical parameters. Dimensions shown in blue.

Setting	Classes	Train	Test
3-Class	3	1,296	1,409
8-Class (balanced)	8	1,864	3,086

TABLE II: Dataset configuration for both classification tasks.

Fig. 3: MSTAR SAR samples for all 8 classes (ROI 64 $\times$ 64 center crop). Top row: magnitude images showing distinct target structures. Bottom row: corresponding phase images, which appear noisy and visually indistinguishable across classes, motivating our investigation into whether quantum models can extract discriminative features from phase.

Strategy	Type	Params	3C Acc(%)	8C Acc(%)	$\Delta_{3C}(\%)$	$\Delta_{8C}$ (%)
S1: MagQT	Hybrid QT	58K	99.57	71.19	+0.00	+0.03
S4: Dual-path	Hybrid QT	61K	91.00	64.45	+0.07	-0.03
S3: I/Q Encoding	Hybrid QT	59K	89.00	53.37	+0.21	-0.13
S5: Pure Quantum	Pure Q	184/224	70.62	37.01	+11.50	+21.65
S2: Joint Complex	Hybrid QT	59K	67.49	59.10	+1.30	-0.60

TABLE III: Performance comparison of encoding strategies on MSTAR dataset. Hybrid QT denotes a hybrid quantum-classical transformer.

Method	Type	Params	Acc (%)	Notes
Classical Methods (10-class)
ResNet [ 23 ]	CNN	$\sim$ 11M	99.67	Center+softmax loss
MS-CNN [ 22 ]	Transfer	$\sim$ 5M	98.83	Transfer learning
A-ConvNets [ 15 ]	CNN	$\sim$ 303K	99.13	Lightweight SAR CNN
Atrous-Inception	CNN	$\sim$ 3M	97.97	Inception variant
Our Quantum Methods (10-class)

TABLE IV: Comparison with classical methods on MSTAR (SOC, 17 ∘

\to

15 ∘ ).

Architecture	$\Delta_{\text{phase}}$ (3C)	$\Delta_{\text{phase}}$ (8C)
Hybrid QT (MagQT)	$\approx 0\%$	$\approx 0\%$
Pure Q	$+11.50\%$	$+21.65\%$

TABLE V: Phase contribution across architectural paradigms.

Strategy	Type	Params	Test Acc	$\Delta_{\text{phase}}$
S1: MagQT	Hybrid QT	58K	69.57%	+1.12%
S4: Dual-path	Hybrid QT	61K	61.92%	+0.52%
S1: Balanced	Hybrid QT	59K	57.35%	-0.06%

TABLE VI: Results on full 10-class MSTAR task.

Fig. 4: Phase contribution across architectures and encoding strategies. In hybrid quantum-classical models, phase contributions remain small, negligible, or negative and do not outperform magnitude-only encoding. In purely quantum models, phase becomes essential, contributing +11.50% (3-class) and +21.65% (8-class). This reveals that phase utility is architecture-dependent, not data-dependent.

SAR ATR

See all 13 papers

May 23, 2026

A Matched Spectral Benchmark of Quantum Inspired Feature Maps

Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed data-encoding map. Amplitude, angle, and basis encoding are evaluated as deterministic feature maps for classical supervised learning under matched output dimensionality and strong classical controls. The benchmark compares these encodings against raw linear models, random Fourier features, polynomial features, PCA, RBF SVMs, and shallow neural networks across diverse classical datasets. Rather than treating performance as a single endpoint, we analyze the geometry of each representation through effective rank, condition number, centered kernel alignment, predictive performance, and practical overhead. The resulting picture is mechanistic: amplitude encoding can remove magnitude information through unit-sphere normalization, angle encoding can become geometrically redundant with raw linear features, and basis encoding can impose a binary Hamming geometry that is poorly aligned with smooth decision structure. These findings do not argue against quantum computation, however, they show that fixed quantum-inspired encoding geometry alone is not a reliable source of machine-learning advantage on classical data.

Toheeb Ogunade, Taofeek Kassim, Etinosa Osaro

Department of Computer Science, University of Lagos, Lagos, Nigeria · Department of Physics, University of Lagos, Lagos, Nigeria · Department of Chemical Engineering, University of Notre Dame, Indiana, USA

Quantum Feature Maps Quantum Machine Learning Quantum-Inspired ML Quantum Data Encoding

Ask PDF

Oct 17, 2026

Margin-Based Generalization for Quantum Machine Learning with Classical Data Encoding

Understanding generalization is essential for assessing the practical viability of quantum machine learning. In many applications, quantum models operate on classical data that must first be encoded into quantum states, making the encoding part of the effective hypothesis class. We develop a margin-based generalization framework for this setting, covering both fixed and trainable quantum data encodings. For fixed encodings, the existing margin bound transfers unchanged. For trainable encodings, we derive a bound using a two-scale covering argument that combines the original margin-dependent term with an additive encoding-capacity term of order

\tilde O(\sqrt{L/m})

, where

L

is the number of trainable encoding parameters and

m

is the training-sample size. Across 19,440 simulated training runs spanning various image datasets, circuit architectures, and optimization settings, the inverse margin performs best among five baseline and two bound-derived complexity measures under conditional-independence and 90th-percentile sign-error criteria, within bootstrap uncertainty. These results provide a unified margin-based view of generalization in quantum machine learning with classical data.

Ju-Young Ryu, Tak Hur, Daniel K. Park

Korea Institute of Science and Technology Information, Republic of Korea · Department of Statistics and Data Science, Yonsei University, Republic of Korea · Department of Applied Mathematics, University of Waterloo, Canada +2

Quantum Machine Learning Generalization Bounds Quantum Data Encoding

Ask PDF

Sep 25, 2026

Learned Compression of SAR Phase-History Data: A Rate-Honest Feasibility Study on GOTCHA

On-board compression of synthetic aperture radar (SAR) phase history is bandwidth-critical, and block-adaptive quantization (BAQ) remains the operational standard. We test whether a small convolutional autoencoder, with its encoder on the sensor, can compete with BAQ on complex phase-history patches from the AFRL GOTCHA collection. Every method is charged for all transmitted bits, rates are reported in bits per complex sample (b/cs), and detection is scored by one-to-one matching of CA-CFAR detections. The autoencoder (28,656 encoder parameters) loses at every rate. At 16 b/cs it reaches -2.87 dB NMSE, against -35.5 dB for 8-bit BAQ with

\pm 3σ

clipping and -41.0 dB with a tuned clipping range. It also loses to a

16 \times 16

block Karhunen-Loève transform (KLT), a local linear coder with a tenth of its encoder cost (-5.39 dB). Running the network in a companded Fourier domain helps, but its detection F1 remains bounded at 33%. The evidence points to this model, its normalization, and its objective, not to a fundamental limit of learned coding. Per patch, the data have modest lag-1 coherence (

|ρ| \approx 0.3

) and patch-specific spectral concentration. Two findings concern evaluation itself. First, 97% of CFAR crossings on raw

64 \times 64

patches are border artifacts of the zero-padded detector. Second, on interior cells BAQ's clipping range decides detection: 8-bit BAQ keeps 69% F1 with tuned clipping but 17% at

\pm 3σ

, and at 8 b/cs or less adaptive FFT thresholding preserves more detections than BAQ. We close with an evaluation protocol for learned radar compression.

Alizishaan Khatri

Wrynx Inc

Synthetic Aperture Radar Convolutional Autoencoder

Ask PDF

Abstract

SAR ATR

Explore similar work

A Matched Spectral Benchmark of Quantum Inspired Feature Maps

Margin-Based Generalization for Quantum Machine Learning with Classical Data Encoding

Learned Compression of SAR Phase-History Data: A Rate-Honest Feasibility Study on GOTCHA