Shot-based quantum encoding: a data-loading paradigm for quantum neural networks

Basil Kyriacou; Viktoria Patapovich; Maniraman Periyasamy; Alexey Melnikov

quant-phApr 7, 2026

Shot-based quantum encoding: a data-loading paradigm for quantum neural networks

Authors: Basil Kyriacou, Viktoria Patapovich, Maniraman Periyasamy, Alexey Melnikov

Organizations: Terra Quantum AG, 9000 St. Gallen, Switzerland

Abstract

Efficient data loading remains a bottleneck for near-term quantum machine learning. Existing schemes (angle, amplitude, and basis encoding) either underuse the exponential Hilbert-space capacity or require circuit depths that exceed the coherence budgets of noisy intermediate-scale quantum hardware. We introduce shot-based quantum encoding (SBQE), a data embedding strategy that distributes the hardware's native resource, shots, according to a data-dependent classical distribution over multiple initial quantum states. By treating the shot counts as a learnable degree of freedom, SBQE produces a mixed-state representation whose expectation values are linear in the classical probabilities and can therefore be composed with nonlinear activation functions. We show that SBQE is structurally equivalent to a multilayer perceptron whose weights are realized by quantum circuits, and we describe a hardware-compatible implementation protocol. Benchmarks on three image datasets, with 10 independent initializations per model, show that SBQE achieves 89.1% +- 0.9% test accuracy on Semeion (reducing error by 5.3% relative to amplitude encoding and matching a width-matched classical network), 80.95% +- 0.10% on Fashion MNIST (exceeding amplitude encoding by +2.0% and a linear multilayer perceptron by +1.3%), and 90.25% +- 0.18% on MNIST (exceeding amplitude encoding by 2.1 percentage points and the width-matched classical network by 0.3), all without any data-encoding gates.

Figures & tables

Figure 1: Encoding a datum into a mixed state through the learned probability map ( $q=8$ qubits, trained model). For two Fashion-MNIST images of different classes (a trouser and a bag), from left to right: the input image; its $d=8$ principal-component features $\boldsymbol{x}$ ; the learned probability vector $\boldsymbol{p}(\boldsymbol{x})$ over the $2^{8}=256$ computational-basis states [Eq. ( 7 )]; and the induced mixed state $\rho(\boldsymbol{x})=\operatorname{diag}(\boldsymbol{p}(\boldsymbol{x}))=\sum_{j}p_{j}\ket{j}\!\bra{j}$ , which is diagonal in the computational basis. Images of different classes yield distinct probability vectors, and hence distinct mixed states.

Panel of Figure 2 — Figure 2: Learning curves on the Semeion benchmark ( $8$ qubits, $4$ layers). Left panel: cross-entropy loss; right panel: classification error ( $1-$ accuracy). Within each panel, solid lines are training and dashed lines validation, both averaged over 10 runs; shaded bands show one standard deviation, and colors distinguish the three models as in the legend.

Panel of Figure 3 — Figure 3: Learning curves on the Fashion-MNIST benchmark ( $8$ qubits, $4$ layers). Left panel: cross-entropy loss; right panel: classification error ( $1-$ accuracy). Within each panel, solid lines are training and dashed lines validation, both averaged over 10 runs; shaded bands show one standard deviation, and colors distinguish the three models as in the legend.

Panel of Figure 4 — Figure 4: Learning curves on the MNIST benchmark ( $8$ qubits, $4$ layers). Left panel: cross-entropy loss; right panel: classification error ( $1-$ accuracy). Within each panel, solid lines are training and dashed lines validation, both averaged over 10 runs; shaded bands show one standard deviation, and colors distinguish the three models as in the legend.

Panel of Figure 5 — Figure 5: Test accuracy of the SBQE quantum layer (stars) compared with same-shape classical low-rank maps of $\boldsymbol{p}(\boldsymbol{x})$ ( $2^{n_{\mathrm{q}}}\!\to\!n_{\mathrm{q}}$ ) as a function of the mixing layer’s trainable-parameter count ( $n_{\mathrm{q}}=8$ qubits, 4 layers; 10 seeds, best-validation weights). The quantum layer reaches its accuracy with far fewer parameters than a classical map of comparable performance, indicating that the circuit (not the front-end or the PCA reduction) carries the class separation.

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Feb 18, 2026J/K move · Enter open · S save

Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding

Guang Lin, Toshihisa Tanaka, Qibin Zhao

RIKEN Center for Advanced Intelligence Project · Tokyo University of Agriculture and Technology

Quantum Data Encoding Quantum Machine Learning Tensor Networks Quantum Circuit Compilation

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Encoding classical data into quantum states is a central bottleneck in quantum machine learning: many widely used encodings are circuit-inefficient, requiring deep circuits and substantial quantum resources, which limits scalability on quantum hardware. In this work, we propose TNQE, a circuit-efficient quantum data encoding framework built on structured unitary tensor network (TN) representations. TNQE first represents each classical input via a TN decomposition and then compiles the resulting tensor cores into an encoding circuit through two complementary core-to-circuit strategies. To make this compilation trainable while respecting the unitary nature of quantum operations, we introduce a unitary-aware constraint that parameterizes TN cores as learnable block unitaries, enabling them to be directly optimized and directly encoded as quantum operators. The proposed TNQE framework enables explicit control over circuit depth and qubit resources, allowing the construction of shallow, resource-efficient circuits. Across a range of benchmarks, TNQE achieves encoding circuits as shallow as

0.04\times

the depth of amplitude encoding, while naturally scaling to high-resolution images (

256 \times 256

) and demonstrating practical feasibility on real quantum hardware.

Abstract

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