Shot-Based Quantum Encoding: A Data-Loading Paradigm for Quantum Neural Networks

2026-04-07

AI Summary

This work addresses the limitations of low data encoding efficiency and constrained circuit depth in current quantum machine learning by proposing a novel measurement-shot-based data embedding method. Specifically, the number of shots is treated as a learnable parameter, and initial quantum resources are allocated according to a classical data-driven probability distribution, thereby constructing a mixed-state representation that eliminates the need for explicit encoding gates. This approach, for the first time, incorporates shots directly into the encoding process and is structurally equivalent to a quantum-weight-implemented multilayer perceptron when combined with nonlinear activation functions. Experimental results demonstrate test accuracies of 89.1% ± 0.9% on Semeion and 80.95% ± 0.10% on Fashion MNIST, significantly outperforming conventional amplitude encoding and linear MLP baselines.

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 non-linear activation functions. We show that SBQE is structurally equivalent to a multilayer perceptron whose weights are realised by quantum circuits, and we describe a hardware-compatible implementation protocol. Benchmarks on Fashion MNIST and Semeion handwritten digits, with ten independent initialisations 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) and 80.95% +/- 0.10% on Fashion MNIST (exceeding amplitude encoding by +2.0% and a linear multilayer perceptron by +1.3%), all without any data-encoding gates.

Problem

• quantum machine learning
• data loading
• quantum encoding
• NISQ hardware
• Hilbert space

Innovation

• Shot-Based Quantum Encoding
• quantum data loading
• mixed-state representation
• quantum neural networks
• NISQ hardware