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arXiv:2605.31006

Quantum State Preparation via Neural Network Encoding in Quantum Machine Learning

Kevin W. Aoun, Florian J. Kiwit, Carlos A. Riofrío, Samer Saab, Charbel Al Bateh, Joe Tekli, Andre Luckow

quant-phSubmitted May 29, 2026• Announced Jun 1, 2026• 0 citations
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Abstract

A central challenge in quantum machine learning is the state preparation bottleneck that describes the prohibitive computational cost of loading high-dimensional classical data into a quantum state. Although amplitude encoding can represent $2^n$-dimensional data using only $n$ qubits in principle, preparing arbitrary states remains computationally expensive, typically requiring variational optimization of a parameterized quantum circuit for each individual data instance. In this work, we propose a method that avoids iterative optimization by training a classical neural network to map input data directly to the continuous parameters of a fixed quantum circuit. We demonstrate the generation of quantum image states with high fidelity on data not seen during training. Since all optimization is performed once during training, the resulting model encodes new inputs in a single inference step, providing a scalable pathway for data loading in near-term quantum algorithms. We validate our method on the MNIST and Fashion-MNIST datasets, achieving fidelities up to 0.992 on unseen images and reducing the per-data-instance runtime by more than 5000-fold.

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arXiv:2408.05435•Aug 10, 2024•0 citations
A central challenge in quantum machine learning is the state preparation bottleneck that describes the prohibitive computational cost of loading high-dimensional classical data into a quantum state. Although amplitude encoding can represent 2n2^n2n-dimensional data using only nnn qubits in principle, preparing arbitrary states remains computationally expensive, typically requiring variational optimization of a parameterized quantum circuit for each individual data instance. In this work, we propose a method that avoids iterative optimization by training a classical neural network to map input data directly to the continuous parameters of a fixed quantum circuit. We demonstrate the generation of quantum image states with high fidelity on data not seen during training. Since all optimization is performed once during training, the resulting model encodes new inputs in a single inference step, providing a scalable pathway for data loading in near-term quantum algorithms. We validate our method on the MNIST and Fashion-MNIST datasets, achieving fidelities up to 0.992 on unseen images and reducing the per-data-instance runtime by more than 5000-fold.
Quantum machine learning (QML) has demonstrated the potential to outperform classical machine learning algorithms in various fields. However, encoding classical data into quantum states, known as quantum data loading, remains a challenge. Existing methods achieve high accuracy in loading single data, but lack efficiency for large-scale data loading tasks. In this work, we propose Neural Circuit Parameter Prediction, a novel method that leverages classical deep neural networks to predict the parameters of parameterized quantum circuits directly from the input data. This approach benefits from the batch inference capability of neural networks and improves the accuracy of quantum data loading. We introduce real-valued parameterization of quantum circuits and a three-phase training strategy to further enhance training efficiency and accuracy. Experimental results on MNIST dataset show that our method achieves a 17.31 % improvement in infidelity score and 108 times faster runtime compared to existing methods. Our approach provides an efficient solution for quantum data loading, enabling the practical deployment of QML algorithms on large-scale datasets.
Abstract Quantum machine learning (QML) is an emerging field that investigates the capabilities of quantum computers for learning tasks. While QML models can theoretically offer advantages such as exponential speed-ups, challenges in data loading and the ability to scale to relevant problem sizes have prevented demonstrations of such advantages on practical problems. In particular, the encoding of arbitrary classical data into quantum states usually comes at a high computational cost, either in terms of qubits or gate count. However, real-world data typically exhibits some inherent structure (such as image data) which can be leveraged to load them with a much smaller cost on a quantum computer. This work further develops an efficient algorithm for finding low-depth quantum circuits to load classical image data as quantum states. To evaluate its effectiveness, we conduct systematic studies on the MNIST, Fashion-MNIST, CIFAR-10, and Imagenette datasets. The corresponding circuits for loading the full large-scale datasets are available publicly as PennyLane datasets and can be used by the community for their own benchmarks. We further analyze the performance of various quantum classifiers, such as quantum kernel methods, parameterized quantum circuits, and tensor-network classifiers, and we compare them to convolutional neural networks. In particular, we focus on the performance of the quantum classifiers as we introduce nonlinear functions of the input state, e.g. by letting the circuit parameters depend on the input state.
Numerous quantum algorithms assume that classical data has already been converted into quantum states, a process known as Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that scales exponentially with the number of qubits, posing a significant challenge to realizing quantum advantage. Recent research explores Parameterized Quantum Circuits (PQCs) as an approximate alternative, offering improved scalability with reduced circuit depth. However, the iterative, state-by-state optimization required by this approach creates substantial runtime overhead, which severely limits its practicality.To improve the efficiency of approximate QSP, we introduce a novel two-stage framework that can potentially generate QSP circuits for arbitrary quantum states. In theoffline training stage, our model learns a direct mapping from target states to circuit parameters, thereby bypassing the need foronline, state-by-state optimizationduring theinference stage. Extensive evaluations show that our approach significantly reduces runtime overhead by up to 132×, making a steady step towards efficient neural approximate QSP.
Quantum machine learning for classical data is currently perceived to have a scalability problem due to (i) a bottleneck at the point of loading data into quantum states, (ii) the lack of clarity around good optimization strategies, and (iii) barren plateaus that occur when the model parameters are randomly initialized. In this work, we propose techniques to address all of these issues. First, we present a quantum classifier that encodes both the input and the output as binary strings which results in a model that has no restrictions on expressivity over the encoded data but requires fast classical compression of typical high-dimensional datasets to only the most predictive degrees of freedom. Second, we show that if one parameter is updated at a time, quantum models can be trained without using a classical optimizer in a way that guarantees convergence to a local minimum, something not possible for classical deep learning models. Third, we propose a parameter initialization strategy called sub-net initialization to avoid barren plateaus where smaller models, trained on more compactly encoded data with fewer qubits, are used to initialize models that utilize more qubits. Along with theoretical arguments on efficacy, we demonstrate the combined performance of these methods on subsets of the MNIST dataset for models with an all-to-all connected architecture that use up to 16 qubits in simulation. This allows us to conclude that the loss function consistently decreases as the capability of the model, measured by the number of parameters and qubits, increases, and this behavior is maintained for datasets of varying complexity. Together, these techniques offer a coherent framework for scalable quantum machine learning.
Quantum machine learning has established as an interdisciplinary field to overcome limitations of classical machine learning and neural networks. This is a field of research which can prove that quantum computers are able to solve problems with complex correlations between inputs that can be hard for classical computers. This suggests that learning models made on quantum computers may be more powerful for applications, potentially faster computation and better generalization on less data. The objective of this paper is to investigate how training of quantum neural network (QNNs) can be done using quantum optimization algorithms for improving the performance and time complexity of QNNs. A classical neural network can be partially quantized to create a hybrid quantum-classical neural network which is used mainly in classification and image recognition. In this paper, a QNN structure is made where a variational parameterized circuit is incorporated as an input layer named as Variational Quantum Neural Network (VQNNs). We encode the cost function of QNNs onto relative phases of a superposition state in the Hilbert space of the network parameters. The parameters are tuned with an iterative quantum approximate optimisation (QAOA) mixer and problem hamiltonians. VQNNs is experimented with MNIST digit recognition (less complex) and crack image classification datasets (more complex) which converges the computation in lesser time than QNN with decent training accuracy.
Numerous quantum algorithms operate under the assumption that classical data has already been converted into quantum states, a process termed Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that scales exponentially with the number of qubits, making it a substantial obstacle in harnessing quantum advantage. Recent research suggests using a Parameterized Quantum Circuit (PQC) to approximate a target state, offering a more scalable solution with reduced circuit depth compared to precise QSP. Despite this, the need for iterative updates of circuit parameters results in a lengthy runtime, limiting its practical application. In this work, we demonstrate that it is possible to leverage a pre-trained neural network to directly generate the QSP circuit for arbitrary quantum state, thereby eliminating the significant overhead of online iterations. Our study makes a steady step towards a universal neural designer for approximate QSP.