Digital quantum computing promises to offer computational capabilities beyond the reach of classical systems, yet its capabilities are often challenged by scarce quantum resources. A critical bottleneck in this context is how to load classical or quantum data into quantum circuits efficiently. Approximate quantum loaders (AQLs) provide a viable solution to this problem by balancing fidelity and circuit complexity. However, most existing AQL methods are either heuristic or provide guarantees only for specific input types, and a general theoretical framework is still lacking. To address this gap, here we reformulate most AQL methods into a unified framework and establish information-theoretic bounds on their approximation error. Our analysis reveals that the achievable infidelity between the prepared state and target state scales linearly with the total entanglement entropy across subsystems when the loading circuit is applied to the target state. In light of this, we develop AQER, a scalable AQL method that constructs the loading circuit by systematically reducing entanglement in target states. We conduct systematic experiments to evaluate the effectiveness of AQER, using synthetic datasets, classical image and language datasets, and a quantum many-body state datasets with up to 50 qubits. The results show that AQER consistently outperforms existing methods in both accuracy and gate efficiency. Our work paves the way for scalable quantum data processing and real-world quantum computing applications.
Journal reference
Fourteenth International Conference on Learning Representations (ICLR 2026)
Digital quantum computing promises to offer computational capabilities beyond the reach of classical systems, yet its capabilities are often challenged by scarce quantum resources. A critical bottleneck in this context is how to load classical or quantum data into quantum circuits efficiently. Approximate quantum loaders (AQLs) provide a viable solution to this problem by balancing fidelity and circuit complexity. However, most existing AQL methods are either heuristic or provide guarantees only for specific input types, and a general theoretical framework is still lacking. To address this gap, here we reformulate most AQL methods into a unified framework and establish information-theoretic bounds on their approximation error. Our analysis reveals that the achievable infidelity between the prepared state and target state scales linearly with the total entanglement entropy across subsystems when the loading circuit is applied to the target state. In light of this, we develop AQER, a scalable AQL method that constructs the loading circuit by systematically reducing entanglement in target states. We conduct systematic experiments to evaluate the effectiveness of AQER, using synthetic datasets, classical image and language datasets, and a quantum many-body state datasets with up to 50 qubits. The results show that AQER consistently outperforms existing methods in both accuracy and gate efficiency. Our work paves the way for scalable quantum data processing and real-world quantum computing applications.
Efficient encoding of classical data into quantum circuits is a critical challenge that directly impacts the scalability of quantum algorithms. In this work, we present an automated compilation framework for resource-aware quantum data loading tailored to a given input vector and target error tolerance. By explicitly exploiting the trade-off between exact and approximate state preparation, our approach systematically partitions the total error budget between precision and approximation errors, thereby minimizing quantum resource costs. The framework supports a comprehensive suite of state-of-the-art methods, including multiplexer-based loaders, quantum read-only memory (QROM) constructions, sparse encodings, matrix product states (MPS), Fourier series loaders (FSL), and Walsh transform-based diagonal operators. We demonstrate the effectiveness of our framework across several applications, where it consistently uncovers non-obvious, resource-efficient strategies enabled by controlled approximation. In particular, we analyze a computational fluid dynamics workflow where the automated selection of MPS state preparation and Walsh transform-based encoding, combined with a novel Walsh-based measurement technique, leads to resource reductions of over four orders of magnitude compared to previous approaches. We also introduce two independent advances developed through the framework: a more efficient circuit for d-diagonal matrices, and an optimized block encoding for kinetic energy operators. Our results underscore the indispensable role of automated, approximation-aware compilation in making large-scale quantum algorithms feasible on resource-constrained hardware.
Faithfully loading classical data into a quantum system is a core problem in quantum machine learning and various quantum information processing tasks. In this work, we propose an efficient quantum autoencoder architecture that can construct a quantum state approximating the unknown classical distribution with high precision and with only linear circuit depth. Simulation experiments show that our proposed method substantially outperforms state-of-the-art methods on a wide range of datasets by evaluating divergences between the loaded distributions and the target distribution, and it also enjoys a faster convergence rate and stability. Moreover, the proposed scheme can be efficiently implemented on near-term hybrid classical-quantum systems with very shallow circuit depths.
Abstract Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups often predicated on access to an efficient data-loading oracle. In practice, constructing a circuit to prepare a generic n-qubit quantum state typically demands computational efforts scaling as O ( 2 n ) , posing a significant challenge for quantum algorithms to outperform their classical counterparts. To address this critical issue, various hybrid quantum–classical approaches have been proposed. However, many of these solutions favor simplistic circuit architectures, which are susceptible to substantial optimization challenges. In this study, we harness quantum circuits as Born machines to generate probability distributions. Drawing inspiration from methods used to investigate electronic structures in quantum chemistry and condensed matter physics, we propose a framework called Adaptive Circuit Learning of Born Machine, which dynamically expands the ansatz circuit. Our algorithm is designed to selectively integrate two-qubit entangled gates that best capture the intricate entanglement present within the target state. Empirical experiments underscore the efficacy of our approach in encoding real-world data through amplitude embedding, demonstrating not only compliance with but also enhancement over the performance benchmarks set by prior research.
Quantum image computing has attracted attention due to its vast storage and faster processing of image data than classical computers. Although classical computing power has grown substantially in the last decade, its abilities have plateaued, struggling to meet the needs of huge datasets. Quantum computers, on the other hand, take advantage of unique qualities like quantum parallelism, superposition, and entanglement to provide faster solutions to complicated problems. Managing huge image data in classical systems necessitates significant memory and hardware resources, which makes quantum computing a possible alternative. Several approaches have arisen for encoding and compressing classical images in the quantum processor. However, one of the most significant limitations is the complexity of quantum state preparation, which translates pixel coordinates to corresponding quantum circuits. Current approaches for representing large-scale images require a huge number of quantum resources including qubit, and qubit connection, which presents significant hurdles. Therefore, this article aims to overview the pixel intensity and state preparation circuit that needs fewer connections, i.e., quantum gates to represent quantum image data, and then explore and design effective compression and processing methods for medium and high-resolution images. This work specializes in emerging quantum models’ potential for enhancing image representation and compression capabilities. It also conducts a comprehensive study of quantum image representation and compression techniques, categorizing existing methods by grayscale and color image types and evaluating their methods, strengths, and limitations. It focuses on crucial difficulties, such as high qubit requirements and complex state preparation, that limit scalability for huge images. This paper also assesses each model’s compression efficacy, which will help future research focus on efficient circuit designs with lower complexity for medium to high-resolution images. It is an essential reference for advancing quantum image processing research since it provides a systematic framework for evaluating quantum image compression and representation algorithms.
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.
Digital–analog quantum computing (DAQC) offers a promising approach to addressing the challenges of building a practical quantum computer. By efficiently allocating resources between digital and analog quantum circuits, DAQC paves the way for achieving optimal performance. We propose an algorithm designed to enhance the performance of quantum annealing. This method employs a quantum gate to estimate the goodness of the final annealing state and find the ground state of combinatorial optimization problems. We explore two strategies for integrating the quantum annealing circuit into the DAQC framework: (1) state preparation, and (2) embedding within the quantum gate. While the former strategy does not yield performance improvements, we discover that the latter enhances performance within a specific range of annealing time. Algorithms demonstrating enhanced performance utilize the imaginary part of the inner product of two states from different quantum annealing settings. This measure reflects not only the energy of the classical cost function but also the trajectory of the quantum dynamics. This study provides an example of how processing quantum data using a quantum circuit can outperform classical data processing, which discards quantum information.