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A Randomized Data Structure for Efficient Quantum Encoding

Johann Maximilian Zollner, Carla Rieger, Martin Werner

Published Nov 3, 2025• 1 citation
Publisher

Abstract

Near-term quantum computers are constrained by limited qubit counts and shallow circuit depth, making them unsuitable for large-scale data processing. To address this challenge, we introduce a framework for randomized data representation that enables the efficient encoding of low-cardinality classical data for quantum circuits, as presented in [12]. Using Bloom filters and fragment-based ensemble learning, our method distributes information on multiple compact quantum circuits to ensure low hardware requirements. The data structure provides the flexibility to trade representation accuracy for representation size. Our evaluation suggests that combining lossy data compression with ensemble-based quantum learning offers a promising direction toward practical quantum machine learning on near-term devices.

DOI
10.1145/3764923.3777404

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Near-term quantum computers are constrained by limited qubit counts and shallow circuit depth, making them unsuitable for large-scale data processing. To address this challenge, we introduce a framework for randomized data representation that enables the efficient encoding of low-cardinality classical data for quantum circuits, as presented in [12]. Using Bloom filters and fragment-based ensemble learning, our method distributes information on multiple compact quantum circuits to ensure low hardware requirements. The data structure provides the flexibility to trade representation accuracy for representation size. Our evaluation suggests that combining lossy data compression with ensemble-based quantum learning offers a promising direction toward practical quantum machine learning on near-term devices.
Abstract Quantum state preparation circuits for loading classical data into quantum computers significantly influence the performance and complexity of variational quantum algorithms within hybrid quantum-classical systems. Since real-world data is often high-dimensional and mapping it to a quantum state is costly and non-trivial, it is transformed on classical computers to overcome limitations regarding quantum register size and circuit complexity. We present a data transformation method using Bloom filters to represent classical data for quantum state preparation circuits. Further, the paper illustrates that tiny fragments of this classical data encoding can be used for quantum machine learning to make an ensemble of the resulting quantum models surprisingly powerful. Due to the representation of the transformed data as a fragmented bit array, the quantum state preparation circuit only relies on a single rotational gate per qubit and small quantum registers. We demonstrate our approach and its representation power in a series of simulations. The simulations indicate that the randomized transformation provides diversity for ensemble models and that even small bit arrays with high error rates in data representation are sufficient for binary classification tasks.
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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 tensor network-based quantum data encoding (TNQE), a circuit-efficient 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 0.04×0.04\times0.04× the depth of amplitude encoding, while naturally scaling to high-resolution images (256×256256 \times 256256×256) and demonstrating practical feasibility on real quantum hardware.
Quantum random access memory (QRAM) is an essential ingredient for many quantum algorithms, such as quantum machine learning models. The quantum resources (qubit counts and circuit depths) required to load classical data into a circuit severely prohibit many reasonably sophisticated demonstrations in the near term. To this end, we propose a method to construct a compact QRAM circuit, leveraging classical preprocessing to design as shallow a circuit with as few auxiliary qubits as possible. The underlying idea is to map data-encoded quantum states into an orthogonal set of quantum states (characterized by a family of parametrized circuits); then one can straightforwardly entangle the data qubits with the address qubits using cnot gates to realize a data-loading QRAM circuit. The nonunitary transformation to convert the orthogonalized quantum states back to the original data-encoded quantum states can be easily achieved with the help of a small set of auxiliary qubits and postselections. Numerical simulations on handwritten digits and Iris data sets are performed to assess the effectiveness of the proposed method, and we also highlight how noise influences quantum circuit performance across diverse configurations using random data sets. The proposed method for constructing a QRAM circuit can potentially facilitate the development and testing of many quantum machine learning methods in the near term.
Abstract Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as “cat states”. We further demonstrate that our approach can efficiently prepare approximate representations of coherent thermal states, wave functions that encode Boltzmann probabilities in their amplitudes. Finally, complementing proposals to characterize the power or usefulness of near-term quantum devices, such as IBM’s quantum volume, we provide a new hardware-independent metric called the qBAS score. It is based on the performance yield in a specific sampling task on one of the canonical machine learning data sets known as Bars and Stripes. We show how entanglement is a key ingredient in encoding the patterns of this data set; an ideal benchmark for testing hardware starting at four qubits and up. We provide experimental results and evaluation of this metric to probe the trade off between several architectural circuit designs and circuit depths on an ion-trap quantum computer.
Abstract Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum kernels are impractical for large datasets as they scale with the square of the dataset size. Here, we measure quantum kernels using randomized measurements. The quantum computation time scales linearly with dataset size and quadratic for classical post-processing. While our method scales in general exponentially in qubit number, we gain a substantial speed-up when running on intermediate-sized quantum computers. Further, we efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth. The encoding is characterized by the quantum Fisher information metric and is related to the radial basis function kernel. Our approach is robust to noise via a cost-free error mitigation scheme. We demonstrate the advantages of our methods for noisy quantum computers by classifying images with the IBM quantum computer. To achieve further speedups we distribute the quantum computational tasks between different quantum computers. Our method enables benchmarking of quantum machine learning algorithms with large datasets on currently available quantum computers.