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.
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.
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.
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.
The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical machine learning. This article suggests a broad architecture that allows the connection between classical data pipelines and quantum algorithms, hybrid quantum-classical models emerge as a promising route to scalable and near-term quantum benefit. At the core of this paradigm lies the Classical-Quantum (CQ) paradigm, in which the qubit states of high-dimensional classical data are encoded using sophisticated classical encoding strategies which encode the data in terms of amplitude and angle of rotation, along with superposition mapping. These techniques allow compression of information exponentially into Hilbert space representations, which, together with reduced sample complexity, allows greater feature expressivity. We also examine variational quantum circuits, quantum gates expressed as trainable variables that run with classical optimizers to overcome decoherence, noise, and gate-depth constraints of the existing Noisy Intermediate-Scale Quantum (NISQ) devices. Experimental comparisons with a Quantum Naive Bayes classifier prove that even small quantum circuits can approximate probabilistic inference with competitive accuracy compared to classical benchmarks, and have much better robustness to noisy data distributionsThis model does not only explain the algorithmic and architectural design of QML, it also offers a roadmap to the implementation of quantum kernels, variational algorithms, and hybrid feedback loops into practice, including optimization, computer vision, and medical diagnostics. The results support the idea that hybrid architectures with strong data encoding and adaptive error protection are key to moving QML out of theory to practice.
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 2n-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.
Machine learning tasks are an exciting application for quantum computers, as it has been proven that they can learn certain problems more efficiently than classical ones. Applying quantum machine learning algorithms to classical data can have many important applications, as qubits allow for dealing with exponentially more data than classical bits. However, preparing the corresponding quantum states usually requires an exponential number of gates and therefore may ruin any potential quantum speedups. Here, we show that classical data with a sufficiently quickly decaying Fourier spectrum after being mapped to a quantum state can be well-approximated by states with a small Schmidt rank (i.e., matrix-product states) and we derive explicit error bounds. These approximated states can, in turn, be prepared on a quantum computer with a linear number of nearest-neighbor two-qubit gates. We confirm our results numerically on a set of 1024 × 1024 -pixel images taken from the `Imagenette' and DIV2K datasets. Additionally, we consider different variational circuit ansätze and demonstrate numerically that one-dimensional sequential circuits achieve the same compression quality as more powerful ansätze.
A prerequisite for many quantum information processing tasks to truly surpass classical approaches is an efficient procedure to encode classical data in quantum superposition states. In this work, we present a circuit-based flip-flop quantum random access memory to construct a quantum database of classical information in a systematic and flexible way. For registering or updating classical data consisting of M entries, each represented by n bits, the method requires O(n) qubits and O(Mn) steps. With post-selection at an additional cost, our method can also store continuous data as probability amplitudes. As an example, we present a procedure to convert classical training data for a quantum supervised learning algorithm to a quantum state. Further improvements can be achieved by reducing the number of state preparation queries with the introduction of quantum forking.