Efficient methods for encoding and compression are likely to pave the way toward the problem of efficient trainability on higher-dimensional Hilbert spaces, overcoming issues of barren plateaus. Here, we propose an alternative approach to variational autoencoders to reduce the dimensionality of states represented in higher dimensional Hilbert spaces. To this end, we build a variational algorithm-based autoencoder circuit that takes as input a dataset and optimizes the parameters of a Parameterized Quantum Circuit (PQC) ansatz to produce an output state that can be represented as a tensor product of two subsystems by minimizing Tr(ρ2). The output of this circuit is passed through a series of controlled swap gates and measurements to output a state with half the number of qubits while retaining the features of the starting state in the same spirit as any dimension-reduction technique used in classical algorithms. The output obtained is used for supervised learning to guarantee the working of the encoding procedure thus developed. We make use of the Bars and Stripes (BAS) dataset for an 8 × 8 grid to create efficient encoding states and report a classification accuracy of 95% on the same. Thus, the demonstrated example provides proof for the working of the method in reducing states represented in large Hilbert spaces while maintaining the features required for any further machine learning algorithm that follows.
Efficient methods for encoding and compression are likely to pave the way toward the problem of efficient trainability on higher-dimensional Hilbert spaces, overcoming issues of barren plateaus. Here, we propose an alternative approach to variational autoencoders to reduce the dimensionality of states represented in higher dimensional Hilbert spaces. To this end, we build a variational algorithm-based autoencoder circuit that takes as input a dataset and optimizes the parameters of a Parameterized Quantum Circuit (PQC) ansatz to produce an output state that can be represented as a tensor product of two subsystems by minimizing Tr(ρ2). The output of this circuit is passed through a series of controlled swap gates and measurements to output a state with half the number of qubits while retaining the features of the starting state in the same spirit as any dimension-reduction technique used in classical algorithms. The output obtained is used for supervised learning to guarantee the working of the encoding procedure thus developed. We make use of the Bars and Stripes (BAS) dataset for an 8 × 8 grid to create efficient encoding states and report a classification accuracy of 95% on the same. Thus, the demonstrated example provides proof for the working of the method in reducing states represented in large Hilbert spaces while maintaining the features required for any further machine learning algorithm that follows.
Abstract Variational quantum circuits (VQC) lie at the forefront of quantum machine learning research. Still, the use of quantum networks for real data processing remains challenging as the number of available qubits cannot accommodate a large dimensionality of data—if the usual angle encoding scenario is used. To achieve dimensionality reduction, Principal Component Analysis is routinely applied as a pre-processing method before the embedding of the classical features on qubits. In this work, we propose an alternative method which reduces the dimensionality of a given dataset by taking into account the specific quantum embedding that comes after. This method aspires to make quantum machine learning with VQCs more versatile and effective on datasets of high dimension. At a second step, we propose a quantum-inspired classical autoencoder model which can be used to encode information in low latent spaces. The power of our proposed models is exhibited via numerical tests. We show that our targeted dimensionality reduction method considerably boosts VQC’s performance, and we also identify cases for which the second model outperforms classical autoencoders in terms of reconstruction loss.
Implementation of variational Quantum Machine Learning (QML) algorithms on Noisy Intermediate-Scale Quantum (NISQ) devices is known to have issues related to the high number of qubits needed and the noise associated with multi-qubit gates. In this paper, we propose a variational QML algorithm using a dressed quantum network to address these issues. Using the "super compressed encoding" scheme that we follow here, the classical encoding layer in our dressed network drastically scales down the input-dimension, before feeding the input to the variational quantum circuit. Hence, the number of qubits needed in our quantum circuit goes down drastically. Also, unlike in most other existing QML algorithms, our quantum circuit consists only of single-qubit gates, making it robust against noise. These factors make our algorithm suitable for implementation on NISQ hardware. To support our argument, we implement our algorithm on real NISQ hardware and thereby show accurate classification using popular machine learning data-sets like Fisher's Iris, Wisconsin's Breast Cancer (WBC), and Abalone. Then, to provide an intuitive explanation for our algorithm's working, we demonstrate the clustering of quantum states, which correspond to the input-samples of different output-classes, on the Bloch sphere (using WBC and MNIST data-sets). This clustering happens as a result of the training process followed in our algorithm. Through this Bloch-sphere-based representation, we also show the distinct roles played (in training) by the adjustable parameters of the classical encoding layer and the adjustable parameters of the variational quantum circuit. These parameters are adjusted iteratively during training through loss-minimization.
Abstract Quantum state preparation is a vital routine in many quantum algorithms, including solution of linear systems of equations, Monte Carlo simulations, quantum sampling, and machine learning. However, to date, there is no established framework of encoding classical data into gate-based quantum devices. In this work, we propose a method for the encoding of vectors obtained by sampling analytical functions into quantum circuits that features polynomial runtime with respect to the number of qubits and provides > 99.9 % accuracy, which is better than a state-of-the-art two-qubit gate fidelity. We employ hardware-efficient variational quantum circuits, which are simulated using tensor networks, and matrix product state representation of vectors. In order to tune variational gates, we utilize Riemannian optimization incorporating auto-gradient calculation. Besides, we propose a ‘cut once, measure twice’ method, which allows us to avoid barren plateaus during gates’ update, benchmarking it up to 100-qubit circuits. Remarkably, any vectors that feature low-rank structure—not limited by analytical functions—can be encoded using the presented approach. Our method can be easily implemented on modern quantum hardware, and facilitates the use of the hybrid-quantum computing architectures.
Whether parameterized quantum circuits (PQCs) can be systematically constructed to be both trainable and expressive remains an open question. Highly expressive PQCs often exhibit barren plateaus, while several trainable alternatives admit efficient classical simulation. We address this question by deriving a finite-sample, dimension-independent concentration bound for estimating the variance of a PQC cost function, yielding explicit trainability guarantees. Across commonly used ansätze, we observe an anticorrelation between trainability and expressibility, consistent with theoretical insights. Building on this observation, we propose a property-based ansatz-search framework for identifying circuits that combine trainability and expressibility. We demonstrate its practical viability on a real quantum computer and apply it to variational quantum algorithms. We identify quantum neural network ansätze with improved effective dimension using over 6× fewer parameters, and for VQE on H2 we achieve UCCSD-like accuracy at substantially reduced circuit complexity.
Variational quantum algorithms (VQAs) have emerged as a promising candidate for realizing quantum advantage in machine learning and optimization tasks on noisy intermediate-scale quantum (NISQ) devices. Despite significant theoretical promise, the practical impact of VQAs is constrained by the exponential growth in computational resources required for classical simulation, the onset of barren plateaus in parameterized landscapes, and the inherent difficulties of scaling classical optimization routines to circuits with many qubits and layers. Addressing these intertwined challenges is essential for both advancing quantum algorithm development and extracting actionable physical insights from modern quantum hardware.This dissertation develops, analyzes, and validates an efficient framework based on approximate tensor ring decompositions for the classical simulation, training, and benchmarking of variational quantum circuits and eigensolvers. The first component of this work formalizes the representation of quantum states and gates within a cyclic tensor ring structure, enabling the compression of parameterized quantum circuits to linear scaling in both qubit number and circuit depth, while preserving essential quantum correlations and entanglement structure. Gate operations are efficiently approximated via truncated singular value decomposition, and novel algorithms for forward propagation and gradient-based training in the tensor ring domain are developed. These methodological advances are systematically benchmarked on standard supervised learning tasks, including Iris and MNIST datasets, and compared to conventional statevector and matrix product state baselines, resulting in competitive accuracy and orders-of-magnitude reductions in simulation cost. Extending this framework, the dissertation also introduces a scalable method for gradient evaluation in variational quantum eigensolvers (VQE) using the approximate tensor ring representation. This approach enables the simulation and training of large circuits for combinatorial optimization problems, supporting practical qubit counts and circuit depths inaccessible to traditional simulation methods. Detailed experiments on the Maximum-Cut optimization problem demonstrate both the computational efficiency and robustness of the tensor ring framework in nontrivial optimization landscapes.Collectively, the results establish approximate tensor ring decomposition as a versatile and powerful framework for advancing quantum machine learning and discrete optimization, supporting both pre-deployment benchmarking on classical hardware and algorithm design for next-generation quantum devices. This work provides a foundation for the further exploration of scalable quantum-classical hybrid algorithms, with implications for quantum simulation, optimization, and beyond.
Variational quantum algorithms (VQAs) are the quantum analog of classical neural networks (NNs). A VQA consists of a parameterized quantum circuit (PQC) which is composed of multiple layers of ansatzes (simpler PQCs, which are an analogy of NN layers) that differ only in selections of parameters. Previous work has identified the alternating layered ansatz as potentially a new standard ansatz in near-term quantum computing. Indeed, shallow alternating layered VQAs are easy to implement and have been shown to be both trainable and expressive. In this work, we introduce a training algorithm with an exponential reduction in training cost of such VQAs. Moreover, our algorithm uses classical shadows of quantum input data, and can hence be run on a classical computer with rigorous performance guarantees. We demonstrate 2-3 orders of magnitude improvement in the training cost using our algorithm for the example problems of finding state preparation circuits and the quantum autoencoder.