We present QuCoWE a framework that learns quantumnative word embeddings by training shallow hardwareefficient parameterized quantum circuits PQCs with a contrastive skipgram objective Words are encoded by datareuploading circuits with controlled ring entanglement similarity is computed via quantum state fidelity and passed through a logitfidelity head that aligns scores with the shiftedPMI scale of SGNSNoiseContrastive Estimation To maintain trainability we introduce an entanglementbudget regularizer based on singlequbit purity that mitigates barren plateaus On Text8 and WikiText2 QuCoWE attains competitive intrinsic WordSim353 SimLex999 and extrinsic SST2 TREC6 performance versus 50100d classical baselines while using fewer learned parameters per token All experiments are run in classical simulation we analyze depolarizingreadout noise and include errormitigation hooks zeronoise extrapolation randomized compiling to facilitate hardware deployment
We present QuCoWE a framework that learns quantumnative word embeddings by training shallow hardwareefficient parameterized quantum circuits PQCs with a contrastive skipgram objective Words are encoded by datareuploading circuits with controlled ring entanglement similarity is computed via quantum state fidelity and passed through a logitfidelity head that aligns scores with the shiftedPMI scale of SGNSNoiseContrastive Estimation To maintain trainability we introduce an entanglementbudget regularizer based on singlequbit purity that mitigates barren plateaus On Text8 and WikiText2 QuCoWE attains competitive intrinsic WordSim353 SimLex999 and extrinsic SST2 TREC6 performance versus 50100d classical baselines while using fewer learned parameters per token All experiments are run in classical simulation we analyze depolarizingreadout noise and include errormitigation hooks zeronoise extrapolation randomized compiling to facilitate hardware deployment
Designing parameterized quantum circuits (PQCs) that are expressive, trainable, and robust to hardware noise is a central challenge for quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices. We present a Domain-Aware Quantum Circuit (DAQC) that leverages image priors to guide locality-preserving encoding and entanglement via non-overlapping DCT-style zigzag windows. The design employs interleaved encode-entangle-train cycles, where entanglement is applied among qubits hosting neighboring pixels, aligned to device connectivity. This staged, locality-preserving information flow expands the effective receptive field without deep global mixing, enabling efficient use of limited depth and qubits. The design concentrates representational capacity on short-range correlations, reduces long-range two-qubit operations, and encourages stable optimization, thereby mitigating depth-induced and globally entangled barren-plateau effects. We evaluate DAQC on MNIST, FashionMNIST, and PneumoniaMNIST datasets. On quantum hardware, DAQC achieves performance competitive with strong classical baselines (e.g., ResNet-18/50, DenseNet-121, EfficientNet-B0) and substantially outperforming Quantum Circuit Search (QCS) baselines. To the best of our knowledge, DAQC, which uses a quantum feature extractor with only a linear classical readout (no deep classical backbone), currently achieves the best reported performance on real quantum hardware for QML-based image classification tasks. Code and pretrained models are available at: https://github.com/gurinder-hub/DAQC.
We present a variety of methods for training complex-valued word embeddings, based on the classical Skip-gram model, with a straightforward adaptation simply replacing the real-valued vectors with arbitrary vectors of complex numbers. In a more "physically-inspired" approach, the vectors are produced by parameterised quantum circuits (PQCs), which are unitary transformations resulting in normalised vectors which have a probabilistic interpretation. We develop a complex-valued version of the highly optimised C code version of Skip-gram, which allows us to easily produce complex embeddings trained on a 3.8B-word corpus for a vocabulary size of over 400k, for which we are then able to train a separate PQC for each word. We evaluate the complex embeddings on a set of standard similarity and relatedness datasets, for some models obtaining results competitive with the classical baseline. We find that, while training the PQCs directly tends to harm performance, the quantum word embeddings from the two-stage process perform as well as the classical Skip-gram embeddings with comparable numbers of parameters. This enables a highly scalable route to learning embeddings in complex spaces which scales with the size of the vocabulary rather than the size of the training corpus. In summary, we demonstrate how to produce a large set of high-quality word embeddings for use in complex-valued and quantum-inspired NLP models, and for exploring potential advantage in quantum NLP models.
The public access to noisy intermediate-scale quantum (NISQ) computers facilitated by IBM, Rigetti, D - Wave, etc., has propelled the development of quantum applications that may offer quantum supremacy in the future large-scale quantum computers. Parameterized quantum circuits (P QC) have emerged as a major driver for the development of quantum routines that potentially improve the circuit's resilience to the noise. PQC's have been applied in both generative (e.g. generative adversarial network) and discriminative (e.g. quantum classifier) tasks in the field of quantum machine learning. PQC's have been also considered to realize high fidelity quantum gates with the available imperfect native gates of a target quantum hardware. Parameters of a P QC are determined through an iterative training process for a target noisy quantum hardware. However, temporal variations in qubit quality metrics affect the performance of a P QC. Therefore, the circuit that is trained without considering temporal variations exhibits poor fidelity over time. In this paper, we present training methodologies for P QC in a completely classical environment that can improve the fidelity of the trained P QC on a target NISQ hardware by as much as 21.91%.
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.
This study investigates classification performance and trainability of variational quantum classifiers on near-term noisy quantum hardware across circuit depth and qubit count regimes within the context of quantum computing and machine learning, an area of growing scientific importance given its implications for hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment. Using gradient-based parameter optimization of parameterized quantum circuits with hardware noise modeling via density matrix simulation and physical execution on IBM Eagle processors, we examine expressibility of parameterized circuits enabling nonlinear decision boundaries in feature Hilbert space, with trainability constrained by barren plateau gradients at large qubit counts in 96 circuit architectures (4 qubit counts x 4 depths x 6 ansatz families) evaluated across 5 classification datasets with 20 random initialization seeds each drawn from IBM Quantum Eagle (127-qubit) and Falcon (27-qubit) processors with noise mitigation via zero-noise extrapolation. Results indicate that 10-qubit, 4-layer VQC achieves 84.2% classification accuracy on the best benchmark, within 3.8 percentage points of classical SVM, but gradient variance decays exponentially with qubit count (variance halving per 2 added qubits), confirming barren plateau scaling (p < 0.001), with 84.2% accuracy, 3.8 pp gap to classical SVM baseline as the primary quantitative benchmark. Concordance between primary and confirmatory measurement approaches exceeded 93%, validating the analytical framework. These findings contribute empirically to quantum computing and machine learning and carry actionable implications for the design of programs and policies targeting hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment.
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters via gradient descent. The high cost of training and low fidelity of current quantum devices, however, restricts much of quantum machine learning to classical simulation. For few-qubit problems with large datasets, training the matrix elements directly, as is done with weight matrices in classical neural networks, can be faster than decomposing data and parameters into gates. We propose a method that trains matrices directly while maintaining unitarity through a single regularization term added to the loss function. A second training step, circuit alignment, then recovers a gate-based architecture from the resulting soft-unitary. On a five-qubit supervised classification task with 1000 datapoints, this two-step process produces a trained variational circuit in under four minutes, compared to over two hours for direct circuit training, while achieving lower binary cross-entropy loss. In a second experiment, soft-unitaries are embedded in a hybrid quantum-classical network for a reinforcement learning cartpole task, where the hybrid agent outperforms a purely classical baseline of comparable size.