Variational quantum circuits (VQCs) -- parameterised quantum circuits trained by classical optimisation of a quantum cost function -- underpin most near-term quantum machine learning, yet systematic guidance on design choices (ansatz structure, encoding, optimiser, gradient estimation) and their interaction with specific ML task requirements remains fragmented. This paper proposes the Variational Quantum Circuit Design Space (VQCDS) framework, characterising 48 VQC configurations (3 ansatz families x 3 encoding strategies x 4 optimisers) across 12 ML benchmark tasks -- regression, classification, generative modelling, and reinforcement learning -- on IBM Quantum Eagle and IonQ Forte. VQCDS finds: LSAD-structured ansatz (Silva et al., 2024) outperforms hardware-efficient ansatz on 10 of 12 tasks (+8.0pp mean AUC, 2.1x lower variance); amplitude encoding outperforms angle encoding for p > 16 features (+12.4% R2); quantum natural gradient descent (QNG) reduces regression convergence by 48.4% vs. Adam; and task-ansatz alignment via mutual information-guided entanglement provides +8.4pp AUC and +14.4% R2 across task types. VQCDS provides an evidence-based VQC design guide covering 48 configuration evaluations across 12 tasks.
Variational quantum circuits (VQCs) -- parameterised quantum circuits trained by classical optimisation of a quantum cost function -- underpin most near-term quantum machine learning, yet systematic guidance on design choices (ansatz structure, encoding, optimiser, gradient estimation) and their interaction with specific ML task requirements remains fragmented. This paper proposes the Variational Quantum Circuit Design Space (VQCDS) framework, characterising 48 VQC configurations (3 ansatz families x 3 encoding strategies x 4 optimisers) across 12 ML benchmark tasks -- regression, classification, generative modelling, and reinforcement learning -- on IBM Quantum Eagle and IonQ Forte. VQCDS finds: LSAD-structured ansatz (Silva et al., 2024) outperforms hardware-efficient ansatz on 10 of 12 tasks (+8.0pp mean AUC, 2.1x lower variance); amplitude encoding outperforms angle encoding for p > 16 features (+12.4% R2); quantum natural gradient descent (QNG) reduces regression convergence by 48.4% vs. Adam; and task-ansatz alignment via mutual information-guided entanglement provides +8.4pp AUC and +14.4% R2 across task types. VQCDS provides an evidence-based VQC design guide covering 48 configuration evaluations across 12 tasks.
The paradigm of variational quantum classifiers (VQCs) encodes classical information as quantum states, followed by quantum processing and then measurements to generate classical predictions. VQCs are promising candidates for efficient utilizations of noisy intermediate scale quantum (NISQ) devices: classifiers involving M-dimensional datasets can be implemented with only [Formula: see text] qubits by using an amplitude encoding. A general framework for designing and training VQCs, however, is lacking. An encouraging specific embodiment of VQCs, quantum circuit learning (QCL), utilizes an ansatz: a circuit with a predetermined circuit geometry and parametrized gates expressing a time-evolution unitary operator; training involves learning the gate parameters through a gradient-descent algorithm where the gradients themselves can be efficiently estimated by the quantum circuit. The representational power of QCL, however, depends strongly on the choice of the ansatz, as it limits the range of possible unitary operators that a VQC can search over. Equally importantly, the landscape of the optimization problem may have challenging properties such as barren plateaus and the associated gradient-descent algorithm may not find good local minima. Thus, it is critically important to estimate (i) the price of ansatz; that is, the gap between the performance of QCL and the performance of ansatz-independent VQCs, and (ii) the price of using quantum circuits as classical classifiers: that is, the performance gap between VQCs and equivalent classical classifiers. This paper develops a computational framework to address both these open problems. First, it shows that VQCs, including QCL, fit inside the well-known kernel method. Next it introduces a framework for efficiently designing ansatz-independent VQCs, which we call the unitary kernel method (UKM). The UKM framework enables one to estimate the first known computationally-determined bounds on both the price of ansatz and the price of any speedup advantages of VQCs: numerical results with datatsets of various dimensions, ranging from 4 to 256, show that the ansatz-induced gap can vary between 10 and 20[Formula: see text], while the VQC-induced gap (between VQC and kernel method) can vary between 10 and 16[Formula: see text]. To further understand the role of ansatz in VQCs, we also propose a method of decomposing a given unitary operator into a quantum circuit, which we call the variational circuit realization (VCR): given any parameterized circuit block (as for example, used in QCL), it finds optimal parameters and the number of layers of the circuit block required to approximate any target unitary operator with a given precision.
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.
The rapid advancements in quantum computing (QC) and machine learning (ML) have led to the emergence of quantum machine learning (QML), which integrates the strengths of both fields. Among QML approaches, variational quantum circuits (VQCs), also known as quantum neural networks (QNNs), have shown promise both empirically and theoretically. However, their broader adoption is hindered by reliance on quantum hardware during inference. Hardware imperfections and limited access to quantum devices pose practical challenges. To address this, the Quantum-Train (QT) framework leverages the exponential scaling of quantum amplitudes to generate classical neural network parameters, enabling inference without quantum hardware and achieving significant parameter compression. Yet, designing effective quantum circuit architectures for such quantum-enhanced neural programmers remains non-trivial and often requires expertise in quantum information science. In this paper, we propose an automated solution using differentiable optimization. Our method jointly optimizes both conventional circuit parameters and architectural parameters in an end-to-end manner via automatic differentiation. We evaluate the proposed framework on classification, time-series prediction, and reinforcement learning tasks. Simulation results show that our method matches or outperforms manually designed QNN architectures. This work offers a scalable and automated pathway for designing QNNs that can generate classical neural network parameters across diverse applications.
Variational quantum circuits (VQCs) are a leading approach to quantum machine learning on near-term devices, yet it remains unclear which circuit architecture yields the best accuracy-parameter trade-off on classical tabular data. We present a systematic empirical comparison of four VQC families -- multi-layer fully-connected (FC-VQC), residual (ResNet-VQC), hybrid quantum-classical transformer (QT), and fully quantum transformer (FQT) -- across five regression and classification benchmarks. Our key findings are: \textbf{(i)}~FC-VQCs achieve 90-96\% of the R2 of attention-based VQCs while using 40-50\% fewer parameters, and consistently outperform equal-capacity MLPs (mean R2=0.829 vs.\ MLP720's 0.753 on Boston Housing, 3-seed average); \textbf{(ii)}~FC-VQC's Type~4 inter-block connectivity provides partial cross-token mixing that approximates the role of attention -- explicit quantum self-attention yields only marginal gains on most datasets while significantly increasing parameter count; \textbf{(iii)}~expressibility saturates at circuit depth~≈3, explaining why shallow VQCs already cover the Hilbert space effectively; \textbf{(iv)}~LayerNorm on the fully quantum transformer improves classification accuracy, suggesting normalization is important when all operations are quantum; \textbf{(v)}~in our noise study on Boston Housing, FQT degrades gracefully under depolarizing noise while QT collapses. All results are validated across three random seeds. These findings provide practical architectural guidance for deploying VQCs on near-term quantum hardware.
With the advancement of quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid quantum-classical algorithms have emerged as promising approaches for addressing certain machine learning tasks. This study investigates the Variational Quantum Classifier (VQC), a hybrid model that integrates parameterized quantum circuits with classical optimization routines, implemented via IBM’s Qiskit framework. We provide a detailed account of the VQC architecture, including feature encoding, ansatz construction, and optimization methodology. To assess its performance, we conduct a comparative analysis between VQC and classical Support Vector Classifiers (SVC) across synthetic and real-world datasets, including Iris and a binary-filtered version of MNIST. Experimental results reveal that classical models consistently achieve higher accuracy and faster training times. However, the VQC demonstrates functional viability, particularly under noise-free conditions and reduced-dimensionality settings. These findings underscore the current limitations of quantum models while highlighting the potential of VQC as a proof-of-concept for quantum-enhanced learning as quantum hardware matures.
ABSTRACT Recent advancements in Quantum Computing and Machine Learning have increased attention to Quantum Machine Learning (QML), which aims to develop machine learning models by exploiting the quantum computing paradigm. One of the widely used models in this area is the Variational Quantum Circuit (VQC), a hybrid model where the quantum circuit handles data inference while classical optimization adjusts the parameters of the circuit. The quantum circuit consists of an encoding layer, which loads data into the circuit, and a template circuit, known as the ansatz, responsible for processing the data. This work involves performing an analysis by considering both Amplitude‐ and Angle‐encoding models, and examining how the type of rotational gate applied affects the classification performance of the model. This comparison is carried out by training the different models on two datasets, Wine and Diabetes, and evaluating their performance. The study demonstrates that, under identical model topologies, the difference in accuracy between the best and worst models ranges from 10% to 30%, with differences reaching up to 41%. Moreover, the results highlight how the choice of rotational gates used in encoding can significantly impact the model's classification performance. The findings confirm that the embedding represents a hyperparameter for VQC models.