Variational Quantum Circuits

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Variational quantum circuits use adjustable gate parameters to prepare quantum states or make predictions, with a classical optimizer typically updating those parameters from measured outcomes. Common approaches include hardware-efficient and problem-inspired ansätze, data re-uploading, quantum kernels, and hybrid models for tasks such as classification, forecasting, and molecular simulation. Work studies how circuit depth, entanglement, initialization, gradient methods, and measurement choices affect expressivity and trainability, especially under barren plateaus and hardware noise. Compact circuits have shown promise on selected benchmarks, but broad practical advantage remains unsettled: results depend on task and hardware, and careful comparisons with tuned, capacity-matched classical models are essential.

Latest papers 107

14 papers in the last four weeks, up 75% on the four weeks before. 0.1% of all new papers.

Mar 20, 2026

Layered Quantum Architecture Search for 3D Point Cloud Classification

We introduce layered Quantum Architecture Search (layered-QAS), a strategy inspired by classical network morphism that designs Parametrised Quantum Circuit (PQC) architectures by progressively growing and adapting them. PQCs offer strong expressiveness with relatively few parameters, yet they lack standard architectural layers (e.g., convolution, attention) that encode inductive biases for a given learning task. To assess the effectiveness of our method, we focus on 3D point cloud classification as a challenging yet highly structured problem. Whereas prior work on this task has used PQCs only as feature extractors for classical classifiers, our approach uses the PQC as the main building block of the classification model. Simulations show that our layered-QAS mitigates barren plateau, outperforms quantum-adapted local and evolutionary QAS baselines, and achieves state-of-the-art results among PQC-based methods on the ModelNet dataset.

Natacha Kuete Meli, Jovita Lukasik, Vladislav Golyanik +1

University of Siegen · MPI for Informatics, SIC

Quantum Neural Networks Point Cloud Classification Variational Quantum Circuits Quantum Circuit Trainability

Mar 17, 2026

Hybrid Classical-Quantum Transfer Learning with Noisy Quantum Circuits

Quantum transfer learning combines pretrained classical deep learning models with quantum circuits to reuse expressive feature representations while limiting the number of trainable parameters. In this work, we introduce a family of compact quantum transfer learning architectures that attach variational quantum classifiers to frozen convolutional backbones for image classification. We instantiate and evaluate several classical-quantum hybrid models implemented in PennyLane and Qiskit, and systematically compare them with a classical transfer-learning baseline across heterogeneous image datasets. To ensure a realistic assessment, we evaluate all approaches under both ideal simulation and noisy emulation using noise models calibrated from IBM quantum hardware specifications, as well as on real IBM quantum hardware. Experimental results show that the proposed quantum transfer learning architectures achieve competitive and, in several cases, superior accuracy while consistently reducing training time and energy consumption relative to the classical baseline. Among the evaluated approaches, PennyLane-based implementations provide the most favorable trade-off between accuracy and computational efficiency, suggesting that hybrid quantum transfer learning can offer practical benefits in realistic NISQ era settings when feature extraction remains classical.

D. Martín-Pérez, F. Rodríguez-Díaz, D. Gutiérrez-Avilés +2

Data Science and Big Data Lab, Pablo de Olavide University, Seville, Spain · Department of Computer Science, University of Seville, Seville, Spain

Quantum Machine Learning Hybrid Quantum-Classical ML Image Classification Variational Quantum Circuits

Mar 15, 2026

IQP Born Machines under Data-dependent and Agnostic Initialization Strategies

Quantum circuit Born machines based on instantaneous quantum polynomial-time (IQP) circuits are natural candidates for quantum generative modeling, both because of their probabilistic structure and because IQP sampling is provably classically hard in certain regimes. Recent proposals focus on training IQP-QCBMs using Maximum Mean Discrepancy (MMD) losses built from low-body Pauli-

Z

correlators, but the effect of initialization on the resulting optimization landscape remains poorly understood. In this work, we address this by first proving that the MMD loss landscape suffers from barren plateaus for random full-angle-range initializations of IQP circuits. We then establish lower bounds on the loss variance for identity and an unbiased data-agnostic initialization. We then additionally consider a data-dependent initialization that is better aligned with the target distribution and, under suitable assumptions, yields provable gradients and generally converges quicker to a good minimum (as indicated by our training of circuits with 150 qubits on genomic data). Finally, as a by-product, the developed variance lower bound framework is applicable to a general class of non-linear losses, offering a broader toolset for analyzing warm-starts in quantum machine learning.

Sacha Lerch, Joseph Bowles, Ricard Puig +3

Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland · Centre for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland · Xanadu, Toronto, ON, M5G 2C8, Canada +3

Quantum Machine Learning Quantum Generative Modeling Variational Quantum Circuits Barren Plateaus

Mar 15, 2026

How to find expressible and trainable parameterized quantum circuits?

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 \times

fewer parameters, and for VQE on

\mathrm{H}_2

we achieve UCCSD-like accuracy at substantially reduced circuit complexity.

Peter Röseler, Dennis Willsch, Kristel Michielsen

Jülich Supercomputing Centre, Forschungszentrum Jülich, 52425 Jülich, Germany · Universität zu Köln, 50923 Köln, Germany · Faculty of Medical Engineering and Technomathematics, University of Applied Sciences Aachen, 52428 Jülich, Germany +1

Variational Quantum Circuits Quantum Circuit Trainability Quantum Neural Networks Variational Quantum Algorithms

Feb 27, 2026

Scaling Quantum Machine Learning without Tricks: Full-Resolution and Diverse Image Generation

Quantum generative modeling is a rapidly evolving discipline at the intersection of quantum computing and machine learning. Contemporary quantum machine learning is generally limited to toy examples or heavily restricted datasets with few elements. This is not only due to the current limitations of available quantum hardware but also due to the absence of inductive biases arising from application-agnostic designs. Current quantum solutions must resort to tricks to scale down high-resolution images, such as relying heavily on dimensionality reduction or utilizing multiple quantum models for low-resolution image patches. Building on recent developments in classical image loading to quantum computers, we circumvent these limitations and train quantum Wasserstein GANs on the established classical MNIST and Fashion-MNIST datasets. Using the complete datasets, our system generates full-resolution images across all ten classes and establishes a new state-of-the-art performance with a single end-to-end quantum generator without tricks. As a proof-of-principle, we also demonstrate that our approach can be extended to color images, exemplified on the Street View House Numbers dataset. We analyze how the choice of variational circuit architecture introduces inductive biases, which crucially unlock this performance. Furthermore, enhanced noise input techniques enable highly diverse image generation while maintaining quality. Finally, we show promising results even under quantum shot noise conditions.

Jonas Jäger, Florian J. Kiwit, Carlos A. Riofrío

BMW Group, Munich, Germany · Department of Computer Science and Institute of Applied Mathematics, University of British Columbia (UBC), Vancouver, Canada · Stewart Blusson Quantum Matter Institute (QMI), Vancouver, Canada +1

Quantum Generative Modeling Image Generation Quantum Machine Learning Variational Quantum Circuits Generative Adversarial Networks

Feb 27, 2026

Comparing Classical and Quantum Variational Classifiers on the XOR Problem

Quantum machine learning applies principles such as superposition and entanglement to data processing and optimization. Variational quantum models operate on qubits in high-dimensional Hilbert spaces and provide an alternative approach to model expressivity. We compare classical models and a variational quantum classifier on the XOR problem. Logistic regression, a one-hidden-layer multilayer perceptron, and a two-qubit variational quantum classifier with circuit depths 1 and 2 are evaluated on synthetic XOR datasets with varying Gaussian noise and sample sizes using accuracy and binary cross-entropy. Performance is determined primarily by model expressivity. Logistic regression and the depth-1 quantum circuit fail to represent XOR reliably, whereas the multilayer perceptron and the depth-2 quantum circuit achieve perfect test accuracy under representative conditions. Robustness analyses across noise levels, dataset sizes, and random seeds confirm that circuit depth is decisive for quantum performance on this task. Despite matching accuracy, the multilayer perceptron achieves lower binary cross-entropy and substantially shorter training time. Hardware execution preserves the global XOR structure but introduces structured deviations in the decision function. Overall, deeper variational quantum classifiers can match classical neural networks in accuracy on low-dimensional XOR benchmarks, but no clear empirical advantage in robustness or efficiency is observed in the examined settings.

Miras Seilkhan, Adilbek Taizhanov

Quantum Machine Learning Variational Quantum Circuits Binary Classification

Feb 26, 2026

Long Range Frequency Tuning for QML

Angle-encoded variational quantum circuits admit a truncated Fourier series representation of their output, but approximating functions with maximum frequency

ω_{\max}

using fixed unary encoding requires

\mathcal{O}(ω_{\max})

encoding gates. Trainable-frequency (TF) circuits promise a reduction by learning the data-encoding prefactors alongside the ansatz parameters, adapting the accessible frequency spectrum to the target during training. We identify a practical barrier that prevents this promise from being realized: the prefactor gradient is suppressed by the spectral gap between the circuit's accessible frequencies and the target spectrum, independently of the ansatz parameters, confining gradient-driven prefactor movement to a narrow neighborhood of initialization. We propose ternary grid initialization -- setting prefactors to

\{1, 3, 9, \ldots, 3^{k-1}\}

-- which ensures every target frequency within

[-ω_{\max}, ω_{\max}]

lies within

\tfrac{1}{2}

unit of the accessible spectrum at initialization, so that the spectral-gap bound no longer constrains the target-driven gradient to be small. This is a necessary condition for reliable convergence, whose sufficiency we establish empirically. On a synthetic benchmark with target frequencies shifted well beyond the standard initialization range, ternary initialization achieves median

R^2 = 0.997

versus

0.18

for unary initialization, with

100\%

of runs achieving

R^2 > 0.95

against

0\%

. CMA-ES with

20\times

the evaluation budget reaches only

25\%

success, confirming the limitation is a property of the optimization landscape rather than of gradient-based optimization specifically. Real-world validation on two benchmark datasets demonstrates consistent advantages over both fixed and trainable unary baselines.

Michael Poppel, Markus Baumann, Sebastian Wölckert +2

LMU Munich & Aqarios GmbH, Munich, Germany · LMU Munich, Munich, Germany

Quantum Machine Learning Variational Quantum Circuits Quantum Circuit Trainability

Feb 19, 2026

Quantum Scrambling Born Machine

Quantum generative modeling, where the Born rule naturally defines probability distributions through measurement of parameterized quantum states, is a promising near-term application of quantum computing. We propose a Quantum Scrambling Born Machine in which a fixed entangling unitary -- acting as a scrambling reservoir -- provides multi-qubit entanglement, while only single-qubit rotations are optimized. We consider three entangling unitaries -- a Haar random unitary and two physically realizable approximations, a finite-depth brickwork random circuit and analog time evolution under nearest-neighbor spin-chain Hamiltonians -- and show that, for the benchmark distributions and system sizes considered, once the entangler produces near-Haar-typical entanglement the model learns the target distribution with weak sensitivity to the scrambler's microscopic origin. Finally, promoting the Hamiltonian couplings to trainable parameters casts the generative task as a variational Hamiltonian problem, with performance competitive with representative classical generative models at matched parameter count.

Marcin Płodzień

Qilimanjaro Quantum Tech, Carrer de Veneçuela 74, 08019 Barcelona, Spain

Quantum Generative Modeling Variational Quantum Circuits

Feb 18, 2026

Illustration of Barren Plateaus in Quantum Computing

Variational Quantum Circuits (VQCs) have emerged as a promising paradigm for quantum machine learning in the NISQ era. While parameter sharing in VQCs can reduce the parameter space dimensionality and potentially mitigate the barren plateau phenomenon, it introduces a complex trade-off that has been largely overlooked. This paper investigates how parameter sharing, despite creating better global optima with fewer parameters, fundamentally alters the optimization landscape through deceptive gradients -- regions where gradient information exists but systematically misleads optimizers away from global optima. Through systematic experimental analysis, we demonstrate that increasing degrees of parameter sharing generate more complex solution landscapes with heightened gradient magnitudes and measurably higher deceptiveness ratios. Our findings reveal that traditional gradient-based optimizers (Adam, SGD) show progressively degraded convergence as parameter sharing increases, with performance heavily dependent on hyperparameter selection. We introduce a novel gradient deceptiveness detection algorithm and a quantitative framework for measuring optimization difficulty in quantum circuits, establishing that while parameter sharing can improve circuit expressivity by orders of magnitude, this comes at the cost of significantly increased landscape deceptiveness. These insights provide important considerations for quantum circuit design in practical applications, highlighting the fundamental mismatch between classical optimization strategies and quantum parameter landscapes shaped by parameter sharing.

Gerhard Stenzel, Tobias Rohe, Michael Kölle +3

LMU Munich

Variational Quantum Circuits Quantum Circuit Trainability Barren Plateaus

Feb 18, 2026

Reinforcement Learning for Parameterized Quantum State Preparation: A Comparative Study

We extend directed quantum circuit synthesis (DQCS) with reinforcement learning from purely discrete gate selection to parameterized quantum state preparation with continuous single-qubit rotations

R_x

,

R_y

, and

R_z

. We compare two training regimes: a one-stage agent that jointly selects the gate type, the affected qubit(s), and the rotation angle; and a two-stage variant that first proposes a discrete circuit and subsequently optimizes the rotation angles with Adam using parameter-shift gradients. Using Gymnasium and PennyLane, we evaluate Proximal Policy Optimization (PPO) and Advantage Actor--Critic (A2C) on systems comprising two to ten qubits and on targets of increasing complexity with

λ

ranging from one to five. Whereas A2C does not learn effective policies in this setting, PPO succeeds under stable hyperparameters (one-stage: learning rate approximately

5\times10^{-4}

with a self-fidelity-error threshold of 0.01; two-stage: learning rate approximately

10^{-4}

). Both approaches reliably reconstruct computational basis states (between 83% and 99% success) and Bell states (between 61% and 77% success). However, scalability saturates for

λ

of approximately three to four and does not extend to ten-qubit targets even at

λ=2

. The two-stage method offers only marginal accuracy gains while requiring around three times the runtime. For practicality under a fixed compute budget, we therefore recommend the one-stage PPO policy, provide explicit synthesized circuits, and contrast with a classical variational baseline to outline avenues for improved scalability.

Gerhard Stenzel, Isabella Debelic, Michael Kölle +4

LMU Munich Department of Computer Science Chair of Mobile and Distributed Systems

Quantum State Preparation Quantum RL Variational Quantum Circuits

Feb 6, 2026

Quantum Attention by Overlap Interference: Predicting Classical and Many-Body Quantum Sequences

We propose a variational quantum implementation of self-attention (QSA)-the core operation in transformers and large language models-which predicts future elements of a sequence by forming overlap-weighted combinations of past data. At variance with previous approaches, our QSA realizes the required nonlinearity through interference of state overlaps and a degree-

k

polynomial kernel, and estimates a loss based on Rényi-

1/2

entropic functionals via two observables' expectation values, avoiding the decoding of amplitude-encoded predictions into classical probabilities. QSA also accommodates a constrained, trainable data-embedding tying state overlaps to data-level similarities. Its dominant end-to-end training complexity scales as

O\left(μ^{-1}k^2Td\right)

, versus

O\left(T d^{k+1}\right)

of the fairest classical comparison, with

μ

a training signal; we show numerically that this allows a complexity advantage in the regime where sequence length

T

dominates the embedding size

d

. In simulations, our QSA-based quantum transformer learns sequence prediction on classical data and on many-body transverse-field Ising trajectories-establishing trainable attention as a practical primitive for quantum dynamical modeling.

Alessio Pecilli, Matteo Rosati

Dipartimento di Ingegneria Civile, Informatica e delle Tecnologie Aeronautiche, Universit`a degli Studi Roma Tre, Via della Vasca Navale 79, 00146 Rome, Italy

Self-Attention Transformer Attention Variational Quantum Circuits Attention Mechanisms Sequence Modeling Quantum Neural Networks

Jan 17, 2026

Trainability-Oriented Hybrid Quantum Regression via Geometric Preconditioning and Curriculum Optimization

Quantum neural networks (QNNs) have attracted growing interest for scientific machine learning, yet in regression settings they often suffer from limited trainability under noisy gradients and ill-conditioned optimization. We propose a hybrid quantum--classical regression framework designed to mitigate these bottlenecks. Our model prepends a lightweight classical embedding that acts as a learnable geometric preconditioner, reshaping the input representation to better condition a downstream variational quantum circuit. Building on this architecture, we introduce a curriculum optimization protocol that progressively increases circuit depth and transitions from SPSA-based stochastic exploration to Adam-based gradient fine-tuning. We evaluate the approach on PDE-informed regression benchmarks and standard regression datasets under a fixed training budget in a simulator setting. Empirically, the proposed framework consistently improves over pure QNN baselines and yields more stable convergence in data-limited regimes. We further observe reduced structured errors that are visually correlated with oscillatory components on several scientific benchmarks, suggesting that geometric preconditioning combined with curriculum training is a practical approach for stabilizing quantum regression.

Qingyu Meng, Yangshuai Wang

Shanghai Jiao Tong University-Chongqing Institute of Artificial Intelligence, Chongqing 401329, China. · Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore.

Quantum Machine Learning Hybrid Quantum-Classical ML Curriculum Learning Variational Quantum Circuits Quantum Circuit Trainability

Dec 10, 2025

Graph-Based Bayesian Optimization for Quantum Circuit Architecture Search with Uncertainty Calibrated Surrogates

Quantum circuit design is a key bottleneck for practical quantum machine learning on complex, real-world data. We present an automated framework that discovers and refines variational quantum circuits (VQCs) using graph-based Bayesian optimization with a graph neural network (GNN) surrogate. Circuits are represented as graphs and mutated and selected via an expected improvement acquisition function informed by surrogate uncertainty with Monte Carlo dropout. Candidate circuits are evaluated with a hybrid quantum-classical variational classifier on the next generation firewall telemetry and network internet of things (NF-ToN-IoT-V2) cybersecurity dataset, after feature selection and scaling for quantum embedding. We benchmark our pipeline against an MLP-based surrogate, random search, and greedy GNN selection. The GNN-guided optimizer consistently finds circuits with lower complexity and competitive or superior classification accuracy compared to all baselines. Robustness is assessed via a noise study across standard quantum noise channels, including amplitude damping, phase damping, thermal relaxation, depolarizing, and readout bit flip noise. The implementation is fully reproducible, with time benchmarking and export of best found circuits, providing a scalable and interpretable route to automated quantum circuit discovery.

Prashant Kumar Choudhary, Nouhaila Innan, Muhammad Shafique +1

Department of Physics, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India · eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, UAE · Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, NYUAD, Abu Dhabi, UAE

Bayesian Optimization Variational Quantum Circuits

Nov 13, 2025

A Versatile Variational Quantum Kernel Framework for Non-Trivial Classification

Quantum kernel methods are a promising branch of quantum machine learning, but their per- formance across data types and encoding choices remains incompletely understood. To address this gap, we developed an algorithmic framework for variational quantum kernels utilizing resource- efficient ansätze for complex classification tasks and introduced a parameter scaling technique to accelerate convergence. We conducted a comprehensive benchmark of this framework on eight chal- lenging, real-world and high-dimensional datasets covering tabular, image, time series, and graph data. Our results show that the proposed quantum kernel demonstrated competitive classification accuracy compared to standard classical kernels in classical simulation, such as the radial basis function (RBF) kernel. This work demonstrates that properly designed quantum kernels can func- tion as versatile, high-performance tools, laying a foundation for quantum-enhanced applications in machine learning. Further research is needed to fully assess the practical performance of quantum methods.

Jiang Yuhan, Matthew Otten

Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA · Department of Chemistry, University of Wisconsin–Madison, Madison, WI 53706, USA

Quantum Kernel Methods Variational Quantum Circuits Quantum Feature Maps

Sep 17, 2025

Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks

Variational quantum circuits (VQCs) are central to quantum machine learning, while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power of learnable activation functions. We unify these directions by introducing the quantum variational activation function (QVAF), a general framework in which parameterized quantum circuits serve as learnable activation functions; in this work we study an efficient single-qubit instantiation called DatA Re-Uploading ActivatioN (DARUAN). We show that DARUAN with trainable data-preprocessing weights can realize an exponentially growing accessible frequency support with the number of re-uploading repetitions; for an explicit geometric choice of these weights, this gives a capacity-level exponential parameter reduction relative to independently parameterized Fourier activations. Embedding DARUAN into KAN yields the quantum-inspired Kolmogorov-Arnold Network (QKAN), which retains the interpretability of the KAN architecture while improving parameter efficiency, expressivity, and generalization. We further introduce layer extension and the hybrid QKAN (HQKAN) architecture to improve scalability and computational efficiency, enabling QKAN modules to act as compact replacements for multi-layer perceptrons (MLPs) in large-scale models. We provide theoretical analysis and extensive experiments on function regression, image classification, and autoregressive generative language modeling, demonstrating the efficiency and scalability of QKANs. Because the single-qubit circuits are efficiently simulable on classical quantum simulators, QKANs have quantum-inspired advantage in parameter efficiency and training stability; DARUANs and QKANs serve as present-day validation of the QVAF concept, and the trained DARUANs are directly executable and feasible on current noisy intermediate-scale quantum (NISQ) hardware for inference validation.

Jiun-Cheng Jiang, Morris Yu-Chao Huang, Tianlong Chen +1

Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei 106319, Taiwan · Physics Division, National Center for Theoretical Sciences, National Taiwan University, Taipei 106319, Taiwan · Department of Computer Science, University of North Carolina at Chapel Hill, NC 27514, USA +1

Quantum Machine Learning Quantum-Inspired ML Kolmogorov-Arnold Networks Variational Quantum Circuits

Apr 5, 2025

Quantum Adaptive Self-Attention for Quantum Transformer Models

A recurring weakness in quantum machine learning (QML) is that reported ``quantum advantages'' are seldom tested against a capacity-matched classical control, leaving it unclear whether a gain comes from the quantum substrate or from the architectural change that accompanies it. Our primary contribution is methodological: a protocol for attributing such gains honestly -- a capacity-matched classical bottleneck of identical parameter budget, transparent reporting of where quantum does not help, and validation on real quantum hardware -- which we develop and apply through a concrete case study. That case study is Quantum Adaptive Self-Attention (QASA), a hybrid Transformer that replaces the value projection of a single encoder layer with a 36-parameter parameterized quantum circuit (PQC), keeping all other layers classical. Across nine synthetic benchmarks and the real-world ETTh1 dataset, QASA improves on a full-capacity classical Transformer for chaotic and trend-dominated signals. To ask whether this is a genuinely quantum effect, we introduce a control rarely applied in quantum machine learning -- a capacity-matched classical bottleneck with the same parameter budget -- and find that it matches the PQC on the error metrics. The gain is therefore attributable to the low-rank value-projection bottleneck (an architectural parsimony principle), not to quantumness; adding further quantum layers only degrades performance and trainability. We accordingly position the quantum layer not as a source of accuracy advantage but as a competitive instantiation of this principle: its low-rank compression onto the signal's intrinsic dimensionality is matched by a classical bottleneck, so the gain is architectural rather than quantum.

Chi-Sheng Chen, En-Jui Kuo

Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan

Hybrid Quantum-Classical ML Transformer Attention Variational Quantum Circuits

Mar 17, 2025

Quantum State Preparation with the QNN-based SRBB Algorithm

In this work, a novel algorithm structured on Lie algebras for the approximate quantum state preparation problem is proposed, addressing a challenge of fundamental importance in many areas of quantum computing. The algorithm uses a variational quantum circuit designed on the Standard Recursive Block Basis (SRBB), a hierarchical construction for the matrix algebra of the

SU(2^n)

group, which is capable of linking the variational parameters with the topology of the Lie group. Compared to the full algebra, using only diagonal components reduces the number of CNOTs by an exponential factor, as well as the circuit depth, in full agreement with the relaxation principle inherent to the approximation methodology of minimizing resources while achieving high accuracy. The desired quantum state is then approximated by a novel quantum neural network, which is designed based on the diagonal SRBB sub-algebra. This approach provides a new scheme for approximate quantum state preparation in a variational framework and a specific use case for the SRBB hierarchy. The performance of the algorithm is assessed with different loss functions, such as fidelity, trace distance, and Frobenius norm, in relation to two optimizers: Adam and Nelder-Mead. The results highlight the potential of SRBB in close connection with the geometry of unitary groups, achieving high accuracy of up to 4 qubits in simulation, but also its current limitations with an increasing number of qubits. Additionally, the approximate SRBB-based QSP algorithm has been tested on real quantum devices to assess its performance with a small number of qubits.

Marco Mordacci, Giacomo Belli, Michele Amoretti

Quantum Software Laboratory University of Parma Parma, Italy

Variational Quantum Circuits Quantum State Preparation Variational Quantum Algorithms Quantum Neural Networks