The last decade has witnessed remarkable progress in the development of quantum technologies.Although fault-tolerant devices likely remain years away, the noisy intermediate-scale quantum devices of today may be leveraged for other purposes.Leading candidates are variational quantum algorithms (VQAs), which have been developed for applications including chemistry, optimization, and machine learning, but whose implementations on quantum devices have yet to demonstrate improvements over classical capabilities.In this Perspective, we propose a variety of ways that the performance of VQAs could be informed by quantum optimal control theory.A major theme throughout is the need for sufficient control resources in VQA implementations; we discuss different ways this need can manifest, outline a variety of open questions, and look to the future.
The last decade has witnessed remarkable progress in the development of quantum technologies.Although fault-tolerant devices likely remain years away, the noisy intermediate-scale quantum devices of today may be leveraged for other purposes.Leading candidates are variational quantum algorithms (VQAs), which have been developed for applications including chemistry, optimization, and machine learning, but whose implementations on quantum devices have yet to demonstrate improvements over classical capabilities.In this Perspective, we propose a variety of ways that the performance of VQAs could be informed by quantum optimal control theory.A major theme throughout is the need for sufficient control resources in VQA implementations; we discuss different ways this need can manifest, outline a variety of open questions, and look to the future.
Variational quantum algorithms (VQAs) are the leading candidates for practical applications of noisy intermediate-scale quantum (NISQ) devices. Recently, pulse-based variational quantum algorithms (p-VQAs) have emerged as a compelling alternative to traditional gate-based VQAs. By optimizing continuous control fields directly on hardware-native Hamiltonians, pulse-based methods are easy to implement and can significantly reduce quantum resource overhead, thereby enhancing the overall performance of quantum algorithms on NISQ devices. In this review, we present a comprehensive survey over recent advances in p-VQAs, covering theory, algorithms, and hardware deployments across various quantum computing platforms. We also review applications of p-VQAs to variational quantum eigensolver in quantum chemistry, quantum approximate optimization algorithm for combinatorial optimization, and quantum machine learning tasks.
Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits (PQCs) with classical optimization, they operate effectively under strict hardware limitations. However, as quantum architectures transition toward early fault-tolerant (EFT) and ultimate fault-tolerant (FT) regimes, the foundational principles and long-term viability of VQAs require systematic reassessment. This review offers an insightful analysis of VQAs and their progression toward the fault-tolerant regime. We deconstruct the core algorithmic framework by examining ansatz design and classical optimization strategies, including cost function formulation, gradient computation, and optimizer selection. Concurrently, we evaluate critical training bottlenecks, notably barren plateaus (BPs), alongside established mitigation strategies. The discussion then explores the EFT phase, detailing how the integration of quantum error mitigation and partial error correction can sustain algorithmic performance. Addressing the FT phase, we analyze the inherent challenges confronting current hybrid VQA models. Furthermore, we synthesize recent VQA applications across diverse domains, including many-body physics, quantum chemistry, machine learning, and mathematical optimization. Ultimately, this review outlines a theoretical roadmap for adapting quantum algorithms to future hardware generations, elucidating how variational principles can be systematically refined to maintain their relevance and efficiency within an error-corrected computational environment.
Variational Quantum Algorithms are a major method of harnessing Noisy Intermediate-Scale Quantum devices to solve classically intractable problems in physics, chemistry, optimization, and machine learning. The current review offers a critical overview of VQAs, with special emphasis on their theoretical backgrounds, algorithmic structures, and application performance within realistic models of noise. Several key variants, such as the Variational Quantum Eigensolver, Quantum Approximate Optimization Algorithm, and Quantum Neural Networks, are compared in terms of noise robustness, ansatz archi- tecture, and hybrid quantum-classical methods of optimization. Benchmarks in fields such as quantum chemistry, finance modeling, and particles and nuclei physics reveal the poten- tial of VQAs in achieving practical quantum advantage. Fundamentally limiting factors 1such as barren plateaus, optimization overhead, and hardware constraints are considered in addition to mitigation strategies, including adaptive construction of ansatz, informed training in the presence of noise, and quantum error correction using QVECTOR. The paper is concluded with an overview of the scalability and future of VQAs in the direction of transitioning toward fault-tolerant quantum computing.
Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits with classical optimization, they operate effectively under strict hardware limitations. However, as quantum architectures transition toward early fault-tolerant (EFT) and ultimate fault-tolerant (FT) regimes, the foundational principles and long-term viability of VQAs require systematic reassessment. This review offers a comprehensive analysis of VQAs and their progression toward the FT regime. We deconstruct the core algorithmic framework by examining ansatz design and classical optimization strategies, including cost function formulation, gradient computation, and optimizer selection. Concurrently, we evaluate critical training bottlenecks, notably barren plateaus (BPs), alongside established mitigation strategies. The discussion then explores the EFT phase, detailing how the integration of quantum error mitigation (QEM) and partial error correction can sustain algorithmic performance. Addressing the FT phase, we analyze the inherent challenges confronting current hybrid VQA models. Furthermore, we synthesize recent VQA applications across diverse domains, including many-body physics, quantum chemistry, machine learning, and mathematical optimization. Ultimately, this review outlines a theoretical roadmap for adapting quantum algorithms to future hardware generations, elucidating how variational principles can be systematically refined to maintain their relevance and efficiency within an error-corrected computational environment.
In recent years, as datasets have grown larger, quantum computing has shown potential in addressing the rapidly increasing costs of data processing due to its superposition and entanglement capabilities. Limited by quantum hardware and the number of controllable qubits, variational quantum algorithms (VQAs) are algorithms suitable for NISQ devices, capable of computation on medium-scale noisy devices. VQAs are hybrid classical-quantum algorithms that use parameterized quantum circuits to prepare parameterized quantum states and employ classical optimizers to minimize objective functions, enabling efficient solutions for complex problems. Classical optimizers reduce the stringent requirements on quantum hardware and can achieve quantum advantage on current devices. This paper systematically elaborates on the core foundational theories of quantum computing and neural networks, with a focus on reviewing the research and application status of VQAs in three main scenarios: machine learning (supervised, unsupervised, and reinforcement learning), solving systems of equations (linear and nonlinear), and network attack detection. It analyzes the current technical bottlenecks in this field and provides prospects for future development, offering a reference for further research on variational quantum algorithms.
Leveraging the principles of quantum mechanics—specifically superposition and parallelism— quantum computation holds the potential to surpass the computational power limitations of classical computers. However, due to constraints such as the limited number of available qubits and the presence of decoherence noise in quantum hardware, designing efficient quantum algorithms capable of running on Noisy Intermediate-Scale Quantum (NISQ) devices has become a pivotal research focus. The Variational Quantum Algorithm (VQA) represents a hybrid quantum-classical computational paradigm that is executable on NISQ devices and can potentially demonstrate quantum advantage. In VQAs, the loss function is evaluated on a quantum computer, optimized by a classical computer, and the updated parameters are subsequently fed back to the quantum circuit for the next iteration. The Quantum Convolutional Neural Network (QCNN) is a prominent implementation within the VQA framework. It performs convolutional and pooling operations via Parameterized Quantum Circuits (PQCs) , endowing it with potentially superior feature extraction capabilities compared to its classical convolutional neural network counterparts. This paper begins with the foundational theories of quantum computing, provides a detailed exposition of the VQA workflow and QCNN architecture, and summarizes VQAs based on PQCs. It then reviews recent research progress on QCNNs from a practical application standpoint and concludes by outlining current challenges and future research directions.