The choreography of quantum mechanical phenomena has catalysed accelerated advances in the emergence of a quantum computational substrate paradigm that yields the potential to solve some of humanities most complex problems through quantum computing speedup requires exponential computational power that exceeds that of today’s most powerful super computers, to confront the world’s most intractable computational challenges in environment, agriculture, health, energy, climate, materials science, precision medicine, autonomous vehicles in smart cities, renewable energy and problems humanity has not yet even imagined. Current quantum computational substrates are limited by circuit depth, noise processes, qubit count, and fault tolerant quantum computational substrates unlikely to be available in the near term. Hybrid quantum algorithms/Variational Quantum Algorithms (VQAs), operate by using a classical optimizer to orchestrate the parameters of a quantum circuit, have become a prominent approach to address these limitations. However, several challenges manifest that include the training, speedup. accuracy, and impactful practical application of VQAs. This paper reviews novel new frontiers in current VQAs, provides an analysis of VQAs, their strengths and limitations, and outlines potential applications in the quest towards yielding practical quantum advantage. Secondly, this paper also reviews and provides an assessment of quantum software development frameworks.
The choreography of quantum mechanical phenomena has catalysed accelerated advances in the emergence of a quantum computational substrate paradigm that yields the potential to solve some of humanities most complex problems through quantum computing speedup requires exponential computational power that exceeds that of today’s most powerful super computers, to confront the world’s most intractable computational challenges in environment, agriculture, health, energy, climate, materials science, precision medicine, autonomous vehicles in smart cities, renewable energy and problems humanity has not yet even imagined. Current quantum computational substrates are limited by circuit depth, noise processes, qubit count, and fault tolerant quantum computational substrates unlikely to be available in the near term. Hybrid quantum algorithms/Variational Quantum Algorithms (VQAs), operate by using a classical optimizer to orchestrate the parameters of a quantum circuit, have become a prominent approach to address these limitations. However, several challenges manifest that include the training, speedup. accuracy, and impactful practical application of VQAs. This paper reviews novel new frontiers in current VQAs, provides an analysis of VQAs, their strengths and limitations, and outlines potential applications in the quest towards yielding practical quantum advantage. Secondly, this paper also reviews and provides an assessment of quantum software development frameworks.
The choreography of quantum mechanical phenomena has catalysed accelerated advances in the emergence of a quantum computational substrate paradigm that yields the potential to solve some of humanities most complex problems through quantum computing speedup requires exponential computational power that exceeds that of today’s most powerful super-computers, to confront the world’s most intractable computational challenges in environment, agriculture, health, energy, climate, materials science, precision medicine, autonomous vehicles in smart cities, renewable energy and problems humanity has not yet even imagined. Current quantum computational substrates are limited by circuit depth, noise processes, qubit count, and fault tolerant quantum computational substrates unlikely to be available in the near term. Hybrid quantum algorithms/Variational Quantum Algorithms (VQAs), operate by using a classical optimizer to orchestrate the parameters of a quantum circuit, have become a prominent approach to address these limitations. However, several challenges manifest that include the training, speedup. accuracy, and impactful practical application of VQAs. This paper reviews novel new frontiers in current VQAs, provides an analysis of VQAs, their strengths and limitations, and outlines potential applications in the quest towards yielding practical quantum advantage. Secondly, this paper also reviews and provides an assessment of quantum software development frameworks.
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.
Through harnessing quantum mechanical phenomena, quantum computing substrates yields the promise of transcending new frontiers in confronting the world’s most intractable computational challenges requiring exponential computational power that exceeds that of today’s most powerful super-computers. The choreography of such quantum mechanical phenomena has catalysed accelerated advances in the emergence of a quantum computational substrate paradigm that yields the potential to solve some of humanities most complex problems through quantum speedup: in environment, agriculture, health, energy, climate, materials science, precision medicine, autonomous vehicles in smart cities, renewable energy and problems humanity has not yet even imagined. However, the manifestation of a practical quantum advantage across several of these areas is unlikely through the exclusive application of a quantum computational substrate. Quantum computational substrates will not replace classical computational substrates, instead, both technologies will synergistically complement each other where quantum computational substrate accelerators functions as a specialised co-processor to a classical computational substrate in computing workloads best suited for the quantum computer, in a heterogenous computational substrate ecosystem comprising other accelerators. This paper reviewed novel new frontiers at the fusion of quantum-classical computational substrates, and findings reveal that practical applications and research remain limited. The opportunity exists, in considering a heterogenous computational substrate ecosystem comprising other accelerators, for practical quantum advantage across a broader set of complex problem domains to be realised sooner
Through harnessing quantum mechanical phenomena, quantum computing substrates yields the promise of transcending new frontiers in confronting the world’s most intractable computational challenges requiring exponential computational power that exceeds that of today’s most powerful super-computers. The choreography of such quantum mechanical phenomena has catalysed accelerated advances in the emergence of a quantum computational substrate paradigm that yields the potential to solve some of humanities most complex problems through quantum speedup: in environment, agriculture, health, energy, climate, materials science, precision medicine, autonomous vehicles in smart cities, renewable energy and problems humanity has not yet even imagined. However, the manifestation of a practical quantum advantage across several of these areas is unlikely through the exclusive application of a quantum computational substrate. Quantum computational substrates will not replace classical computational substrates, instead, both technologies will synergistically complement each other where quantum computational substrate accelerators functions as a specialised co-processor to a classical computational substrate in computing workloads best suited for the quantum computer, in a heterogenous computational substrate ecosystem comprising other accelerators. This paper reviewed novel new frontiers at the fusion of quantum-classical computational substrates, and findings reveal that practical applications and research remain limited. The opportunity exists, in considering a heterogenous computational substrate ecosystem comprising other accelerators, for practical quantum advantage across a broader set of complex problem domains to be realised sooner.
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.
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.