Abstract: This paper explores hybrid quantum-classical optimization algorithms implemented across multiple quantum software development kits (SDKs): Qiskit and Cirq,. We evaluate the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) in terms of convergence rate, final cost value, and fidelity, using both simulators and real quantum hardware backends. Our results offer comparative insights into SDK performance and propose a standardized benchmarking approach for future quantum algorithm research. Keywords: Hybrid Quantum Algorithms, Qiskit, Cirq, VQE, QAOA, Quantum SDKs, Quantum Optimization, NISQ
Abstract: This paper explores hybrid quantum-classical optimization algorithms implemented across multiple quantum software development kits (SDKs): Qiskit and Cirq,. We evaluate the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) in terms of convergence rate, final cost value, and fidelity, using both simulators and real quantum hardware backends. Our results offer comparative insights into SDK performance and propose a standardized benchmarking approach for future quantum algorithm research. Keywords: Hybrid Quantum Algorithms, Qiskit, Cirq, VQE, QAOA, Quantum SDKs, Quantum Optimization, NISQ
This paper presents a qualitative analysis of hybrid quantum-classical computing approaches aimed at solving complex optimization problems using near-term quantum processors. Hybrid algorithms leverage the strengths of quantum and classical computing to tackle computationally intensive tasks often constrained by current quantum hardware limitations. Through an extensive literature review and synthesis of recent empirical studies, we benchmark various hybrid algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE), focusing on their performance, scalability, and practical applicability on noisy intermediate-scale quantum (NISQ) devices. The study highlights the advantages, challenges, and future prospects of integrating hybrid quantum-classical computation in optimization domains, providing a comprehensive framework and qualitative insights into benchmarking methodologies and critical performance metrics.
Abstract The emergence of noisy intermediate-scale quantum (NISQ) devices has fueled the development of hybrid quantum-classical algorithms for machine learning (ML), promising potential advantages over classical methods. However, the practical efficacy of these algorithms remains uncertain due to challenges like noise susceptibility, trainability issues, and a lack of rigorous benchmarking. This study presents a comprehensive empirical evaluation of two flagship hybrid algorithms the Variational Quantum Eigensolver (VQE) for classification and the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization against state-of-the-art classical baselines under equivalent resource constraints. Through extensive simulations incorporating realistic noise models, we demonstrate that while these quantum approaches achieve competitive performance (e.g., 91.2% accuracy for VQE on a binary classification task), they consistently underperformed optimized classical models like Support Vector Machines (94.8% accuracy) and require orders of magnitude more computational time. Furthermore, we provide empirical validation of critical barriers to scalability, including the barren plateau phenomenon and significant performance degradation under noise, even with advanced error mitigation. Our results indicate that for the tasks studied, current NISQ era algorithms do not yet provide a tangible quantum advantage. This work contributes a rigorous benchmarking framework and a critical, realistic assessment of the field, suggesting that future progress hinges on fundamental algorithmic innovations and hardware improvements rather than incremental refinements of existing paradigms.
This study examines the current technological components of quantum computing through a multi layered approach. It begins by comparing quantum and classical computers across fundamental aspects such as information representation, computational power, fault tolerance, and computational complexity, with the key differences summarized in a technical comparison table. Subsequently, the study analyzes the primary architectural approaches in quantum hardware, including superconducting qubits, trapped ion systems, and photonic platforms. On the software side, quantum programming languages such as Qiskit, Cirq, and PennyLane are evaluated in terms of their features, supported infrastructures, and learning curves. The significance of variational quantum algorithms tailored for the noisy intermediate-scale quantum (NISQ) era namely, the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA) along with hybrid computing systems, is also emphasized. Overall, this work aims to provide a comprehensive overview of the current state of modern quantum computing from both hardware and software perspectives, highlighting key developments and ongoing progress in the field.
Quantum computing has emerged as a transformative paradigm capable of solving complex computational problems that are intractable for classical computers. Central to the advancement of this technology is the development of efficient quantum algorithms and high fidelity simulations that enable the design, testing, and optimization of quantum solutions before deployment on physical hardware. This study focuses on the design and implementation of quantum algorithms tailored for solving a variety of quantum problems, including quantum chemistry, optimization, and cryptography. Using state of the art simulation platforms such as Qiskit, Cirq, and Pennylane, algorithm performance was evaluated in terms of accuracy, execution time, scalability, and resilience to noise. Benchmarks demonstrate that algorithms such as the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) achieve significant speedups in problem specific domains, while hybrid quantum–classical methods provide robust pathways for near term quantum advantage. Simulation results reveal that algorithmic efficiency can be significantly improved through optimized circuit depth, qubit connectivity mapping, and advanced error mitigation techniques. The findings highlight the potential of simulation driven quantum algorithm development in accelerating the practical realization of quantum computing applications across disciplines such as materials discovery, molecular modeling, secure communications, and complex optimization tasks.
This study presents a rigorous empirical evaluation of the Quantum Approximate Optimization Algorithm (QAOA) within a hybrid quantum-classical framework for solving the NP-hard Max-Cut problem. Using Python and Qiskit Aer statevector simulations, we benchmark QAOA (depths p = 2 and p = 3) against established classical algorithms, including simulated annealing, the Goemans–Williamson algorithm, and greedy heuristics, across Erdős–Rényi and regular graphs with 4 to 20 nodes (100 instances per size). Results demonstrate that low-depth QAOA suffers from significant performance degradation, achieving a 0.467 approximation ratio at 20 nodes compared to 0.856 for Goemans–Williamson, alongside a 210× runtime overhead. Convergence analysis further reveals low optimality probabilities and high iteration costs, highlighting limitations of variational optimization in NISQ-era devices. This work provides a reproducible benchmarking framework and contributes to a realistic assessment of near-term quantum advantage.
Portfolio optimization is a fundamental problem in quantitative finance that seeks to maximize risk-adjusted returns while managing investment risk. With the advent of quantum computing, there is growing interest in applying quantum algorithms to solve complex optimization problems. This paper presents a comprehensive comparative study of quantum and classical approaches to portfolio optimization, specifically comparing the Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), and classical mean-variance optimization. We evaluate these methods on both real market data and synthetic datasets with varying correlation structures. Our experimental results show that while classical methods currently outperform quantum approaches on near-term quantum devices in terms of solution quality and computational efficiency, quantum algorithms demonstrate conceptual viability and promise for future applications as quantum hardware improves. The classical method achieves optimal Sharpe ratios of 1.2-1.8, while QAOA and VQE achieve 80-95% and 75-90% of classical performance respectively. This work provides insights into the current state and future potential of quantum computing for financial optimization.