Noisy intermediate-scale quantum (NISQ) algorithms (2101.08448v2)

Abstract: A universal fault-tolerant quantum computer that can solve efficiently problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement towards realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e. qubits that are not error-corrected, and therefore perform imperfect operations in a limited coherence time. In the search for quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry and combinatorial optimization. The goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, we provide a thorough summary of NISQ computational paradigms and algorithms. We discuss the key structure of these algorithms, their limitations, and advantages. We additionally provide a comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices.

• The paper presents a comprehensive review of NISQ algorithms, emphasizing variational quantum algorithms and their efficient resource utilization.
• It details optimization strategies and error mitigation techniques that enhance the performance of noisy quantum devices for complex computational tasks.
• The review highlights future prospects by exploring both theoretical insights and practical applications in quantum chemistry, physics, and combinatorial optimization.

Overview of "Noisy intermediate-scale quantum (NISQ) algorithms"

The paper by Kishor Bharti et al. provides a comprehensive review of algorithms and computational paradigms designed for Noisy Intermediate-Scale Quantum (NISQ) computers, which are characterized by their use of hundreds of noisy, non-error-corrected qubits. These devices, although not fully quantum error-corrected, hold promise for solving classically intractable problems across various domains, including physics, machine learning, quantum chemistry, and combinatorial optimization. The authors aim to delineate the current landscape of NISQ algorithms, discuss their potential applications, and explore the challenges these technologies face.

Structure and Contributions

The paper is structured to cover the foundational aspects of NISQ algorithms, their capabilities, limitations, and practical applications. Key areas encompassed by the paper include:

1. NISQ Paradigms: The review explores various computational paradigms specific to NISQ devices. These paradigms exploit the limited resources of NISQ computers to achieve tasks that are otherwise demanding for classical computers. The paper highlights both variational quantum algorithms (VQAs) and other approaches like quantum annealing and Gaussian boson sampling.
2. Algorithmic Design and Applications: Central to the paper are variational quantum algorithms, which leverage a parameterized quantum circuit (PQC) optimized by classical computation. The review details the construction and optimization strategies for these circuits, emphasizing applications to quantum chemistry, materials science, and optimization problems.
3. Resource Optimization: The paper discusses the importance of optimizing quantum resources and mitigating errors, given the noise and limited coherence times in NISQ devices. Techniques such as error mitigation, algorithmic improvements, and efficient qubit mappings are explored to maximize NISQ devices' utility.
4. Theoretical Implications: The review considers computational complexity and theoretical underpinnings crucial for understanding the scope and limitations of NISQ algorithms. These include insights into algorithmic scalability, expressibility, and the challenge of 'barren plateaus' in optimization landscapes.
5. Future Perspectives: The discussion extends to potential future developments in quantum computing and the role of NISQ devices in advancing these technologies. The authors speculate on the impact of continued hardware advancements and the development of more sophisticated algorithms on achieving quantum advantage.

Numerical Results and Theoretical Insights

The paper highlights several numerical results and theoretical claims that are central to comprehending NISQ algorithms' strengths and limitations:

• Quantum Advantage Potential: While achieving quantum advantage with NISQ devices remains a long-term goal, the authors argue that specialized tasks could see substantial benefits from current NISQ capabilities. These include specific sampling problems and certain instances of optimization challenges.
• Benchmarking Efforts: The review describes efforts to benchmark quantum devices, emphasizing metrics like quantum volume, which gauge a device's effective performance beyond mere qubit count.
• Error Mitigation: Applying error mitigation techniques is crucial in extending the computational reach of NISQ devices. Strategies such as zero-noise extrapolation and probabilistic error cancellation demonstrate potential to harness noisy hardware effectively.

Implications and Future Directions

The implications of advancing NISQ algorithms range from practical applications, such as improved solutions for complex optimization problems, to deeper theoretical insights into quantum algorithm design. The review emphasizes the need for collaborative efforts between theorists, practitioners, and engineers to address the multifaceted challenges of NISQ computing.

Future developments are anticipated in several areas:

• Progress in VQAs: Enhancements in the design and training of VQAs could significantly impact their applicability, especially as quantum hardware scales and coherence times improve.
• Broader Algorithmic Innovations: Encouraging innovation in algorithm design could lead to new frameworks that better exploit NISQ device characteristics.
• Error Mitigation Research: Continued research into error mitigation techniques will be crucial, as these methods may bridge the gap between noisy computations and the ultimate goal of fault-tolerant quantum computing.

Overall, this comprehensive review informs both current research directions and the realistic expectations of NISQ computing's capabilities. By illuminating both the achievements and challenges inherent to NISQ technologies, the authors guide future endeavors in quantum computing research and application.