Developments in Quantum Algorithms and Computational Complexity for Quantum Computational Models

Quantum algorithms and computational complexity have emerged as pivotal areas of research in the last few decades, driven by the potential of quantum computing to revolutionize various fields. The exploration of different computational models from a quantum perspective has led to significant advancements and intriguing questions. The query model remains the most standard framework for quantum algorithms, but researchers have also delved into automata-like models, communication protocols, and the quantum circuit model, which is widely used in current quantum devices. Additionally, adiabatic computation has garnered attention for its unique approach to quantum problem-solving. Despite these advancements, there remain substantial gaps in our understanding, particularly in the practical implementation of these models and their scalability. Ongoing debates and significant studies continue to push the boundaries of what is possible, highlighting the need for a more comprehensive investigation into these diverse quantum computational models.

This Research Topic aims to gather a collection of articles that reflect the latest developments in quantum algorithms and computational complexity across various quantum computational models. The primary objective is to bridge the gap between fundamental research and practical applications, including the implementation of algorithms on current quantum devices. Specific questions to be addressed include the efficiency of different quantum models, the development of new quantum algorithms, and the practical challenges of implementing these algorithms on existing quantum hardware. Hypotheses to be tested may involve the comparative performance of quantum versus classical algorithms in specific problem domains and the potential for hybrid quantum-classical approaches.

To gather further insights into the developments in quantum algorithms and computational complexity, we welcome articles addressing, but not limited to, the following themes:

- Quantum algorithms
- Quantum query model
- Quantum circuits
- Quantum automata
- Quantum stream processing algorithms
- Quantum communication complexity
- Models of quantum computation
- Quantum cryptography
- Quantum machine learning
- Hybrid algorithms
- Quantum complexity theory
- Quantum information theory
- Tensor networks
- Adiabatic computing
- Quantum error correction