Recently, Assistant Researcher Jiang Zhang from Quantum Algorithm Group collaborated with international peers to systematically elucidate the research history and significant theoretical and experimental advances in the development of non-adiabatic holonomic quantum computation from adiabatic geometric quantum computation. The related paper, titled "Geometric and Holonomic Quantum Computation", was published on August 2, 2023, in "Physics Reports".

Achieving high-precision quantum gates is the foundation for enhancing the computational power of quantum computers. However, noise from the environment and control affects the precision of qubit manipulation. Therefore, overcoming the impact of noise and achieving noise-resistant quantum computing is an important research topic in quantum information science. Geometric phases have characteristics that depend solely on the evolution path of the quantum system, independent of the evolution details. Therefore, quantum computing based on geometric phases exhibits noise resistance.

The quantum computing based on non-adiabatic and non-Abelian geometric phases, known as non-adiabatic holonomic quantum computation, has gained widespread attention due to its advantages in full geometricity and rapid implementation, free from the restrictions of adiabatic conditions. After over a decade of development, both the theory and experiments of non-adiabatic holonomic quantum computation have made significant progress, evolving from two-step to one-step schemes and from basic schemes to optimized schemes with multiple coherent protection. Experimental schemes based on various physical systems, including nuclear magnetic resonance, ion traps, superconducting circuits, diamond color centers, and Rydberg atoms, have been proposed. Dozens of experimental works published in top journals have confirmed the feasibility of the theory.

The first author of this extensive review paper is Assistant Researcher Jiang Zhang from our institute's quantum algorithm team. The co-authors include six scholars from China, Canada, Germany, Sweden, and Singapore. The research was supported by the National Natural Science Foundation of China and other projects.

Link：

https://www.sciencedirect.com/science/article/pii/S0370157323002065

Figure 1. Schemes for realizing geometric quantum gates based on the evolution along geodesics

Figure 2. The level structures and control methods for non-adiabatic holonomic quantum gates using a three-level system.