Geometric Quantum Computing

Jincheng Zhang

This paper introduces the Geometric-Algebraic Hybrid Quantum Computing (GAHQ) framework, a novel algorithmic approach designed to efficiently perform high-precision geometric operations and leverage quantum entanglement for accelerated computation and storage. Traditional methods struggle with the complexities of accurate geometric calculations, prompting the development of this framework. GAHQ integrates geometric transformations with algebraic operations, employing quantum entanglement to enhance computational efficiency and storage capabilities. This paper details the design of the GAHQ algorithm, its theoretical advantages, and initial experimental results demonstrating its potential for significant advancements in geometric computation and quantum information processing.

Eduardo Jose Bayro-Corrochano

Erik Sjöqvist, Vahid Azimi Mousolou, Carlo M. Canali

Yuansheng Wang, Bao-Jie Liu, Shi‐Lei Su +1 more

Non-adiabatic geometric quantum computation (NGQC) provides a promising way for implementing robust quantum gate operation. However, NGQC has no obvious advantage over the dynamical scheme in dealing with control errors. Here, we show a new geometric scheme, called Floquet geometric quantum computation (FGQC), in which error-resistant geometric gates based on periodically driven two-level systems can be constructed via a new non-Abelian geometric phase proposed in a recent work [V. Noviĉenko \emph{et al}, Phys. Rev. A 100, 012127 (2019) ]. Based on Rydberg atoms, the experimental feasibility of our proposal is demonstrated through numerical simulation using the recent experimental parameters. In addition, the numerical simulation of our geometric gates in the presence of global control error shows that the FGQC gates are more robust over NGQC and dynamical gate (DG). We further analytically prove the superiority of FGQC in terms of robustness against global control error. Consequently, our work makes an important step towards robust geometric quantum computation.

G. Falci, Rosario Fazio, G. Massimo Palma +2 more

Jincheng Zhang

Geometric Information Theory (GIT) offers a novel approach to quantum computation by leveraging geometric structure as a fundamental basis for quantum information. This paper explores the integration of GIT with quantum computing, focusing on the design of a quantum algorithm specifically tailored for efficient processing of large geometric datasets. We present a detailed conceptual framework, outlining the core mechanisms and potential benefits of this hybrid approach. The research demonstrates the feasibility of utilizing geometric structures as a key component of a quantum computation, aiming to significantly enhance computational performance for complex geometric tasks.