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arXiv:1311.7470 · Quantum Information Processing

Conceptual aspects of geometric quantum computation

Erik Sjöqvist, Vahid Azimi Mousolou, Carlo M. Canali

Published Jul 7, 2016• 28 citations
arXivHTMLPDF
DOI
10.1007/s11128-016-1381-1

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Non-adiabatic holonomic quantum computation, which recently attained a considerable attention, offers a promising approach for implementation of fast, universal, and robust quantum information processing. In this all-geometric approach, quantum gates are all based on non-adiabatic extensions of the geometric Berry phase effects. Apart from its fundamental and conceptual aspects, physical realizations of proposed mathematical structures play central role in the development of large-scale quantum computation. Here, we propose an experimentally feasible nano-engineered solid-state structure to realize geometric quantum computation via non-adiabatic quantum holonomies. We use a system of three coupled quantum dots containing a single electron, where two states of a double quantum-dot charge qubit interact through an intermediate quantum dot. Careful control of the inter-dot tunneling parameters makes it possible to create a geometric model system, which allows for robust and efficient quantum information processing.
Human cognition is a complex process facilitated by the intricate architecture of human brain. However, human cognition is often reduced to quantum theory based events in principle because of their correlative conjectures for the purpose of analysis for reciprocal understanding. In this paper, we begin our analysis of human cognition via formal methods and proceed towards quantum theories. Human cognition often violate classic probabilities on which formal representation of conceptual spaces are built. Further, geometric representation of conceptual spaces proposed by Gardenfors discusses the underlying content but lacks a systematic approach (Gardenfors, 2000; Kitto et. al, 2012). However, the aforementioned views are not contradictory but different perspective with a gap towards sufficient understanding of human cognitive process. A comprehensive and systematic approach to model a relatively complex scenario can be addressed by vector space approach of conceptual spaces as discussed in literature. In this research, we have proposed an approach that uses both formal representation and Gardenfors geometric approach. The proposed model of high dimensional formal representation of conceptual space is mathematically analysed and inferred to exhibit quantum aspects. Also, the proposed model achieves cognition, in particular, consciousness. We have demonstrated this process of achieving consciousness with a constructive learning scenario. We have also proposed an algorithm for conceptual scaling of a real world scenario under different quality dimensions to obtain a conceptual scale.
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.