Quantum Computing and Quantum Coherence

David Peter Divincenzo, Daniel Loss

Jincheng Zhang

This paper presents a novel approach to analyzing the computational complexity of quantum algorithms by leveraging the concept of quantum coherence. Traditional methods for assessing quantum complexity often rely on circuit depth, qubit count, or gate complexity, which can be insufficient in capturing the nuances of quantum computation. We introduce a framework that explicitly incorporates the calculation of quantum coherence, recognizing it as a fundamental resource in quantum computation. The core idea is that the precision and duration of quantum coherence directly correlate with the computational effort required. We define a mathematical model that quantifies coherence decay and its impact on algorithm execution time. This model allows us to derive tighter bounds on the complexity of quantum algorithms, particularly those that rely heavily on sustained coherence. Furthermore, we explore the implications of coherence limitations on the feasibility of certain quantum algorithms and suggest potential strategies for mitigating these effects. This work contributes a new perspective on quantum complexity analysis, providing a more accurate and potentially more scalable method for evaluating quantum algorithms.

Maimaitiyiming Tusun, Xing Rong, Jiangfeng Du

Quantum computation provides a great speedup over its classical counterpart in solving some hard problems. The advantages of quantum computation come from the coherent superposition principle of quantum mechanics. Spin system is one of the most significant candidates to realize quantum computation. In this review, we focus on the recent experimental progress related to quantum coherence and some fundamental concepts such as the uncertainty principle in the spin systems. We shall first briefly introduce the quantum description of qubit, coherence, and decoherence. Based on this picture, preserving quantum coherence and detection of weak magnetic fields are presented. We also discuss the realization of precise quantum coherent control, adiabatic quantum factorization algorithm, and two aspects of uncertainty relations.

Jincheng Zhang

This paper proposes a novel computation architecture centered around the exploitation of quantum coherence. The core concept involves structuring a computational system to leverage the inherent parallelism afforded by quantum coherence, thereby aiming to significantly enhance computational efficiency compared to traditional architectures. We outline a framework where interconnected quantum systems operate in a manner that maximizes the duration of quantum coherence, allowing for parallel processing of multiple computational tasks simultaneously. The architecture is designed to mitigate decoherence effects, a primary challenge in quantum computing, through strategic system design and operational protocols. This approach represents a fundamentally new paradigm in computation, shifting from sequential, deterministic operations to a massively parallel, probabilistic one based on the quantum mechanical principles of superposition and coherence. The potential impact of this architecture extends across various fields, including scientific simulations, optimization problems, and machine learning, where the ability to process vast amounts of data concurrently offers a transformative advantage. ---

Pablo Paz Juan