Quantum computers may possess much greater computing power than classical computers.But it is one of key step for implementation of quantum computer to use geometric quantum phase to realize high-fidelity universal quantum gates,and its characteristic is to utilize global geometric features to avoid noise influence in some regions,then high-fidelity quantum gates are realized.In this paper,first we briefly introduce both fundamental and existing difficulties of quantum computer,finally discuss geometric quantum phase having relation with scheme such as nuclear magnetic resonance(NMS)、cavity-QED and superconducting Josephson-junction.
Quantum computers may possess much greater computing power than classical computers.But it is one of key step for implementation of quantum computer to use geometric quantum phase to realize high-fidelity universal quantum gates,and its characteristic is to utilize global geometric features to avoid noise influence in some regions,then high-fidelity quantum gates are realized.In this paper,first we briefly introduce both fundamental and existing difficulties of quantum computer,finally discuss geometric quantum phase having relation with scheme such as nuclear magnetic resonance(NMS)、cavity-QED and superconducting Josephson-junction.
From the prinecple of quanturn mechanics,we explain that quantuare computation is a theoretical basis of quantum computer.Quantum computers may provide much greater computing power than classical computers.Using geometric quantum phase to realize high-fidelity universal quantum gates is the key to realize quantum computer and its characteristic is to utilize global geometric features to avoid noise influence in some regions,thus realizing high-fidelity quantum gates.First,we briefly introduce the fundamental principle of quantum computation and existing difficulties of quantum computer implementation;finally,we discuss geometric quantum phase related to scheme of quantum computer implementation such as nuclear magnetic resonance(NMS)、cavity-QED and superconducting Josephson-junction.
實現可集成的量子計算的關鍵步驟是實現保真度足夠高的一組普適量子邏輯門 .最近幾年發展的幾何量子計算使用幾何位相來實現量子邏輯門 ,其特點是利用幾何位相的整體幾何性質來避免某些局域的無規噪聲的影響 ,從而實現較高保真度的量子門 .文章先簡要介紹常規幾何量子邏輯門的概念 ,然后重點介紹最近提出的非常規幾何量子計算 :量子計算中使用的邏輯門的總位相既包含有幾何位相 ,又包含有動力學位相 ,但它僅依賴于一些幾何特征 .而且 ,對于任意的量子位輸入態 ,在量子門操作過程中積累的位相要么是零 ,要么是僅依賴幾何特征的位相 . \nThe physical implementation of a universal set of high-fidelity quantum gates is a key step in quantum computation. Geometric quantum computation is a promising scenario to achieve high-fidelity quantum gates. In this scheme, quantum gates are realized based on geometric phases, which are dependent only on some global geometric features. In this Communication, we present an overview of geometric quantum computation, especially the unconventional geometric quantum computation recently proposed by us. In the latter scheme, the total phase accumulated in a gate operation consists of both geometric and dynamic components, but for any input state it still only depends on the global geometric features.
A fundamental challenge of quantum computation is being able to scale up a large number of high fidelity quantum gates while noise and error are affecting the gate’s physical control parameters. This dissertation focuses on the fidelity of single-qubit quantum gates constructed by a change in quantum geometric phase, while the control parameters are affected by random noise and systematic error. A unified model of geometric quantum computation is developed, in which a qubit state is controlled by a composite Hamiltonian, resulting in a multiple-segment rotation of the quantum state and allowing characterization of evolution paths depending on the associated geometric and dynamic phase. The fidelity of the quantum gates in the presence of different noise error is compared for pu rely geometric, hybrid (having both geometric and dynamic phase), and conventional dynamic quantum gates built on single Hamiltonians. Results showed hybrid quantum gates had the highest fidelities, followed by geometric gates, and conventional dynamic gates had the lowest fidelities. In addition, there was indication in some cases higher fidelities result from gates created from a larger number of segments in the quantum state rotation. These results can be understood by the relation of the control parameters with the evolution path geometry. By translating between control parameters, our model can be applied to different systems for quantum computation, including: the laser manipulation of a two-level atom, laser manipulation of trapped ions, nuclear magnetic resonance, polarization states of photons, superconducting qubits in cavity QED, and quantum dots.
We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.
The geometric phase stands as a foundational concept in quantum physics, revealing deep connections between geometric structures and quantum dynamical evolution. Unlike dynamical phases, geometric phases exhibit intrinsic resilience to certain types of perturbation, making them particularly valuable for quantum information processing, where maintaining coherent quantum operations is essential. This article provides a review of geometric phases in the context of universal quantum gate construction, i.e., the geometric quantum computation (GQC), with special attention to recent progress in nonadiabatic implementations that enhance gate fidelity and/or operational robustness. We first review a unified theoretical framework that can encompass all existing nonadiabatic GQC approaches, then systematically examine the design principles of nonadiabatic geometric gates with a particular focus on how optimal control techniques can be leveraged to improve the accuracy and noise resistance. In addition, we conducted detailed numerical comparisons of various nonadiabatic GQC protocols, offering a quantitative assessment of their respective performance characteristics and practical limitations. Through this focused investigation, our aim is to provide researchers with both fundamental insights and practical guidance for advancing geometric approaches in quantum computing.
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum computation using only geometric effects appearing in quantum phases. It is then finally discussed how this geometric way of performing quantum gates can lead to a stable, large scale, intrinsically fault-tolerant quantum computer.