Quantum algorithm for a set of quantum 2SAT problems

We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability(Q2SAT)problem,which is a generalization of 2-satisfiability(2SAT)problem.For a Q2SAT problem,we construct the Hamiltonian which is similar to that of a Heisenberg chain.All the solutions of the given Q2SAT problem span the subspace of the degenerate ground states.The Hamiltonian is adiabatically evolved so that the system stays in the degenerate subspace.Our numerical results suggest that the time complexity of our algorithm is O(n^3.9)for yielding non-trivial solutions for problems with the number of clauses m=dn(n-1)/2(d■0.1).We discuss the advantages of our algorithm over the known quantum and classical algorithms.     

Exact Equivalence between Quantum Adiabatic Algorithm and Quantum Circuit Algorithm

We present a rigorous proof that quantum circuit algorithm can be transformed into quantum adiabatic algorithm with the exact same time complexity. This means that from a quantum circuit algorithm of L gates we can construct a quantum adiabatic algorithm with time complexity of O(L). Additionally, our construction shows that one may exponentially speed up some quantum adiabatic algorithms by properly choosing an evolution path.     

绝热演化中一般量子态的几何相位

在绝热演化中的几何相位（即Berry相位）被推广到包括非本征态的一般量子态.这个新的几何相位同时适用于线性量子系统和非线性量子系统.它对于后者尤其重要因为非线性量子系统的绝热演化不能通过本征态的线性叠加来描述.在线性量子系统中,新定义的几何相位是各个本征态Berry相位的权重平均.     

非线性朗道-基纳隧穿

介绍一种新的量子隧穿———非线性朗道-基纳隧穿.这种隧穿一般发生在有相互作用的二能级系统中,比如光晶格中的玻色-爱因斯坦凝聚物和分子磁体.相对于传统的线性朗道-基纳隧穿,非线性朗道-基纳隧穿由排斥相互作用带来的非线性会增强隧穿的概率.特别是当非线性非常强时,系统的绝热性会遭到破坏;一个无穷小的线性驱动都会造成有限的隧穿概率.     

Matter wave interference of dilute Bose gases in the critical regime

Ultra-cold atomic gases provide a new chance to study the universal critical behavior of phase transition. We study theoretically the matter wave interference for ultra-cold Bose gases in the critical regime. We demonstrate that the interference in the momentum distribution can be used to extract the correlation in the Bose gas. A simple relation between the interference visibility and the correlation length is found and used to interpret the pioneering experiment about the critical behavior of dilute Bose gases [Science 315 1556(2007)]. Our theory paves the way to experimentally study various types of ultra-cold atomic gases with the means of matter wave interference.     

Majorana modes in solid state systems and its dynamics

We review the properties of Majorana fermions in particle physics and point out that Majorana modes in solid state systems are significantly different. The key reason is the concept of anti-particle in solid state systems is different from its counterpart in particle physics. We define Majorana modes as the eigenstates of Majorana operators and find that they can exist both at edges and in the bulk. According to our definition, only one single Majorana mode can exist in a system no matter at edges or in the bulk. Kitaev’s spinless p-wave superconductor is used to illustrate our results and the dynamical behavior of the Majorana modes.     

凝聚态理论和材料计算研究进展

文章介绍了中国科学院物理研究所凝聚态理论与材料计算实验室的历史渊源和发展现状,重点介绍了该室研究人员自2001年以来在表面与半导体物理、强关联物理、自旋与轨道电子学、冷原子与玻色-爱因斯坦凝聚体、固体物理中的贝里相位效应、低维量子输运与量子信息等方向所做的研究工作.     

数学是物理的

数学是抽象的，它使用的符号和概念，以及研究的对象可以完全和实际的物体无关.但是数学家和计算机都是物理的实体，受物理规律的约束.这个无法逃避的基本事实会影响数学的发展.通过仔细分析图灵机，本文指出图灵和他同时代科学家忽略了一个基本的物理可能，信息的载体可以是量子系统.这个疏忽使得他们提出的计算机模型只能处理经典信息，能力受到极大限制.哥德尔不完全定理则反映了这样一个事实：数学家和计算机是由有限多的原子和分子构成，他们只能从有限的假设或公理出发，利用有限的符号和字母，完成有限步的推导.因此即使加上未来所有的数学家和计算机，他们能证明的数学定理一定是可数无穷多的.但是世界上有不可数多的数学命题，这样总是存在很多数学命题你既无法证明也无法证伪.朗道尔(Landauer)曾经说，信息是物理的；在同样的意义上，数学是物理的.