Lorentz quantum computer

A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gates are constructed and their universality is proved.As an application,a search algorithm is designed for this computer model and is found to be exponentially faster than Grover's search algorithm.

Imaginary Time Crystal of Thermal Quantum Matter

Temperature is a fundamental thermodynamic variable for matter.Physical observables are often found to either increase or decrease with it,or show a non-monotonic dependence with peaks signaling underlying phase transitions or anomalies.Statistical Held theory has established connection between temperature and time:a quantum ensemble with inverse temperatureβis formally equivalent to a dynamic system evolving along an imaginary time from 0 to iβin the space one dimension higher.Here we report that a gas of hard-core bosons interacting with a thermal bath manifests an unexpected temperature-periodic oscillation of its macroscopic observables,arising from the microscopic origin of space-time locked translational symmetry breaking and crystalline ordering.Such a temperature crystal,supported by quantum Monte Carlo simulation,generalizes the concept of purely spatial density-wave order to the imaginary time axis for Euclidean action.

Logarithmic Quantum Time Crystal

We investigate a time-independent many-boson system,whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit.Out of these quasi-degenerate ground states we construct a quantum state that evolves in time with a period that is logarithmically proportional to the number of particles,that is,T~log N.This boson system in such a state is a quantum time crystal as it approaches the ground state in the thermodynamic limit.The logarithmic dependence of its period on the total particle number N makes it observable experimentally even for systems with very large number of particles.Possible experimental proposals are discussed.

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.

Resonant Quantum Search with Monitor Qubits

We present an algorithm for the generalized search problem(searching k marked items among N items)based on a continuous Hamiltonian and exploiting resonance.This resonant algorithm has the same time complexity O(√N/k)as the Grover algorithm.A natural extension of the algorithm,incorporating auxiliary"monitor"qubits,can determine k precisely,if it is unknown.The time complexity of our counting algorithm is O(√N),similar to the best quantum approximate counting algorithm,or better,given appropriate physical resources.

Quantum Algorithm for Approximating Maximum Independent Sets

We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states,which generates quantum annealing in a secondary Hamiltonian.For both sparse and dense random graphs G,numerical simulation suggests that our algorithm on average finds an independent set of size close to the maximum size α(G) in low polynomial time.The best classical algorithms,by contrast,produce independent sets of size about half of α(G)in polynomial time.

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.

Superfluid phases and excitations in a cold gas of d-wave interacting bosonic atoms and molecules

Motivated by recent advances in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to have three interesting superfluid phases: atomic, molecular, and atomic–molecular. In great contrast to what was previously known about the p-wave case, the atomic superfluid is found to be momentum-independent for the d-wave case discussed here. The Bogoliubov spectra above each superfluid phase are obtained both analytically and numerically.

Superfluidity of Bose Einstein condensates in ultracold atomic gases

Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose-Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters, such as interaction strength and density. The new superfluid, Bose-Einstein condensate （BEC）, offers various advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, it is convenient to tune almost all the parameters of a BEC, for example, the kinetic energy by spin--orbit coupling, the density by the external potential, and the interaction by Feshbach resonance. Great efforts have been devoted to studying these new aspects, and the results have greatly enriched our understanding of superfluidity. Here we review these developments by focusing on the stability and critical velocity of various superfluids. The BEC systems considered include a uniform superfluid in free space, a superfluid with its density periodically modulated, a superfluid with artificially engineered spinorbit coupling, and a superfluid of pure spin current. Due to the weak interaction, these BEC systems can be well described by the mean-field Gross-Pitaevskii theory and their superfluidity, in particular critical velocities, can be examined with the aid of Bogoliubov excitations. Experimental proposals to observe these new aspects of superfluidity are discussed.

Ehrenfest Time at the Transition from Integrable Motion to Chaotic Motion

Ehrenfest time depends differently on the Planck constant in integrable motion and chaotic motion. We study how its dependence on the Planck constant changes when there is a continuous transition from regular motion to chaotic motion. We find that the dependence is a weighted compromise between its two distinct dependences in regular and chaotic motions. The study is carried out with the system of periodically driven anharmonic oscillator. As the system is quite typical, the result may apply generally.

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.

Holographic axion model: A simple gravitational tool for quantum matter

This is a complete and exhaustive review on the so-called holographic axion model—a bottom-up holographic system characterized by the presence of a set of shift symmetric scalar bulk fields whose profiles are taken to be linear in the spatial coordinates.This simple model implements the breaking of translational invariance of the dual field theory by retaining the homogeneity of the background geometry and therefore allowing for controllable and fast computations. The usages of this model are very vast and they are a proof of the spectacular versatility of the framework. In this review, we touch upon all the up-to-date aspects of this model from its connection with massive gravity and effective field theories, to its role in modeling momentum dissipation and elastic properties ending with all the phenomenological features and its hydrodynamic description. In summary, this is a complete guide to one of the most used models in Applied Holography and a must-read for any researcher entering this field.

Repulsive gravitational effect of a quantum wave packet and experimental scheme with superfluid helium

当量力学，严肃，和热力学同时被考虑时，我们考虑量波浪包的重力的效果。在严肃的热力学的起源的假设下面，我们建议一个一般方程描述量波浪包的重力的效果。在古典限制，这个方程同意引力的牛顿法律。为量波浪包，然而，它预言排斥重力的效果。我们用超流体氦建议一个试验性的计划测试这排斥重力的效果。我们的研究证明与象超导的 gravimetry 和冷原子 interferometry 那样的现在的技术，为超流体氦的排斥重力的效果的测试在试验性的活动范围以内。

Quantum-classical correspondence in integrable systems

We find that the quantum-classical correspondence in integrable systems is characterized by two time scales. One is the Ehrenfest time below which the system is classical;the other is the quantum revival time beyond which the system is fully quantum. In between, the quantum system can be well approximated by classical ensemble distribution in phase space. These results can be summarized in a diagram which we call Ehrenfest diagram. We derive an analytical expression for Ehrenfest time, which is proportional to h-1/2. According to our formula, the Ehrenfest time for the solar-earth system is about 1026 times of the age of the solar system. We also find an analytical expression for the quantum revival time, which is proportional to h-1. Both time scales involve ω(I), the classical frequency as a function of classical action. Our results are numerically illustrated with two simple integrable models. In addition, we show that similar results exist for Bose gases, where 1/N serves as an effective Planck constant.

人机交互量子系统非平衡稳态中的自发对称破缺和局域化

物理系统的时间演化一般用微分方程来描述,而数值求解微分方程往往需要将时空分立化,将微分方程变换成为差分方程,在这一分立化的过程往往伴随着累积误差的产生,进而降低模拟精度,但是,在量子电路计算系统中,“演化时间”表示量子线路的层数,只能取分立的数值。因此,在这类系统中,由时间分立化带来的累积误差不再是数值误差,而会带来物理上可观测的效果。本文提出了一种由反馈和时间分立化导致的新的量子动力学:人机交互量子动力学,这一动力学的特点是在保持了演化的么正性的前提下,系统能量不断耗散,最终达到一种非平衡稳态,这一非平衡稳态中可能涌现出超越平衡态框架的新的物理现象和物理机制,例如发生在零维系统的自发对称破缺,以及一种不同与安德森局域化的新的量子局域化机制。

超冷世界的理想外尔拓扑物质

Chiral symmetry played a spectacular role in the qualitative understanding of the low energy effective theory of quantum chromodynamics(QCD)and in the formulation of the standard model of electroweak and strong interactions in high energy physics.For the former,it is through the chiral symmetry breaking phenomena such as the emergence of pions.

Nanoporous Vesicular Membranes of Amphiphilic Polymers Containing Trans/Cis Isomers

Nanoporous membranes and vesicles are interesting systems with potential in applications offering channels for material exchange.Herein,nanoporous membranes and polymersomes are developed by self-assembly of trans-and cis-stereoisomers of amphiphilic polymers.Two polymers,PEG550-TPEChol and PEG550-SS-TPE-SS-Chol,containing a central tetraphenylethene(TPE),a cholesterol(Chol),and a poly(ethylene glycol)(PEG550)are studied.

Majorana modes in solid state systems and its dynamics

我们在粒子物理考察 Majorana 费米子的性质并且指出在固体的 Majorana 模式声明系统是显著地不同的。关键原因是在稳固的州的系统的反粒子的概念与它在粒子物理的对应物不同。我们把 Majorana 模式定义为 Majorana 操作员的 eigenstates 并且发现他们能在边并且在体积存在。根据我们的定义，一个仅仅单个 Majorana 模式能在一个系统存在在边或在体积不管。Kitaevs 无纺纱的 p 波浪超导体被用来说明我们的结果和 Majorana 模式的动态行为。

Construction of maximally localized Wannier functions

我们在场为构造最大地局部性的 Wannier 的一个一般方法工作。它由三步组成：拣局部性的试用波浪功能的(i) ，(ii ) 执行完整的乐队设计，并且(iii ) 有 L 的 orthonormalizing ? wdin 方法。我们的方法能够没有进一步的最小化，生产最大地局部性的 Wannier 功能，并且没有使用 supercells，它能正直地被用于随机的潜力。我们的方法的有效性为简单乐队和合成乐队被表明。