Quantum virial coefficients of molecular nitrogen

We report virial coefficients up to third order in density for molecular nitrogen, investigating 103 temperatures in the range (15 K, 3000 K). All calculations are based on an ab initio-based potential taken from the literature. Path-integral Monte Carlo (PIMC) is applied to account for nuclear quantum effects, and these results are compared to a more approximate but faster semiclassical treatment. Additionally, we examine a PIMC approach that employs semiclassical beads for the path-integral images, but find that it offers marginal advantage. A recently developed orientation sampling algorithm is used in conjunction with Mayer sampling to compute precise virial coefficients. We find that, within the precision of our calculations of the second-order coefficient (B₂), semiclassical methods are adequate for temperatures greater than 250 K, and are needed to correct classical behaviour for temperatures as high as 800 K. For the third-order coefficient (B₃), the semiclassical methods are adequate above 150 K, and are required up to the highest temperature examined (3000 K) in order to correct the classical treatment within the precision of the calculations. However, three-body contributions to the potential are much more significant than nuclear quantum effects for the evaluation of B₃.     

Semiclassical theory of molecular collisions: Real and complex-valued classical trajectories for collinear atom Morse oscillator collisions

Real and complex-valued classical trajectories have been calculated for the collinear collision of an atom with a Morse oscillator. They are used in three semiclassical approximations for the transition probability: a Bessel uniform approximation, an Airy uniform approximation and a primitive semiclassical approximation. Comparison with exact quantum results shows that the Bessel uniform approximation is accurate even for near elastic collisions where the Airy and primitive approximations break down. The Airy and Bessel approximations agree quite closely for inelastic collisions however. The primitive semiclassical approximation is less accurate than either the Airy or Bessel approximation.     

Displacement echoes: classical decay and quantum freeze

Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase-space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value because of quantum effects. Our analytical results are corroborated by numerical simulations.     

Realization of -bit semiclassical quantum Fourier transform on IBM's quantum cloud computer

To overcome the difficulty of realizing large-scale quantum Fourier transform(QFT) within existing technology, this paper implements a resource-saving method(named t-bit semiclassical QFT over Z_(2~n)), which could realize large-scale QFT using an arbitrary-scale quantum register. By developing a feasible method to realize the control quantum gate Rk, we experimentally realize the 2-bit semiclassical QFT over Z_(2~3) on IBM's quantum cloud computer, which shows the feasibility of the method. Then, we compare the actual performance of 2-bit semiclassical QFT with standard QFT in the experiments.The squared statistical overlap experimental data shows that the fidelity of 2-bit semiclassical QFT is higher than that of standard QFT, which is mainly due to fewer two-qubit gates in the semiclassical QFT. Furthermore, based on the proposed method, N = 15 is successfully factorized by implementing Shor's algorithm.     

A nonadiabatic semi-classical method for dynamics of atoms in optical lattices

We develop a semi-classical method to simulate the motion of atoms in a dissipative optical lattice. Our method treats the internal states of the atom quantum mechanically, including all nonadiabatic couplings, while position and momentum are treated as classical variables. We test our method in the one-dimensional case. Excellent agreement with fully quantum mechanical simulations is found. Our results are much more accurate than those of earlier semi-classical methods based on the adiabatic approximation.     

Quantum zeta function for perturbed cat maps

The behavior of semiclassical approximations to the spectra of perturbed quantum cat maps is examined as the perturbation parameter brings the corresponding classical system into the nonhyperbolic regime. The approximations are initially accurate but large errors are found to appear in the traces and in the coefficients of the characteristic polynomial after nonhyperbolic structures appear. Nevertheless, the eigenvalues obtained from them remain accurate up to large perturbations. (c) 1995 American Institute of Physics.     

Deterministic controlled bidirectional remote state preparation in dissipative environments

It is a significant subject to explore effective quantum communication protocol and enhance the efficiency of the transmission process in noisy environments. In this paper, we investigate the bidirectional controlled remote preparation of an arbitrary single-qubit state in the presence of dissipative environments by using two EPR states as the entanglement source. We first construct the quantum circuit of our scheme by means of unitary matrix decomposition procedure, then the effects of the Markovian and non-Markovian environmental noises acting on the EPR states are considered through the analytical derivation and numerical calculations of the corresponding average fidelity. Moreover, we adopt two methods of weak measurement reversal (WMR) and detuning modulation to improve the average fidelity. Our results show that the average fidelity can be remarkably enhanced under appropriate conditions of the WMR strength and the detuning. Compared with the average fidelity behaviors in dissipative environments, it is also shown that the two methods for fidelity improvement are more efficient in the non-Markovian regime than in the Markovian regime.     

How to utilize a Grover search in general programming

It is widely believed that quantum computers (if realized) will be more powerful than today’s computers from the viewpoint of computational complexity. However, it is not obvious how to utilize quantum computers in practical situations. For practical purposes, a Grover search may be one of the most promising quantum algorithms known so far. Thus, in this paper, we propose an efficient framework where we can use Grover search for general programming. Our framework has the following steps. (1) A programmer writes a program by using standard C++ programming language. (2) Some if expressions within for loops in the C++ source code are chosen as candidates to be performed as a Grover search on a quantum computer. (3) The framework automatically generates a corresponding quantum circuit for each Grover search chosen in (2). Unlike the existing quantum circuit design methods, we can treat large problems in our quantum circuit design. (4) By evaluating the number of primitive quantum gates in the quantum circuit generated in (3), the framework determines whether the processing time of the quantum circuit is faster than the processing time of the corresponding if expression on a classical computer. If the framework determines that the quantum circuit is faster, it generates some interface source codes for a classical computer. Thus, in our framework, a programmer can use a Grover search with almost no effort.     

二维椭圆量子台球中的谱分析

研究了二维椭圆台球中的量子谱和经典轨道之间的对应关系.为尝试求解没有解析波函数和本征能量又不能分离变量的体系，采用了定态展开方法(expansion method for stationary states，简称EMSS)得到尽可能精确的数值解，这是闭合轨道理论被推广到计算开轨道的情况.比较了傅里叶变换谱和经典轨道，发现量子谱的峰位置与经典轨道的长度在可分辨的范围内符合得很好，这是半经典理论为经典与量子力学的联系提供桥梁作用的又一个例子. 关键词： 椭圆量子台球 定态展开方法 闭合轨道理论 量子谱     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

Algebraically Self-Consistent Quasiclassical Approximation on Phase Space

The Wigner–Weyl mapping of quantum operators to classical phase space functions preserves the algebra, when operator multiplication is mapped to the binary * operation. However, this isomorphism is destroyed under the quasiclassical substitution of * with conventional multiplication; consequently, an approximate mapping is required if algebraic relations are to be preserved. Such a mapping is uniquely determined by the fundamental relations of quantum mechanics, as is shown in this paper. The resultant quasiclassical approximation leads to an algebraic derivation of Thomas–Fermi theory, and a new quantization rule which—unlike semiclassical quantization—is non-invariant under action transformations of the Hamiltonian, in the same qualitative manner as the true eigenvalues. The quasiclassical eigenvalues are shown to be significantly more accurate than the corresponding semiclassical values, for a variety of 1D and 2D systems. In addition, certain standard refinements of semiclassical theory are shown to be easily incorporated into the quasiclassical formalism.     

Experimental quantum state tomography via compressed sampling

A fundamental difficulty in demonstrating quantum state tomography is that the required resources grow exponentially with the system size. For pure states and nearly pure states, the task of tomography can be more efficient. We proposed two methods for state reconstruction, by (1) minimizing entropy and (2) maximizing likelihood. The algorithm of compressed sampling is employed to solve the optimization problem. Experiments are demonstrated considering 4-qubit photonic states. The results show that (1) much fewer measurements than the standard tomography are sufficient to obtain high fidelity, and (2) the method of maximizing likelihood is more accurate and noise robust than the original reconstruction method of compressed sampling. Furthermore, the physical meaning of the methods of minimizing entropy and maximizing likelihood is clear.     

Classical breathers and quantum coherent states in discrete NLS systems

We present a comparison of quantum and “semiclassical” trajectories of coherent states that correspond to classical breather solutions of finite discrete nonlinear Schrödinger (DNLS) lattices. The main goal is to explain earlier numerical observations of recurrent return to the vicinity of initial coherent states corresponding to stable breathers that are also spatially localized. This effect can be considered as a quantum manifestation of classical spatial localization. We show that these phenomena are encoded in a simple expression for the distance between the quantum and semiclassical states that involves the basic frequencies of the classical and quantum systems, as well as the breather amplitude and quantum spectral decomposition of the system. A corollary is that recurrence phenomena are robust under perturbation of the initial conditions for stable breathers.     

Quantum Andreev map: a paradigm of quantum chaos in superconductivity

We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for a large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time.