Implementation of the Fredkin gate with a three-qubit mixed-spin Heisenberg model

We show that a local unitary(LU) equivalent Fredkin gate can be obtained from the free evolution of three mixed-spin qubits by virtue of numerical simulation with only one step.The spin-1 qubit acts as the control qubit,and two spin-1/2 qubits,which interact with the spin-1 qubit via the first neighbor spin interaction,respectively,play the role of target qubits.We also examine the imperfect Fredkin gate operation by considering the effects of nonidentical coupling constants,uniform and inhomogeneous magnetic fields.     

用激光-二能级原子系统实现一位通用量子逻辑门

使用代数动力学方法，对激光-二能级原子系统的含时薛定谔方程进行求解.该系统哈密顿量具有SU(2)代数结构，得到了严格解.基于严格解，适当调节单模激光场的频率和振幅以及短脉冲激光与二能级原子的二阶虚光子作用强度，可实现一位通用量子逻辑门. 关键词： 代数动力学 激光-二能级原子系统 一位量子逻辑门     

Reduction of two two-body operators in the effective hyperfine hamiltonian to one-body operators

The two two-body operators representing the effect of far configurations on the contact hyperfine interaction in annl ^N n′s configuration are shown to reduce to one-body operators. In such a configuration the operator for the contact hyperfine field is (a _nlS_nl +a_n,ss_n′s), where a_nl and a_n′s take the same values in all terms of the configuration. A discrepancy between expectation values of these two-body operators deduced from experiment and calculated values is explained.     

有限维算符整函数幂级数展开的简单实现

在量子力学算符可表示为有限维矩阵形式的情况下,利用线性代数中Hamilton—Cayley定理,针对算符整函数的无穷幂级数展开,给出化简方法．     

Mapping properties of wave and scattering operators for two-body Schrödinger operators

The modified wave and scattering operators are shown to be bounded between weighted L ²-spaces for two-body Schrödinger operators with long range potentials.     

Buckyball quantum computer: realization of a quantum gate

We have studied a system composed by two endohedral fullerene molecules. We have found that this system can be used as good candidate for the realization of quantum gates. Each of these molecules encapsules an atom carrying a spin, therefore they interact through the spin dipole interaction. We show that a phase gate can be realized if we apply static and time dependent magnetic fields on each encased spin. We have evaluated the operational time of a π-phase gate, which is of the order of ns. We made a comparison between the theoretical estimation of the gate time and the experimental decoherence time for each spin. The comparison shows that the spin relaxation time is much larger than the π-gate operational time. Therefore, this indicates that, during the decoherence time, it is possible to perform some thousands of quantum computational operations. Moreover, through the study of concurrence, we get very good results for the entanglement degree of the two-qubit system. This finding opens a new avenue for the realization of quantum computers.     

Comments on the properties of one- and two-body double tensor operators

Recently, the parity, charge, time and Hermitian conjugation properties of one-body tensor operators have been reexamined and the Racah algebra has been formally extended to two-body tensor operators. In this paper we consider several important aspects related to these problems. First, we present a proof of the communication relations for two-body operators which was previously postulated. Then, comparing the reduced matrix elements for one- and two-body operators we find the normalization constant for the latter. We subsequently show that the P- and T-conjugation relations for tensor operators are relativistically invariant. Finally, we analyze the question of Hermitian conjugation of double tensor operators and conclude that previously stated conditions on their ranks were too restrictive and resulted in omissions of some terms from theoretical analyses. We show examples of tensor operators which were customarily neglected but indeed should be retained in the effective Hamiltonian.     

全同粒子两体算符的另一类非对角矩阵元

推导了玻色子和费米子两体算符在占有数表象下的另一类非对角矩阵元.     

Matrix elements of two-body operators between three-body hyperspherical basis states

Matrix elements of two-body operators between three-body spherically symmetric hyperspherical basis states are expressed through the Clebsch-Gordon coefficients and explicitly written functions of a radial variable.     

二次量子化中单体和两体算符的一种启发式推导

二次量子化是研究生和高年级本科生量子力学课程中的重要内容.如何从一次量子化中的多粒子哈密顿量及波函数出发,自然地导出二次量子化中由产生和湮没算符表示的单体和两体算符,是一个既关键且又使初学者较难理解的步骤.以全同费米子系统为例,本文给出该步骤的一种自然且具有启发性的推导方法.该方法仅依赖于:多粒子波函数的对称性假设,Fock空间中“真空填充”的概念,以及全反对称多粒子波函数与Fock态的等价性.     

Phonon dispersion in graphite using a two-body potential approach

A two-body potential has been proposed for graphite. In addition to the Born-Mayer constants A and ϱ, the proposed potential contains two parameters for the stability of the crystal along a and c axis. The potential parameters were determined with the help of experimental elastic constants. Using this potential, the phonon dispersion in graphite is calculated in (ooq) and (qoo) directions. The interactions were considered up to two neighbours in the plane and one neighbour between the planes. The theoretical results are in good agreement with the available experimental ones, especially the agreement for the A_2u out of plane mode at 868 cm⁻¹     

The Schur function realization of vertex operators

We present a realization of untwisted vertex operators in terms of operations on Schur functions. Calculations of matrix elements and traces of products of vertex operators are performed using results from the classical theory of symmetric functions. The concepts of compound, composite and supersymmetric Schur functions naturally appear in this context. Furthermore, a trace formula for a product of vertex operators turns out to be a generalization of a MacDonald identity reformulated in terms of Schur functions.     

用惯性力分析二体问题

利用惯性力分析二体问题.     

Optimizing a phase gate using quantum interference

A controlled interference is proposed to reduce, by two orders of magnitude, the decoherence of a quantum gate for which the gate fidelity is limited by coupling to states other than the /0> and /1> qubit states. This phenomenon is demonstrated in an ultracold neutral atom implementation of a phase gate using qubits based on motional states in individual wells of an optical lattice.     

Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate

Rabi nutations of a single nuclear spin in a solid have been observed. The experiments were carried out on a single electron and a single 13C nuclear spin of a single nitrogen-vacancy defect center in diamond. The system was used for implementation of quantum logical NOT and a conditional two-qubit gate (CROT). Density matrix tomography of the CROT gate shows that the gate fidelity achieved in our experiments is up to 0.9, good enough to be used in quantum algorithms.     

Width of a two-body coupled-channel resonance

We study the width of a two-body resonance in a coupled-channel system. We demonstrate how the width does not come only determined by the available phase space for its decay to the detection channel, but it greatly depends on the relative position of the mass of the resonance with respect to the masses of the coupled-channels generating the state. Our results are consistent with the experimental observation of narrow hadrons lying well above their lowest decay threshold.     

On two-body decays of a scalar glueball

We study two-body decays of a scalar glueball. We show that in QCD a spin-0 pure glueball (a state with only gluons) cannot decay into a pair of light quarks if chiral symmetry holds exactly, i.e., the decay amplitude is chirally suppressed. However, this chiral suppression does not materialize itself at the hadron level such as in decays into π⁺π^- and K⁺K^-. We show this explicitly in the two cases with the glueball much lighter and much heavier than the QCD scale using low-energy theorems and perturbative QCD. For a heavy glueball, using QCD factorization based on an effective Lagrangian, we find that the hadronization into ππ and KK leads to a large difference between Br(π⁺π^-) and Br(K⁺K^-); even the decay amplitude is not chirally suppressed. Our results can provide some understanding of the partonic contents if Br(ππ) or Br(KK̄) is measured reliably.     

Simple separable expansions for calculating matrix elements of two-body local interactions with harmonic oscillator functions

A simple method is proposed to calculate the matrix elements of two-body local interactions using a harmonic oscillator basis (HOF). Using the properties of HOF, it is shown that any local potential can be replaced by a simple series for the purpose of calculating matrix elements. This series can be reduced to a finite sum when evaluating a matrix element. Its terms are separable functions of the coordinates of the two particles; hence the advantage of the method. In the present article we treat the most important components of the two-body interaction, namely central, two-body spin-orbit, and tensor forces. As a representation we have chosen spherical harmonic oscillator functions expressed with spherical coordinates. This technique appears to be very well adapted to and efficient for Hartree-Fock calculations in any representation of the HOF. A very interesting feature of this formulation is that it can be easily extended to calculations employing generalized HOF as defined by Wong.