Xiwen Zhu

Experimental implementation of remote state preparation by nuclear magnetic resonance

Abstract We have experimentally implemented remote state preparation of a qubit from a hydrogen to a carbon nucleus in molecules of carbon-13 labeled chloroform 13 CHCl 3 over interatomic distances using liquid-state nuclear magnetic resonance techniques. Full RSP of a special ensemble of qubits, i.e., a qubit chosen from either an equatorial or a polar great circle on a Bloch sphere with Patis scheme, was achieved with one cbit communication.

Experimental implementation of dense coding using nuclear magnetic resonance

Quantum dense coding has been demonstrated experimentally in terms of quantum logic gates and circuits in quantum computation and NMR technique. Two bits of information have been transmitted through manipulating one of the maximally entangled two-state quantum pairs, which is completely consistent with the original ideal of the Bennett-Wiesner proposal. Although information transmission happens between spins over interatomic distance, the scheme of entanglement transformation and measurement can be used in other processes of quantum information and quantum computing.

Experimental implementation of Hogg's algorithm on a three-quantum-bit NMR quantum computer

Using nuclear magnetic resonance (NMR) techniques with a three-qubit sample, we have experimentally implemented the highly structured algorithm for the satisfiability problem with one variable in each clause proposed by Hogg. A simplified temporal averaging procedure was employed to prepare the three-qubit pseudopure state. The algorithm was completed with only a single evaluation of the structure of the problem and the solutions were found theoretically with probability 100%, results that outperform both unstructured quantum and the best classical search algorithms. However, about 90% of the corresponding experimental fidelities can be attributed to the imperfections of manipulations.

Preparation of pseudo-pure states by line-selective pulses in nuclear magnetic resonance

Abstract An alternative method of preparing the pseudo-pure state of a spin system for quantum computation in liquid-state nuclear magnetic resonance (NMR) is demonstrated experimentally. Applying specific line-selective pulses with appropriately chosen flipping angles simultaneously and then a field gradient pulse we acquire straightforwardly all pseudo-pure states for two qubits in a single experiment quite efficiently. The signal intensity from the pseudo-pure state prepared in this way is the same as that of temporal averaging. As an example of an application, a highly structured search algorithm – Hoggs algorithm – is also performed on the pseudo-pure state |0 0〉 prepared by the method.

Stable orbits embedded in a chaotic attractor for a trapped ion interacting with a laser field

The interaction between a trapped ion and a resonant laser standing wave is studied under the analytical approximation. Periodic orbits next to the heteroclinic one and their stability conditions are derived from the Rayleigh perturbation method. Theoretical analysis reveals the stable periodic orbits to be embedded in the Melnikov chaotic attractor. The corresponding numerical results show that fitting control parameters into the stability conditions can control chaos in the system.

Avalanche dynamics in the Bak-Sneppen evolution model observed with a standard distribution width of fitness

We introduce the standard distribution width of fitness to characterize the global and individual features of an ecosystern described by the Bak-Sneppen evolution model. Through tracking this quantity in evolution, a different hierarchy of avalanche dynamics, the w(0) avalanche, is observed. The corresponding gap equation and the self-organized threshold w(c) are obtained. The critical exponents tau, gamma and rho, which describe the behaviour of the avalanche size distribution, the average avalanche size and the relaxation to attractor, respectively, are calculated by numerical simulation. The exact master equation and gamma equation are derived, and the scaling relations are established among the critical exponents of this new avalanche.

ORIGIN AND MANIFESTATION OF THE ANHARMONIC POTENTIAL FELT BY AN ION-CLOUD IN AN ACTUAL PAUL TRAP

The anharmonic potential felt by a single-species ions confined in a rf quadrupole trap which results from a non-ideal trap configuration and the charge distribution of the ion cloud is studied. The rf resonance-absorption spectra are explained by a Duffing oscillator and a representation of the line-shape parameter η is derived. Forη > 0.77, the electric signals will exhibit hysteresis. The relation with the anharmonic potential is discussed.

Numerical instability in Rayleigh-Schrödinger quantum mechanics

The most physically interesting systems are not exactly solvable in quantum mechanics. For one-dimensional bound systems without exact solutions, we analytically and numerically find that the Rayleigh-Schrodinger perturbed series sensitively depends on an unsolvable integration, which leads to numerical instability in quantum mechanics. By using an exact formal solution of the non-homogeneous Schrodinger equation, we demonstrate the existence of analytically bound states and propose a simple scheme to truncate infinity so that the instability difficulty is avoided.

Realization of quantum discrete Fourier transform with NMR

The pulse sequences of the logic operations used in quantum discrete Fourier transform are designed for the experiment of nuclear magnetic resonance(NMR), and 2-qubit discrete Fourier transforms are implemented experimentally with NMR. The experimental errors are examined and methods for reducing the errors are proposed.

An interferometric complementarity experiment in a bulk nuclear magnetic resonance ensemble

We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability D quantifying the amount of which-way (WW) information to the fringe visibility V characterizing the wave feature of a quantum entity, in a bulk ensemble by nuclear magnetic resonance (NMR) techniques. We are primarily concerned about the intermediate cases: partial fringe visibility and incomplete WW information. We propose a quantitative measure of D by an alternative geometric strategy and investigate the relation between D and entanglement. By measuring D and V independently, it turns out that the duality relation D2 + V2 = 1 holds for pure quantum states of the markers.