Ximing Fang

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.

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.

Experimental realization of a highly structured search algorithm

The highly structured search algorithm proposed by Hogg [Phys. Rev. Lett. 80 (1998) 2473] is implemented experimentally for the 1-SAT problem in a single search step by using nuclear magnetic resonance technique with two-qubit sample. It is the first demonstration of the Hoggs algorithm, and can be readily extended to solving the 1-SAT problem for more qubits in one step if the appropriate samples possessing more qubits are experimentally feasible

Experimental testing of complementarity for ensemble-averaged spin states

We tested wave-particle duality with the ensemble-averaged spin states of C-13 nuclei in (CHCl3)-C-13 using the spin states of H-1 nuclei as the path marker. It turns out that wave-particle duality holds when one merely measures the probability density of quantum states, and that wave- and particle-like behaviour is simultaneously observed when measuring populations and coherences in a single nuclear magnetic resonance experiment. The effects of path-marking schemes and the causes of the appearance and disappearance of wave behaviour are analysed.

Energy gaps of a trapped ion interacting with a laser field

We consider the secular motion of an ion stored in a Paul trap and interacting with a standing laser field. It is shown that the Schrodinger equation of the system is analogous to the linearized equation of a classically chaotic system. From the mathematical simulation between the two systems we reveal several new properties in the fully quantum treatment. The results lead to some parameter and energy gaps in which the motional ground state does not exist.