Chain Of Nuclear Spins Research Articles

Scales of Time Where the Quantum Discord Allows an Efficient Execution of the DQC1 Algorithm

The power of one qubit deterministic quantum processor (DQC1) (Knill and Laflamme (1998)) generates a nonclassical correlation known as quantum discord. The DQC1 algorithm executes in an efficient way with a characteristic time given byτ=Tr[Un]/2n, whereUnis annqubit unitary gate. For pure states, quantum discord means entanglement while for mixed states such a quantity is more than entanglement. Quantum discord can be thought of as the mutual information between two systems. Within the quantum discord approach the role of time in an efficient evaluation ofτis discussed. It is found that the smaller the value oft/Tis, wheretis the time of execution of the DQC1 algorithm andTis the scale of time where the nonclassical correlations prevail, the more efficient the calculation ofτis. A Mösbauer nucleus might be a good processor of the DQC1 algorithm while a nuclear spin chain would not be efficient for the calculation ofτ.

Diamond as a Solid State Quantum Computer with a Linear Chain of Nuclear Spins System

By removing a 12C atom from the tetrahedral configuration of the diamond, replacing it by a 13C atom, and repeating this in a linear direction, it is possible to have a linear chain of nuclear spins one half and to build a solid state quantum computer. One qubit rotation, controlled-not (CNOT) and controlled-controlled-not (CCNOT) quantum gates are obtained immediately from this configuration. CNOT and CCNOT quantum gates are used to determined the design parameters of this quantum computer.

Simulation of static and random errors on Grover's search algorithm implemented in an Ising nuclear spin chain quantum computer with a few qubits

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first- and second-neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called the fidelity. We analyse the behaviour of the fidelity as a function of the noise intensity for static and random noise on either the Larmor frequencies or the Rabi frequency, and we compare our results to theoretical predictions and numerical simulations which are based on more abstract quantum computer models.

Quantum Computation in a Ising Spin Chain Taking into Account Second Neighbor Couplings

We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms can be performed with the help of appropriate radio-frequency pulses. In addition to the standard nearest-neighbor Ising coupling, we also allow for a second neighbor coupling. It is shown, how to apply the 2π k method in this more general setting, where the additional coupling eventually allows to save a few pulses. We illustrate our results with two numerical simulations: the Shor prime factorization of the number 4 and the teleportation of a qubit along a chain of 3 qubits. In both cases, the optimal Rabi frequency (to suppress non-resonant effects) depends primarily on the strength of the second neighbor interaction.

Entanglement in alternating open chains of nuclear spins s = 1/2 with the XY Hamiltonian

Entanglement is studied in an open alternating chain of nuclear spins s = 1/2 with spin-spin couplings in an external magnetic field under the thermodynamic equilibrium conditions. A reduced density matrix has been calculated for an arbitrarily chosen spin pair. The entanglement of the spin pair has been estimated according to the Wootters criterion. The temperature at which an entangled state appears in a chosen pair has been determined. It has been shown that the numerical characteristics of the entanglement are oscillating functions of the position of the spin pair in the chain.

Experimental demonstration of a stimulated polarization wave in a chain of nuclear spins

A stimulated wave of polarization, which implements a simple mechanism of quantum amplification, is experimentally demonstrated in a chain of four J-coupled nuclear spins, irradiated by a weak radio-frequency transverse field. The ‘quantum domino’ dynamics, a wave of flipped spins triggered by a flip of the first spin, has been observed in fully 13C-labelled sodium butyrate.

Teleportation in a nuclear spin quantum computer

We present a procedure for quantum teleportation in a nuclear spin quantum computer in which quantum logic gates are implemented by using selective electromagnetic pulses. A sequence of pulses is combined with single-spin measurements in the ${\ensuremath{\sigma}}^{z}$ basis for fast transfer of information in a spin quantum computer. We simulated this procedure for quantum teleportation in a nuclear spin chain with a large number (201) of spins. The systematic errors generated in the process of teleportation due to the non-resonant effects are analyzed in detail. We demonstrate that a $``2\ensuremath{\pi}k''$ method provides a significant reduction of errors.

Approaching five-bit NMR quantum computing

Nuclear-magnetic-resonance (NMR) quantum computation is a fruitful arena in which to develop and demonstrate an enhanced capability for quantum control over molecular systems, regardless of the prospects, which may be limited, for building a quantum computer superior to a conventional computer for any computing task. We demonstrate a five-bit NMR quantum computer that distinguishes among various functions on four bits, making use of quantum parallelism, an example of the Deutsch-Jozsa problem. Its construction draws on the recognition of the sufficiency of linear coupling along a chain of nuclear spins, the synthesis of a suitably coupled molecule containing four distinct nuclear species, and the use of a multichannel spectrometer. Radio-frequency pulse sequences are described to execute controlled-NOT gates on two adjoining spins while leaving the other three spins essentially unaffected.

Simulations of quantum-logic operations in a quantum computer with a large number of qubits

We report the first simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain in which selective excitations of spins is provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum control-not (CN) gate implementation for remote qubits which provides the long-distance entanglement. Our approach can be applied to any implementation of quantum logic gates involving a large number of qubits.

Time-resolved observation of spin waves in a linear chain of nuclear spins

The experimental observation of spin waves by NMR spectroscopy is reported for a linear chain consisting of five scalar coupled 13C spins of lysine. Selective excitation of a first spin and evolution under an effective planar zero-quantum Hamiltonian with terms 2 πJ i, i+1 ( I ix I i+1, x + I iy I i+1, y ) leads to the propagation of a damped spin-wave packet bouncing back and forth at the chain ends. The effective planar Hamiltonian is generated by the application of a multiple pulse sequence.