Abstract:
We report on the implementation of Burgers equation as a type-II quantum computation on an NMR quantum information processor. Since the flow field evolving under the Burgers equation develops sharp features over time, this is a better test of liquid state NMR implementations of type-II quantum computers than the previous examples using the diffusion equation. In particular, we show that Fourier approximations used in the encoding step are not the dominant error. Small systematic errors in the collision operator accumulate and swamp all other errors. We propose, and demonstrate, that the accumulation of this error can be avoided to a large extent by replacing the single collision operator with a set of operators with random errors and similar fidelities. Experiments have been implemented on 16 two-qubit sites for eight successive time steps for the Burgers equation.

Abstract:
We study experimentally a system comprised of linear chains of spin-1/2 nuclei that provides a test-bed for multi-body dynamics and quantum information processing. This system is a paradigm for a new class of quantum information devices that can perform particular tasks even without universal control of the whole quantum system. We investigate the extent of control achievable on the system with current experimental apparatus and methods to gain information on the system state, when full tomography is not possible and in any case highly inefficient.

Abstract:
Transport of quantum information in linear spin chains has been the subject of much theoretical work. Experimental studies by nuclear spin systems in solid-state by NMR (a natural implementation of such models) is complicated since the dipolar Hamiltonian is not solely comprised of nearest-neighbor XY-Heisenberg couplings. We present here a similarity transformation between the XY-Heisenberg Hamiltonian and the grade raising Hamiltonian, an interaction which is achievable with the collective control provided by radio-frequency pulses in NMR. Not only does this second Hamiltonian allows us to simulate the information transport in a spin chain, but it also provides a means to observe its signature experimentally.

Abstract:
We apply optimal control theory (OCT) to the design of refocusing pulses suitable for the CPMG sequence that are robust over a wide range of B0 and B1 offsets. We also introduce a model, based on recent progress in the analysis of unitary dynamics in the field of quantum information processing (QIP), that describes the multiple refocusing dynamics of the CPMG sequence as a dephasing Pauli channel. This model provides a compact characterization of the consequences and severity of residual pulse errors. We illustrate the methods by considering a specific example of designing and analyzing broadband OCT refocusing pulses of length 10 t180 that are constrained by the maximum instantaneous pulse power. We show that with this refocusing pulse, the CPMG sequence can refocus over 98% of magnetization for resonance offsets up to 3.2 times the maximum RF amplitude, even in the presence of +/- 10% RF inhomogeneity.

Abstract:
In a dynamic nuclear polarization experiment on a 40 mM solution of 4-amino-TEMPO in a 40:60 water/glycerol mixture, we have observed that the bulk dipolar reservoir is cooled to a spin temperature of 15.5 micro-K, following microwave irradiation for 800 s. This is significantly cooler than the 35 mK spin temperature of the Zeeman reservoir. Equilibration of the two reservoirs results in a 50 % increase in the NMR signal intensity, corresponding to a Zeeman spin temperature of 23 mK. In order to achieve this polarization directly, it was necessary to irradiate the sample with microwaves for 1500 s. Cooling of the dipolar reservoir occurs during polarization transport through the magnetic field gradient around the paramagnetic impurity, and is rapidly communicated to the bulk by dipolar spin diffusion. As dipolar spin diffusion is significantly faster than Zeeman spin diffusion, the bulk dipolar reservoir cools faster than the Zeeman reservoir. This process can be exploited to rapidly polarize the nuclear spins, by repeatedly cooling the dipolar system and transferring the polarization to the Zeeman reservoir.

Abstract:
Quantum computers will be unique tools for understanding complex quantum systems. We report an experimental implementation of a sensitive, quantum coherence-dependent localization phenomenon on a quantum information processor (QIP). The localization effect was studied by emulating the dynamics of the quantum sawtooth map in the perturbative regime on a three-qubit QIP. Our results show that the width of the probability distribution in momentum space remained essentially unchanged with successive iterations of the sawtooth map, a result that is consistent with localization. The height of the peak relative to the baseline of the probability distribution did change, a result that is consistent with our QIP being an ensemble of quantum systems with a distribution of errors over the ensemble. We further show that the previously measured distributions of control errors correctly account for the observed changes in the probability distribution.

Abstract:
We present experimental results which demonstrate that nuclear magnetic resonance spectroscopy is capable of efficiently emulating many of the capabilities of quantum computers, including unitary evolution and coherent superpositions, but without attendant wave-function collapse. Specifically, we have: (1) Implemented the quantum XOR gate in two different ways, one using Pound-Overhauser double resonance, and the other using a spin-coherence double resonance pulse sequence; (2) Demonstrated that the square root of the Pound-Overhauser XOR corresponds to a conditional rotation, thus obtaining a universal set of gates; (3) Devised a spin-coherence implementation of the Toffoli gate, and confirmed that it transforms the equilibrium state of a four-spin system as expected; (4) Used standard gradient-pulse techniques in NMR to equalize all but one of the populations in a two-spin system, so obtaining the pseudo-pure state that corresponds to |00>; (5) Validated that one can identify which basic pseudo-pure state is present by transforming it into one-spin superpositions, whose associated spectra jointly characterize the state; (6) Applied the spin-coherence XOR gate to a one-spin superposition to create an entangled state, and confirmed its existence by detecting the associated double-quantum coherence via gradient-echo methods.

Abstract:
We report an ensemble nuclear magnetic resonance (NMR) implementation of a quantum lattice gas algorithm for the diffusion equation. The algorithm employs an array of quantum information processors sharing classical information, a novel architecture referred to as a type-II quantum computer. This concrete implementation provides a test example from which to probe the strengths and limitations of this new computation paradigm. The NMR experiment consists of encoding a mass density onto an array of 16 two-qubit quantum information processors and then following the computation through 7 time steps of the algorithm. The results show good agreement with the analytic solution for diffusive dynamics. We also describe numerical simulations of the NMR implementation. The simulations aid in determining sources of experimental errors, and they help define the limits of the implementation.

Abstract:
Control over spin dynamics has been obtained in NMR via coherent averaging, which is implemented through a sequence of RF pulses, and via quantum codes which can protect against incoherent evolution. Here, we discuss the design and implementation of quantum codes to protect against coherent evolution. A detailed example is given of a quantum code for protecting two data qubits from evolution under a weak coupling (Ising) term in the Hamiltonian, using an ``isolated'' ancilla which does not evolve on the experimental time scale. The code is realized in a three-spin system by liquid-state NMR spectroscopy on 13C-labelled alanine, and tested for two initial states. It is also shown that for coherent evolution and isolated ancillae, codes exist that do not require the ancillae to initially be in a (pseudo-)pure state. Finally, it is shown that even with non-isolated ancillae quantum codes exist which can protect against evolution under weak coupling. An example is presented for a six qubit code that protects two data spins to first order.

Abstract:
Quantum information processing by liquid-state NMR spectroscopy uses pseudo-pure states to mimic the evolution and observations on true pure states. A new method of preparing pseudo-pure states is described, which involves the selection of the spatially labeled states of an ancilla spin with which the spin system of interest is correlated. This permits a general procedure to be given for the preparation of pseudo-pure states on any number of spins, subject to the limitations imposed by the loss of signal from the selected subensemble. The preparation of a single pseudo-pure state is demonstrated by carbon and proton NMR on 13C-labeled alanine. With a judicious choice of magnetic field gradients, the method further allows encoding of up to 2^N pseudo-pure states in independent spatial modes in an N+1 spin system. Fast encoding and decoding schemes are demonstrated for the preparation of four such spatially labeled pseudo-pure states.