Quantum information processing offers potentially great advantages over classical information processing, both for efficient algorithms and for secure communication. Therefore, it is important to establish that scalable control of a large number of quantum bits (qubits) can be achieved in practice. There are a rapidly growing number of proposed device technologies for quantum information processing. Of these technologies, those exploiting nuclear magnetic resonance (NMR) have been the first to demonstrate non-trivial quantum algorithms with small numbers of qubits. To compare different physical realizations of quantum information processors, it is necessary to establish benchmark experiments that are independent of the underlying physical system, and that demonstrate reliable and coherent control of a reasonable number of qubits. Here we report an experimental realization of an algorithmic benchmark using an NMR technique that involves coherent manipulation of seven qubits. Moreover, our experimental procedure can be used as a reliable and efficient method for creating a standard pseudopure state, the first step for implementing traditional quantum algorithms in liquid state NMR systems. The benchmark and the techniques can be adapted for use with other proposed quantum devices.

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We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear magnetic resonance. We believe this to be the first explicit physical realization of such a simulation.PACS numbers: 03.67.-a,76.60.-k In 1982, Richard Feynman proposed that a quantum system would be more efficiently simulated by a computer based on the principles of quantum mechanics rather than by one based on classical mechanics [1]. Recently, it has been pointed out that it should be possible to efficiently approximate any desired Hamiltonian within the standard model of a quantum computer by a sparsely coupled array of two-state systems [2][3][4]. Many of the concepts of quantum simulation are implicit in the average Hamiltonian theory developed by Waugh and colleagues to design NMR pulse sequences which implement a specific desired effective NMR Hamiltonian [5]. Here we show the first explicit simulation of one quantum system by another; namely the simulation of the kinematics and dynamics of a truncated quantum oscillator by an NMR quantum information processor [6,7]. Quantum simulations are shown for both an undriven harmonic oscillator and a driven anharmonic oscillator.A general scheme for quantum simulation is summarized by the following diagram:The object is to simulate the effect of the evolution |s U −→ |s(T ) using the physical system P . To do this, S is related to P by an invertible map φ which determines a correspondence between all the operators and states of S and of P . In particular, the propagator U maps to V T = φ −1 U φ. The challenge is to implement V T using propagators V i arising from the available external interactions with intervening periods of natural evolution esufficient class of simple operations (logic gates) are implementable in the physical system, the Universal Computation Theorem [8][9][10] guarantees that any operator (in particular V T ) can be composed of natural evolutions in P and external interactions. For unitary maps φ, we may write V T = e −iHpT /h where H p ≡ φ −1 H s φ can be identified with the average Hamiltonian of Waugh. After |p VT −→ |p T , the final map φ −1 takes |p T → |s(T ) thereby effecting the simulation |s → |s(T ) . Note that H s (T ) can be a time dependent Hamiltonian and that T is viewed as a parameter when mapped to P . This implies that the physical times t i (T ) are parameterized by the simulated time T .Liquid state NMR quantum computers are well suited for quantum simulations because they have long spin relaxation times (T 1 and T 2 ) as well as the flexibility of using a variety of molecular samples. In particular, the coupling between the nuclear spins, usually dominated by the 'scalar' coupling (J), may be reduced at will by means of radiofrequency pulses. Typically spin 1/2 nuclei are used. Thus, the kinematics of any 2 N level quantum system could be simulated using a given N -spin molecule.We ...

Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be simulated by a quantum computer. A basis mapping between the systems dictates the average Hamiltonian in the quantum computer needed to implement the desired Hamiltonian in the simulated system. The flexibility of the procedure is illustrated with NMR on 13 C labelled Alanine by creating the non-physical Hamiltonian σzσzσz corresponding to a three body interaction.

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NMR images of laser polarized 3He gas were obtained at 21 G using a simple, homebuilt instrument. At such low fields magnetic resonance imaging (MRI) of thermally polarized samples (e.g., water) is not practical. Low-field noble gas MRI has novel scientific, engineering, and medical applications. Examples include portable systems for diagnosis of lung disease, as well as imaging of voids in porous media and within metallic systems.

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Magnetic resonance imaging using laser-polarized 129Xe is a new technique first demonstrated by Albert et. al. (Nature 370, 1994) who obtained a 129Xe image of an excised mouse lung. This paper describes the factors influencing the accumulation of inhaled, polarized 129Xe in human tissue. The resulting model predicts the 129Xe magnetization in different tissues as a function of the time from the start of inhalation, the tissue perfusion rate and partition coefficient for xenon, and the relevant T1 decay times. The relaxation times of 129Xe in biological tissues are not yet known precisely. Substitution of estimated values for these parameters results in an expected signal-to-noise ratio (SNR) from polarized 129Xe MR in the brain of approximately 2% of the equivalent SNR from proton MR.