Yehuda Sharf

NMR Based Quantum Information Processing: Achievements and Prospects

Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMR-based QIP capable of reaching 10-30 qubits.

Quantum simulation of a three-body-interaction Hamiltonian on an NMR quantum computer

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 {sup 13}C labeled alanine by creating the nonphysical Hamiltonian {sigma}{sub z}{sigma}{sub z}{sigma}{sub z} corresponding to a three-body interaction. (c) 1999 The American Physical Society.

Hadamard Products of Product Operators and the Design of Gradient-Diffusion Experiments for Simulating Decoherence by NMR Spectroscopy

An extension of the product operator formalism of NMR is introduced, which uses the Hadamard matrix product to describe many simple spin 1/2 relaxation processes. The utility of this formalism is illustrated by deriving NMR gradient-diffusion experiments to simulate several decoherence models of interest in quantum information processing, along with their Lindblad and Kraus representations.

Spatially encoded pseudopure states for NMR quantum-information processing

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.

Quantum codes for controlling coherent evolution

Control over spin dynamics has been obtained in nuclear magnetic resonance (NMR) via coherent averaging, which modifies the effective internal Hamiltonian, and via quantum codes, which can protect against decoherent evolution. Here, we discuss the design and implementation of quantum codes that enable modification of the internal Hamiltonian. A detailed example is given of a quantum code for protecting two data spins from evolution under a weak coupling term in the Hamiltonian, using an “isolated” ancilla that does not evolve on the experimental time scale. The code is realized in a three-spin system by liquid-state NMR spectroscopy on 13C-labeled alanine, and tested for two initial states. It is also shown that with internal interactions 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 nonisolated ancillae, quantum codes exist which can protect against evolution under weak coupling. An example is presented f...