Quantum Simulations on an NMR Quantum Computer

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Most of the current work on implementations of quantum algorithms concentrates on the algorithms for factoring and database searching. From a physics perspective, however, the original suggestion by Feynman, that quantum processors may be the only possibility to efficiently simulate quantum mechanical systems, offers a more exciting perspective. In this project, we plan to implement some interesting simulation algorithms using liquid state NMR. Quantum simulations on quantum computers involve two types of mapping: The state (or density operator) of the physical system to be studied must be mapped onto the state (or density operator) of the quantum computer, and the Hamiltonian of the physical system must be implemented in the quantum computer. The quantum computer typically is a system of qubits (spins 1/2), while the physical system may be a spin system, a boson- or fermion system. Finding a suitable mapping is therefore often a nontrivial task. We expect that quantum simulations hold the biggest potential in the field of mesoscopic physics, where classical computers are not powerful enough for exact calculations and asymptotic solutions do not hold. As a starting point, we plan to implement the coupling Hamiltonian of the BCS theory of superconductivity. Using two- and three particle implementations for the initial experiments, we will study the issues involved in scaling the computation to larger systems, which may become available in future generations of quantum computers. For this initial work, we will concentrate on unitary evolutions, combined with adiabatic variation of the Hamiltonian. In a future phase, it will be interesting to extend the simulation to open systems by including non-unitary evolution.