Quantum Simulations on a Quantum Computer

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 [2–4]. 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: