We report heating rate measurements in a microfabricated gold-onsapphire surface electrode ion trap with trapping height of approximately 240 µm. Using the Doppler recooling method, we characterize the trap heating rates over an extended region of the trap. The noise spectral density of the trap falls in the range of noise spectra reported in ion traps at room temperature. We find that during the first months of operation the heating rates increase by approximately one order of magnitude. The increase in heating rates is largest in the ion loading region of the trap, providing a strong hint that surface contamination plays a major role for excessive heating rates. We discuss data found in the literature and possible relation of anomalous heating to sources of noise and dissipation in other systems, namely impurity atoms adsorbed on metal surfaces and amorphous dielectrics.

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm to find the low-lying spectrum of a Hamiltonian. While the number of elementary quantum gates required does scale polynomially with the size of the system, it increases inversely to the desired error bound ǫ. Making such simulations robust to decoherence using fault-tolerance constructs requires an additional factor of ∼ 1/ǫ gates. These constraints are illustrated by using a three qubit nuclear magnetic resonance system to simulate a pairing Hamiltonian, following the algorithm proposed by Wu, Byrd, and Lidar [1].The unknown properties and dynamics of a given quantum system can often be studied by using a well-known and controllable quantum system to mimic the behavior of the original system. This technique of quantum simulation is one of the fundamental motivations for the study of quantum computation [2][3][4], and is particularly of interest because a quantum simulation may be performed using space and time resources comparable to the original system. Such "efficient" scaling is dramatically better than the exponentially large resource requirements to simulate any general quantum system with a classical computer, as Feynman originally observed [2].Recent work has continued to arouse great interest in quantum simulation, because it offers the possibility of solving computationally hard problems without requiring the resources necessary for algorithms such as factoring [5] and searching [6]. Experimental results have demonstrated simulations of a truncated oscillator and of a three-body interaction Hamiltonian, using a nuclear magnetic resonance (NMR) quantum computer [7,8], and explored various solid-state models on two qubit systems [9][10][11][12]. Interest has also extended to simulating complex condensed matter systems with quantum optical systems [13], demonstrated vividly by the observation of a superfluid to Mott insulator transition in a Bose-Einstein condensate [14].Often overlooked in the discussion of quantum simulations, however, is the question of desired precision (or error ǫ) in the final measurement results. Current quantum simulation techniques generally scale poorly with desired precision; they demand an amount of space or time which increases as 1/ǫ, broadly translating into a number of quantum gates which grows exponentially with the desired number of bits in the final answer. Why is this scaling behavior so poor, and what is its physical origin?Consider as a specific example the problem of calculating the energy gap ∆ between the ground state |G and the first excited state |E 1 , of a Hamiltonian H. ∆ can be found using the following steps: 1) map the Hilbert space of the system to be simulated to n qubits, 2) prepare the computer in the state |Ψ I = c G |G + c E |E 1 , 3) evolve under the Hamiltonian for times t i , 4) extra...