An investigation of precision and scaling issues in nuclear spin and trapped-ion quantum simulators

Abstract

Quantum simulation offers the possibility of using a controllable quantum-mechanical system to implement the dynamics of another quantum system, performing calculations that are intractable on classical computers for all but the smallest systems. This great possibility carries with it great challenges, two of which motivate the experiments with nuclear spins and trapped ions presented in this thesis. The first challenge is determining the bounds on the precision of quantities that are calculated using a digital quantum simulator. As a specific example, we use a three-qubit nuclear spin system to calculate the low-lying spectrum of a pairing Hamiltonian. We find that the simulation time scales poorly with the precision, and increases further if error correction is employed. In addition, control errors lead to yet more stringent limits on the precision. These results indicate that quantum simulation is more efficient than classical computation only when a limited precision is acceptable and when no efficient classical approximation is known. The second challenge is the scaling-up of small quantum simulators to incorporate tens or hundreds of qubits. With a specific goal of analog quantum simulation of spin models in two dimensions, we present novel ion trap designs, a lattice ion trap and a surface-electrode elliptical ion trap. We experimentally confirm a theoretical model of each trap, and evaluate the suitability of each design for quantum simulation. We find that the relevant interaction rates are much higher in the elliptical trap, at the cost of additional systematic control errors.

(cont.) We also explore the interaction of ions over a wire, a potentially more scalable system than the elliptical trap. We calculate the expected coupling rate and decoherence rates, and find that an extremely low capacitance (O(fF)) between the coupling wire and ground is required, as well as ion-wire distances of O(50 [mu]m) to realize a motional coupling of 0(1 kHz). In pursuit of this situation, we measure the effect on a single ion of a floating wire's static and induced ac voltages as a function of the ion-wire distance.