Ph.D. Thesis - Physics

An Investigation of Precision and Scaling Issues in Nuclear Spin and
Trapped-Ion Quantum Simulators
by
Robert J. Clark
Abstract
Submitted to the Department of Physics
on April 28, 2009, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Physics
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.
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 µm) to realize a motional coupling of
O(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.
Thesis Supervisor: Isaac L. Chuang
Title: Associate Professor of Electrical Engineering and Computer Science
and Associate Professor of Physics
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