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

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Clark, Robert J., Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Isaac L. Chuang.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/53210

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/53210