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Leonid Levitov. Farrell, Matthew W Massachusetts Institute of Technology. Dept. of Physics. Massachusetts Institute of Technology. Department of Physics 2009-01-30T16:49:44Z 2009-01-30T16:49:44Z 2008 2008 http://hdl.handle.net/1721.1/44466 297177469 Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2008. Includes bibliographical references (leaf 43). Quantum computation offers the promise of speeding up many calculations that are intractable on classical computers, including but not limited to factoring and the simulation of quantum mechanical systems. Quantum computation is achieved by replacing the bits of a classical computer with quoits. Qubits generalize bits by allowing not only the classical states of zero and one, but also any arbitrary superposition of zero and one. These qubits are implemented as two-state systems by mapping the classical one and zero states to two orthogonal quantum states. The qubits are then manipulated by varying the Hamiltonian of the two-state systems with time. The standard method to manipulate a two-state system is to drive it weakly using Rabi dynamics. This approach is ineffective for a large scale quantum computer because the rotation is slow, and decoherence breaks the fragile state before the computation can be completed. To address this problem, we developed a method to rapidly rotate a qubit by an arbitrary angle. This is achieved by abandoning Rabi oscillations, and instead using a strong, rapidly changing field to coherently rotate the spin. We rapid drive the system through an avoided crossing and back again by giving the on diagonal term of the Hamiltonian a parabolic time dependence. In this paper, I contrast the standard method of spin rotation via Rabi oscillations with our protocol. Then, I discuss the various numerical simulations used to evaluate our protocol. Finally, I present some experimental evidence suggesting the protocol will be effective when implemented. Then, I discuss experimental findings and computational results of our method. We found regions of parameter space that allow a qubit to be rapidly rotated by any angle from zero to nearly ~r. This new protocol for arbitrary qubit rotation is a significant improvement over techniques relying on Rabi oscillations, reducing the time needed to transition qubits. (cont.) Our protocol deserves further study and refinement for its potential to speed up and, thusly, reduce the problem of decoherence in quantum computation. by Matthew W. Farrell. S.B. 43 leaves eng Massachusetts Institute of Technology 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. http://dspace.mit.edu/handle/1721.1/7582 Physics. Nonadiabatic control of a superconducting qubit via strong driving Thesis application/pdf Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="92fa48cf-6b09-4197-8fad-4b5ef36fb503"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Nonadiabatic control of a superconducting qubit via strong driving</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2008</PublicationDate> <Authors> <Author> <DisplayName>Farrell, Matthew W</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Physics.</Keyword> <Abstract>Quantum computation offers the promise of speeding up many calculations that are intractable on classical computers, including but not limited to factoring and the simulation of quantum mechanical systems. Quantum computation is achieved by replacing the bits of a classical computer with quoits. Qubits generalize bits by allowing not only the classical states of zero and one, but also any arbitrary superposition of zero and one. These qubits are implemented as two-state systems by mapping the classical one and zero states to two orthogonal quantum states. The qubits are then manipulated by varying the Hamiltonian of the two-state systems with time. The standard method to manipulate a two-state system is to drive it weakly using Rabi dynamics. This approach is ineffective for a large scale quantum computer because the rotation is slow, and decoherence breaks the fragile state before the computation can be completed. To address this problem, we developed a method to rapidly rotate a qubit by an arbitrary angle. This is achieved by abandoning Rabi oscillations, and instead using a strong, rapidly changing field to coherently rotate the spin. We rapid drive the system through an avoided crossing and back again by giving the on diagonal term of the Hamiltonian a parabolic time dependence. In this paper, I contrast the standard method of spin rotation via Rabi oscillations with our protocol. Then, I discuss the various numerical simulations used to evaluate our protocol. Finally, I present some experimental evidence suggesting the protocol will be effective when implemented. Then, I discuss experimental findings and computational results of our method. We found regions of parameter space that allow a qubit to be rapidly rotated by any angle from zero to nearly ~r. This new protocol for arbitrary qubit rotation is a significant improvement over techniques relying on Rabi oscillations, reducing the time needed to transition qubits.</Abstract> <Abstract>(cont.) Our protocol deserves further study and refinement for its potential to speed up and, thusly, reduce the problem of decoherence in quantum computation.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>