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University of Bradford

1.
Hadhrami, Hilal Al.
Phase space methods in finite quantum * systems*.

Degree: PhD, 2009, University of Bradford

URL: http://hdl.handle.net/10454/4250

Quantum systems with finite Hilbert space where position x and momentum p take values in Z(d) (integers modulo d) are considered. Symplectic tranformations S(2ξ,Z(p)) in ξ-partite finite quantum systems are studied and constructed explicitly. Examples of applying such simple method is given for the case of bi-partite and tri-partite systems. The quantum correlations between the sub-systems after applying these transformations are discussed and quantified using various methods. An extended phase-space x-p-X-P where X, P ε Z(d) are position increment and momentum increment, is introduced. In this phase space the extended Wigner and Weyl functions are defined and their marginal properties are studied. The fourth order interference in the extended phase space is studied and verified using the extended Wigner function. It is seen that for both pure and mixed states the fourth order interference can be obtained.

Subjects/Keywords: 530.1; Phase space methods; Finite quantum systems; Finite Hilbert space; Symplectic tranformations; Bi-partite and tri-partite systems; Wigner function

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Hadhrami, H. A. (2009). Phase space methods in finite quantum systems. (Doctoral Dissertation). University of Bradford. Retrieved from http://hdl.handle.net/10454/4250

Chicago Manual of Style (16^{th} Edition):

Hadhrami, Hilal Al. “Phase space methods in finite quantum systems.” 2009. Doctoral Dissertation, University of Bradford. Accessed April 19, 2021. http://hdl.handle.net/10454/4250.

MLA Handbook (7^{th} Edition):

Hadhrami, Hilal Al. “Phase space methods in finite quantum systems.” 2009. Web. 19 Apr 2021.

Vancouver:

Hadhrami HA. Phase space methods in finite quantum systems. [Internet] [Doctoral dissertation]. University of Bradford; 2009. [cited 2021 Apr 19]. Available from: http://hdl.handle.net/10454/4250.

Council of Science Editors:

Hadhrami HA. Phase space methods in finite quantum systems. [Doctoral Dissertation]. University of Bradford; 2009. Available from: http://hdl.handle.net/10454/4250

University of Kansas

2.
Mao, Bo.
Coherent Manipulation of Multi-* Partite* Quantum States in a Qubit-TLS System via Landau-Zener Transition.

Degree: PhD, Physics & Astronomy, 2010, University of Kansas

URL: http://hdl.handle.net/1808/7429

A radio frequency (rf) superconducting quantum interference device (SQUID) is a macroscopic quantum object consisting of a superconducting loop interrupted by a Josephson junction. Superconducting phase quantum bits (qubits) based on rf SQUIDs have been proven to be one of the most promising candidates for building a quantum computer. They exploit the unique resources of quantum superposition and entanglement and are exponentially faster than classical computers in solving certain problems, such as factoring. Compared to other approaches to quantum computing, superconducting phase qubits allow stronger and more flexible inter-qubit coupling and thus are easier to scale up. However, phase qubits couple to the environment and are subject to considerable decoherence. The resulting coherence time (also called decoherence time) is on the order of 100 ns, about two orders of magnitude shorter than that required for fault-tolerant quantum computing. One possible solution is to develop faster quantum gates in phase qubits. In this dissertation, coherent manipulation of multi-partite quantum states via Landau-Zener (LZ) transitions was investigated in a phase qubit, which was coupled to two microscopic two-level systems (TLSs) embedded in the tunnel barrier of the Josephson junction. The qubit chip was measured at temperatures below 30 mK in an ultra-low noise environment with excellent electrical and magnetic filtering and shielding. All parameters of the phase qubit were calibrated independently. The phase qubit's decoherence times have been carefully measured as well. Fast and precise coherent control of the tripartite quantum states has been successfully demonstrated by the observation of the Landau-Zener-Stückelberg (LZS) interference in the coupled qubit-TLS system. Furthermore, it is shown that utilizing LZ transitions to create multi-partite entangled states, such as the W state, is significantly more efficient than conventional methods which require a sequence of single-qubit and two-qubit gates. Hence, coherent manipulation of multi-partite quantum states via LZ transitions is a promising basis for a new family of fast multi-qubit quantum gates.
*Advisors/Committee Members: Han, Siyuan (advisor), Marfatia, Danny (cmtemember), Wu, Judy (cmtemember), Zhao, Hui (cmtemember), Hui, Rongqing (cmtemember).*

Subjects/Keywords: Condensed matter physics; Coherent control; Lz transition; Qubit-tls; Rf squid phase qubit; Tri-partite quantum system

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Mao, B. (2010). Coherent Manipulation of Multi-Partite Quantum States in a Qubit-TLS System via Landau-Zener Transition. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/7429

Chicago Manual of Style (16^{th} Edition):

Mao, Bo. “Coherent Manipulation of Multi-Partite Quantum States in a Qubit-TLS System via Landau-Zener Transition.” 2010. Doctoral Dissertation, University of Kansas. Accessed April 19, 2021. http://hdl.handle.net/1808/7429.

MLA Handbook (7^{th} Edition):

Mao, Bo. “Coherent Manipulation of Multi-Partite Quantum States in a Qubit-TLS System via Landau-Zener Transition.” 2010. Web. 19 Apr 2021.

Vancouver:

Mao B. Coherent Manipulation of Multi-Partite Quantum States in a Qubit-TLS System via Landau-Zener Transition. [Internet] [Doctoral dissertation]. University of Kansas; 2010. [cited 2021 Apr 19]. Available from: http://hdl.handle.net/1808/7429.

Council of Science Editors:

Mao B. Coherent Manipulation of Multi-Partite Quantum States in a Qubit-TLS System via Landau-Zener Transition. [Doctoral Dissertation]. University of Kansas; 2010. Available from: http://hdl.handle.net/1808/7429