Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems
An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we...
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/120573 |
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| author | Jeong Ryeol Choi |
| author_facet | Jeong Ryeol Choi |
| author_sort | Jeong Ryeol Choi |
| collection | DOAJ |
| description | An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms. |
| format | Article |
| id | doaj-art-1279aa41933f4d0ebd2ca6b24c604469 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-1279aa41933f4d0ebd2ca6b24c6044692025-02-03T05:52:47ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/120573120573Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing SystemsJeong Ryeol Choi0Department of Radiologic Technology, Daegu Health College, Buk-gu, Daegu 702-722, Republic of KoreaAn adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.http://dx.doi.org/10.1155/2015/120573 |
| spellingShingle | Jeong Ryeol Choi Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems Advances in Mathematical Physics |
| title | Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems |
| title_full | Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems |
| title_fullStr | Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems |
| title_full_unstemmed | Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems |
| title_short | Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems |
| title_sort | hamiltonian dynamics and adiabatic invariants for time dependent superconducting qubit oscillators and resonators in quantum computing systems |
| url | http://dx.doi.org/10.1155/2015/120573 |
| work_keys_str_mv | AT jeongryeolchoi hamiltoniandynamicsandadiabaticinvariantsfortimedependentsuperconductingqubitoscillatorsandresonatorsinquantumcomputingsystems |