Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems

Choi, Jeong Ryeol

doi:10.1155/2015/120573

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…For the case that λ(t) is not a constant, it is necessary to use the quantum theory of time-dependent harmonic oscillators [9,23,24] in order to manage the Schrödinger equation, Equation (17) with Equation (12). According to that theory, the phases and the eigenfunctions in the transformed system are given in terms of time functions as [24] αn(t)=−(n+1/2)γ1(t), trueα˜l(t)=−(l+1/2)γ2(t), ϕn′(x,t)=()κ1(t)/π2nn!1/2Hnκ1(t)xexp−…”

Section: Resultsmentioning

confidence: 99%

“…The investigation of nanodevices regarding their application in quantum information science, including quantum computing, is a promising research topic. In particular, research into nanomechanical resonators in which the parameters are dependent on time is quite necessary for the advancement of the quantum information technology [7,8,9,10,11]. Now, it is possible to design quantum computing devices with a reliable architecture for multi-qubit operations in the GHz-frequency range by coupling mechanical resonators to Josephson phase qubits [12].…”

Section: Introductionmentioning

confidence: 99%

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Quantum Characteristics of a Nanomechanical Resonator Coupled to a Superconducting LC Resonator in Quantum Computing Systems

Choi

2018

Nanomaterials

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The mechanical and quantum properties of a nanomechanical resonator can be improved by connecting it to a superconducting resonator in a way that the resonator exhibits new phenomena that are possibly available to novel quantum technologies. The quantum characteristics of a nanomechanical resonator coupled to a superconducting resonator have been investigated on the basis of rigorous quantum solutions of the combined system. The solutions of the Schrödinger equation for the coupled system have been derived using the unitary transformation approach. The analytic formula of the wave functions has been obtained by applying the adiabatic condition for time evolution of the coupling parameter. The behavior of the quantum wave functions has been analyzed for several different values of parameters. The probability densities depicted in the plane of the two resonator coordinates are distorted and rotated due to the coupling between the resonators. In addition, we have shown that there are squeezing effects in the wave packet along one of the two resonator coordinates or along both the two depending on the magnitude of several parameters, such as mass, inductance, and angular frequencies.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Characteristics of a Nanomechanical Resonator Coupled to a Superconducting LC Resonator in Quantum Computing Systems

Choi

2018

Nanomaterials

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“…The study of such variation for specific systems may allow us to gain insight in understanding the underlying mechanism associated with the invariants 19 . The mechanics of such adiabatic invariance can be applied to analyzing dynamical properties of superconducting qubits in adiabatic quantum computation 8 , 26 .…”

Section: Introductionmentioning

confidence: 99%

The Rayleigh–Lorentz invariant for superconducting resonators and optimal adiabatic qubit-information detection

Choi

2021

Sci Rep

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Dynamical properties of a resonator can be analyzed using the Rayleigh–Lorentz invariant which is not an exact constant but varies more or less over time depending on variations of parameters. We investigate the time behavior of this invariant for a superconducting nano-resonator in order for better understanding of qubit-information detection with the resonator. Superconducting resonators which uses parametric resonance in a Josephson junction circuit can be utilized in implementing diverse next generation nano-optic and nano-electronic devices such as quantum computing systems. Through the analyses of the temporal evolution of the invariant, we derive a condition for optimal adiabatic qubit-information detection with the resonator. This condition is helpful for controlling the dynamics of the resonators over long periods of time. It is necessary to consider it when designing a nano-resonator used for quantum nondemolition readouts of qubit states, crucial in quantum computation.

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“…The study of such variation for specific systems may allow us to gain insight in understanding the underlying mechanism associated with the invariants [14]. The mechanics of such adiabatic invariance can be applied to analyzing dynamical properties of superconducting flux qubits in adiabatic quantum computation [8,21].…”

Section: Introductionmentioning

confidence: 99%

The Rayleigh-Lorentz Invariant and Optimal Adiabatic Qubit-Information Detection for Superconducting Qubit Resonators

Choi

2020

Preprint

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Dynamical properties of a resonator can be analyzed using the Rayleigh-Lorentz invariant which is not an exact constant but varies more or less over time. We investigate the time behavior of this invariant for a flux qubit resonator in order for better understanding of qubit-information detection with the resonator. Flux qubit resonators can be utilized in implementing diverse next generation nano-optic and nano-electronic devices such as quantum computing systems. Through the analyses of the temporal evolution of the invariant, we derive a condition for optimal adiabatic qubit-information detection with the resonator. This condition is helpful for controlling the dynamics of qubit resonators over long periods of time. It is necessary to consider it when designing a nano-resonator used for quantum nondemolition readouts of qubit states, crucial in quantum computation.

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Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems

Cited by 4 publications

References 24 publications

Quantum Characteristics of a Nanomechanical Resonator Coupled to a Superconducting LC Resonator in Quantum Computing Systems

Quantum Characteristics of a Nanomechanical Resonator Coupled to a Superconducting LC Resonator in Quantum Computing Systems

The Rayleigh–Lorentz invariant for superconducting resonators and optimal adiabatic qubit-information detection

The Rayleigh-Lorentz Invariant and Optimal Adiabatic Qubit-Information Detection for Superconducting Qubit Resonators

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