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Modern Physics Letters B

INVESTIGATION OF DECOHERENCE OF SUPERCONDUCTING FLUX QUBIT ENTANGLED WITH THE ENVIRONMENT

Yinghua Ji, Yanyan Jiang

Published Mar 30, 2008• 2 citations
Publisher

Abstract

In the Born–Markov approximation, decoherence property of superconducting quantum circuit with a flux qubit is investigated. Using Kirchhoff's laws of classical circuit and quantum theory, we derive a Hamiltonian of the circuit. Then, combining with the Bloch–Redfield equation and in the two-level approximation, the energy relaxation time and the decoherence time of superconducting qubits is studied. Compared to the spin-boson model, this method not only investigates a decoherence being caused by the dissipative environment, but also the decoherence being generated by the dissipative elements in a superconducting electronic circuit. Hence, it is good for studying the decoherence of superconducting qubits.

DOI
10.1142/s021798490801505x

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In the Born–Markov approximation, decoherence property of superconducting quantum circuit with a flux qubit is investigated. Using Kirchhoff's laws of classical circuit and quantum theory, we derive a Hamiltonian of the circuit. Then, combining with the Bloch–Redfield equation and in the two-level approximation, the energy relaxation time and the decoherence time of superconducting qubits is studied. Compared to the spin-boson model, this method not only investigates a decoherence being caused by the dissipative environment, but also the decoherence being generated by the dissipative elements in a superconducting electronic circuit. Hence, it is good for studying the decoherence of superconducting qubits.
In Born-Markov approximation,according to Bloch-Redfield equation,the method to calculate the relaxation time T1 and decoherence time T2 of superconducting qubit is given.Based on this,the decoherence phenomenon of superconducting flux qubit with mutual inductance coupling is investigated.The energy relaxation time T1 and decoherence time T2 of this superconducting qubit is also obtained.The results show that for the flux qubit under investigation,the dephasing time T,the energy relaxation time T1 from high level |j〉 to low level |i〉,and the decoherence time T2 of the quantum system are all proportional to dissipation when other conditions are invariant and the environment thermal bath is equivalent to a pure resistance.
We present a multilevel quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external impedances, shunt resistors) are described using the Caldeira-Leggett model. The master equation for the superconducting phases in the Born-Markov approximation is derived and brought into the Bloch-Redfield form in order to describe multilevel dissipative quantum dynamics of the circuit. The model takes into account leakage effects, i.e., transitions from the allowed qubit states to higher excited states of the system. As a special case, we truncate the Hilbert space and derive a two-level (Bloch) theory with characteristic relaxation (T1){(T}_{1})(T1​) and decoherence (T2){(T}_{2})(T2​) times. We apply our theory to the class of superconducting flux qubits; however, the formalism can be applied for both superconducting flux and charge qubits.
We derive Bloch-Redfield function with flux biased superconducting circuit in the framework classical circuit theory.Under two-level approximation,we discuss the influence of the different environment impedancses and the coupling strength on the decoherence of the magnetic flux qubit.We find that: under certain condition,the decoherence time decreases as the coupling strength increases,and when the environment impedance is pure impedance,the decoherence time increases as the impedance increases while the environment impedance consists of the resistor and capacitor,the influence of the different circuit elements on the decoherence time is different.
In the Born-Markov approximation and two-level approximation, and using the Bloch-Redfield equation, the decoherence property of superconducting quantum circuit with a flux qubit is investigated.The influence on decoherence of the mutual inductance coupling between the circuit components is complicated.The mutual inductance coupling between different loops will decrease the decoherence time.However, the mutual inductance coupling of the same loop, in a certain interval, will increase the decoherence time.Therefore, we can control the decoherence time by changing the mutual inductance parameters such as the strength and direction of coupling.
In Born—Markov approximation, this paper calculates the energy relaxation time T 1 and the decoherence time T 2 of a floating flux qubit by solving the set of Bloch—Redfield equations. It shows that there are two main factors influencing the floating flux qubits: coupling capacitor in the circuit and the environment resistor. It also discusses how to improve the quantum coherence time of a qubit. Through shunt connecting/ series connecting inductive elements, an inductive environment resistor is obtained and further the reactance component of the environment resistor is improved, which is beneficial to the enhancement of decoherence time of floating flux qubits.
The quantum computation needs to maintain the quantum state coherent and the entanglement, but these two characteristics are very easy to be destructed by the decoherent process,therefore,how to overcome the effect of decoherence is the key to implement quantum computation.The Hamiltonian of the superconducting circuit was derived from circuit graph theory,and multilevel dissipative dynamics was studied by the Bloch-Redfield function.Finally,under two-level approximation,the influence of mutual inductance on the decoherence of the magnetic flux qubit was discovered.And how to change the mutual inductance tO reduce the decoherence time of the magnetic flux quantum bit was discussed.