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Multi-level quantum description of decoherence in superconducting qubits

Guido Burkard·Roger H. Koch·David P. DiVincenzo
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Abstract

We present a multi-level 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 multi-level 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 (T_1) and decoherence (T_2) 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.

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Guido Burkard, Roger H. Koch, David P. DiVincenzo. 2004-02-17. Multi-level quantum description of decoherence in superconducting qubits. https://doi.org/10.1103/physrevb.69.064503

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