Multilevel quantum description of decoherence in superconducting qubits

By G. Burkard, R. Koch, David P. DiVincenzo. 2003

157 citations recorded by the source corpus.

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 ${(T}_{1})$ 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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Citations in the corpus

Introduction to quantum electromagnetic circuits (2016, background): “For a more mathematically complete discussion of networks, see [20].”
Decoherence in solid-state qubits (2008, methodology): “Md(t) is a symmetric matrix containing all the dissipative dynamics of φ, [96].”
Widely Tunable On-Chip Microwave Circulator for Superconducting Quantum Circuits (2017, methodology): “As a confirmation of these simulations, an analytical study of the same circuit was also made, using a graph theoretical approach [134, 135] to solve for the circuit’s eigenfrequencies with Kirchoff’s current and voltage laws.”
Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems (2012, background): “…allows one to encode a qubit in the lowest two levels of a SC circuit for implementing quantum computing and simulation (Buluta and Nori, 2009; Burkard et al., 2004; Clarke and Wilhelm, 2008; Georgescu and Nori, 2011; Makhlin et al., 2001; Nation et al., 2012; Wendin and Shumeiko, 2007; You…”