Suppressing chaos with mixed superconducting-qubit devices

Abstract

In quantum information processing, a tension between two different tasks occurs: while qubits’ states can be preserved by one isolating them, quantum gates can be realized only through qubit-qubit interactions. In arrays of qubits, weak coupling leads to states being spatially localized and strong coupling leads to delocalized states. Here we study the average energy level spacing and the relative entropy of the distribution of the level spacings (Kullback-Leibler divergence from Poisson distribution and Gaussian orthogonal ensemble) to analyze the crossover between localized and delocalized (chaotic) regimes in linear arrays of superconducting qubits. We consider both transmons and capacitively shunted flux qubits, which enables us to tune the qubit anharmonicity. Arrays with uniform anharmonicity, comprising only transmons or flux qubits, display remarkably similar dependencies of level statistics on the coupling strength. In systems with alternating anharmonicity, for typical disorder in the qubit frequencies the localized regime is found to be more resilient to the increase in qubit-qubit coupling strength in comparison with arrays with a single qubit type. Our results, which we also confirm using generalized Bose-Hubbard models, support the design of devices that incorporate different qubit types to achieve higher performances.

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