Abstract
Superconducting Josephson junction qubits constitute the main current technology for many applications, including scalable quantum computers and thermal devices. Theoretical modeling of such systems is usually done within the two-level approximation. However, accurate theoretical modeling requires taking into account the influence of the higher excited states without limiting the system to the two-level qubit subspace. Here, we study the dynamics and control of a superconducting transmon using the numerically exact stochastic Liouville–von Neumann equation approach. We focus on the role of state leakage from the ideal two-level subspace for bath induced decay and single-qubit gate operations. We find significant short-time state leakage due to the strong coupling to the bath. We quantify the leakage errors in single-qubit gates and demonstrate their suppression with derivative removal adiabatic gates (DRAG) control for a five-level transmon in the presence of decoherence. Our results predict the limits of accuracy of the two-level approximation and possible intrinsic constraints in qubit dynamics and control for an experimentally relevant parameter set.
Highlights
Recent developments in quantum devices are based on the highfidelity control of two-level systems
Optimization of leakage-free driving for single-qubit gates in the absence of decoherence has been previously investigated within the derivative removal adiabatic gates (DRAG) method which successfully reduces the leakage errors[8,9,10]
In ref. 17 it has been shown that a truncation to N = 5 lowest eigenstates is enough for accurate studies of single excitation and low-temperature dynamics
Summary
Recent developments in quantum devices are based on the highfidelity control of two-level systems. Highfidelity and error-free computing in particular requires a detailed understanding of the dynamics and control in the presence of these higher energy states for experimental circuits. Studies in dynamics and control of superconducting qubits are restricted to weak coupling to the background or heat bath This is because most of the quantum computing devices require ultra-weak coupling between the qubit and the environment during gate operations. We further study the influence of higher energy states in controlling the transmon, focusing in single-qubit gate fidelities in the presence of a dissipative environment. We quantify leakage error in single-qubit quantum gates and study the performance of DRAG control techniques in the presence of decoherence for experimentally relevant parameters. Published in partnership with The University of New South Wales energy levels and decoherence in the quantum gate operations and other applications relying on coherent qubit control protocols
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