State leakage during fast decay and control of a superconducting transmon qubit

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.

Mitigating Errors on Superconducting Quantum Processors Through Fuzzy Clustering

“…To reduce leakage and unwanted phase rotations, the drive pulses are DRAG (Derivative Reduction Adiabatic Gate) shaped. [54][55][56][57][58] To optimize the fidelity of the gate with respect to power, DRAG shape and frequency, we employ a combination of Motzoi calibration and the All-XY technique. [55,56] For more information on the calibration procedure, we refer to the Supporting Information.…”

Benchmarking quantum logic operations relative to thresholds for fault tolerance

“…independent n-qubit process matrix. Various common sources of non-Markovianity in NISQ systems include leakage out of the computation basis states [88][89][90][91][92][93] , unwanted entangling interactions (e.g., static ZZ coupling) with qubits outside of the studied system, drift in qubit parameters 94 (e.g., stochastic fluctuations in transition frequencies), unwanted coupling to environmental systems with memory beyond the timescale of a cycle (e.g., two-level fluctuators and nonequilibrium quasiparticles 80,[95][96][97] ), and qubit heating 98 ; see Fig. 5a.…”

Unfolding Correlation from Open-Quantum-System Master Equations

“…where 𝜎 ± = (𝜎 𝑥 ±𝑖𝜎 𝑦 )/2 are the raising and lowering operators of the system qubit, with 𝜎 𝑥 and 𝜎 𝑦 being the Pauli matrices, and similarly Σ 𝑘 ± are the raising and lowering operators associated with the 𝑘th TLS of the bath. This model is important in the context of quantum computation applications as it can model the bath in some experimental setups for realization of a qubit [60][61][62]. The effect of the bath on the dynamics of the system is usually encompassed in the spectral density function 𝐽 (𝜔) = 𝑘 𝑔 2 𝑘 𝛿(𝜔 − 𝜔 𝑘 ).…”