Hidden two-qubit dynamics of a four-level Josephson circuit

Abstract

Multi-level control of quantum coherence exponentially reduces communication and computation resources required for a variety of applications of quantum information science. However, it also introduces complex dynamics to be understood and controlled. These dynamics can be simplified and made intuitive by employing group theory to visualize certain four-level dynamics in a 'Bell frame' comprising an effective pair of uncoupled two-level qubits. We demonstrate control of a Josephson phase qudit with a single multi-tone excitation, achieving successive population inversions between the first and third levels and highlighting constraints imposed by the two-qubit representation. Furthermore, the finite anharmonicity of our system results in a rich dynamical evolution, where the two Bell-frame qubits undergo entangling-disentangling oscillations in time, explained by a Cartan gate decomposition representation. The Bell frame constitutes a promising tool for control of multi-level quantum systems, providing an intuitive clarity to complex dynamics.

Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities

“…Here, we focus on the realization with superconducting anharmonic multilevel circuits due to significant experimental progress in this scope [57][58][59][60][61].…”

“…We note that there are other suitable ways to map multilevel systems on two-qubit systems such as "Bell-state" encoding [60]. However, it is crucial that the diagonal elements of qubit matrices (3) are composed of the diagonal elements of density matrix (2).…”

“…1). Superconducting circuits with Josephson junctions have been considered in early works [38][39][40][41][42][43] as well as in recent theoretical [44][45][46][47][48] and experimental studies [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66]. Noncomposite quantum systems can be realized through a variety of physical platforms, which include, but are not limited to photons [67] and NMR systems [68].…”

“…Noncomposite quantum systems can be realized through a variety of physical platforms, which include, but are not limited to photons [67] and NMR systems [68]. Nevertheless, progress in experiments with multilevel systems based on superconducting circuits forces us to focus our study on this environment [49][50][51][52][53][54][55][56][57][58][59][60][61].…”

“…In the recent experimental study [60], isomorphic correspondence between a four-level qudit and a two-qubit quantum system has been used to explore "hidden" two-qubit dynamics of a four-level superconducting circuit with the Josephson junction. In fact, this straightforwardly demonstrates a potential resource of noncomposite systems realized as multilevel superconducting circuits for quantum technologies.…”