Quantum Chaos for Nonlinear Kerr-Like Oscillator

A. Kowalewska-Kudłaszyk, Joanna K. Kalaga, W. Leoński

Hayato Goto

Jorge Chávez-Carlos, Miguel A. Prado Reynoso, Rodrigo G. Cortiñas +5 more

Abstract Kerr parametric oscillators are potential building blocks for fault-tolerant quantum computers. They can stabilize Kerr-cat qubits, which offer advantages toward the encoding and manipulation of error-protected quantum information. The recent realization of Kerr-cat qubits made use of the nonlinearity of transmon superconducting circuits and a squeezing drive. Increasing nonlinearities can enable faster gate times, but, as shown here, can also induce chaos and melt the qubit away. We determine the region of validity of the Kerr-cat qubit and discuss how its disintegration could be experimentally detected. The danger zone for parametric quantum computation is also a potential playground for investigating quantum chaos with driven superconducting circuits.

Wu -, Xinxing, Жу +1 more

Hayato Goto, Taro Kanao

A Kerr-nonlinear parametric oscillator (KPO) can generate a quantum superposition of two oscillating states, known as a Schr\"odinger cat state, via quantum adiabatic evolution and can be used as a qubit for gate-based quantum computing and quantum annealing. In this work, we investigate complex dynamics, i.e., chaos, in two coupled nondissipative KPOs at a few-photon level. After showing that a classical model for this system is nonintegrable and consequently exhibits chaotic behavior, we provide quantum counterparts for the classical results, which are quantum versions of the Poincar\'e surface of section and its lower-dimensional version defined with time integrals of the Wigner and Husimi functions and also the initial and long-term behavior of out-of-time-ordered correlators. We conclude that some of them can be regarded as quantum signatures of chaos, together with energy-level spacing statistics (conventional signature). Thus, the system of coupled KPOs is expected to offer not only an alternative approach to quantum computing but also a promising platform for the study on quantum chaos.

A. Kowalewska-Kudłaszyk, Joanna K. Kalaga, W. Leoński

We propose a Wigner-function-based parameter that can be used as an indicator of quantum chaos. This parameter is defined as "entropy" from the time dependence of "nonclassicality" proposed by A. Kenfack and K. Zyczkowski [J. Opt. B 6, 394 (2004)]. We perform our considerations for the system of damped nonlinear (Kerr-like) oscillator excited by a series of ultrashort external pulses.