Phase relaxation of the quantum parametric oscillator

FRANCESCO IACHELLO, Colin Coane, Jayameenakshi Venkatraman

Abstract We study the symmetries of the Liouville superoperator of one dimensional parametric oscillators, especially the so-called squeeze-driven Kerr oscillator, and discover a remarkable quasi-spin symmetry su(2) at integer values of the ratio η = ω / K of the detuning parameter ω to the Kerr coefficient K, which reflects the symmetry previously found for the Hamiltonian operator. We find that the Liouvillian of an su(2) representation | j , m j ⟩ has a characteristic double-ellipsoidal structure, and calculate the relaxation time T X for this structure. We then study the phase transitions of the Liouvillian which occur as a function of the parameters ξ = ε 2 / K and η = ω / K . Finally, we study the temperature dependence of the spectrum of eigenvalues of the Liouvillian. Our findings may have applications in the generation and stabilization of states of interest in quantum computing.

Boris Ya Zel'dovich, A. M. Perelomov, В. С. Попов

Paul Kinsler

Hiroaki Mishima, Yuki Izumida

The transitionless tracking (TT) algorithm enables the exact tracking of quantum adiabatic dynamics in an arbitrary short time by adding a counterdiabatic Hamiltonian to the original adiabatic Hamiltonian. By applying Husimi's method originally developed for a quantum parametric oscillator (QPO) to the transitionless QPO achieved using the TT algorithm, we obtain the transition probability generating function with a time-dependent parameter constituted with solutions of the corresponding classical parametric oscillator (CPO). By obtaining the explicit solutions of this CPO using the phase-amplitude method, we find that the time-dependent parameter can be reduced to the frequency ratio between the Hamiltonians without and with the counterdiabatic Hamiltonian, from which we can easily characterize the result achieved by the TT algorithm. We illustrate our theory by showing the trajectories of the CPO on the classical phase space, which elucidate the effect of the counterdiabatic Hamiltonian of the QPO.

Hongxiang Shen, Nobuyuki Yoshikawa

Abstract Josephson parametric oscillators (JPOs) have potential as fundamental building blocks for large-scale quantum annealing systems. To scale up such systems, both readout and control circuits need to be implemented at cryogenic temperatures. Adiabatic quantum flux parametron (AQFP) circuits are well suited for such environments due to their ultra-low power consumption. This paper proposes a phase-state readout scheme for JPOs based on AQFP circuits, which enables real-time digitization of oscillation phases. A JPO was fabricated, and the concept was experimentally validated at 4.2 K. After confirming stable oscillations in the JPO, a digital readout method using AQFP circuits was demonstrated. Analysis of the probability of obtaining a logical ‘1’ at the output revealed a clear phase-dependent behavior. Furthermore, our simulations predicted a readout fidelity of nearly 100% at millikelvin temperatures, demonstrating the feasibility of AQFP-based phase-state readout for future large-scale quantum annealing systems.

В. С. Попов, A. M. Perelomov