Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2212.13682 · Physical Review Applied

Correlated Oscillations in Kerr Parametric Oscillators with Tunable Effective Coupling

T. Yamaji, Shumpei Masuda, Aiko Yamaguchi, T. Satoh, A. Morioka, Y. Igarashi, Masayuki Shirane, Tsuyoshi Yamamoto

Published Jul 26, 2023• 20 citations
arXivHTMLPDF

Abstract

We study simultaneous parametric oscillations in a system composed of two distributed-element-circuit Josephson parametric oscillators in the single-photon Kerr regime coupled via a static capacitance. The energy of the system is described by a two-bit Ising Hamiltonian with an effective coupling whose amplitude and sign depend on the relative phase between parametric pumps. We demonstrate that the binary phases of the parametric oscillations are correlated with each other, and that the parity and strength of the correlation can be controlled by adjusting the pump phase. The observed correlation is reproduced in our simulation taking pure dephasing into account. The present result demonstrates the tunability of the Hamiltonian parameters by the phase of external microwave, which can be used in the Ising machine hardware composed of the Kerr parametric oscillator network.

DOI
10.1103/physrevapplied.20.014057

Related papers

Quantum annealing in capacitively coupled Kerr parametric oscillators using frequency-chirped drives

T. Yamaji, S. Masuda, Y. Kano +7 more

We study parametric oscillations of two capacitively coupled Kerr parametric oscillators (KPOs) with frequency-chirped two- and one-photon drives. The two-KPO system adiabatically evolves from the initial vacuum state to an oscillation state corresponding to a solution state in quantum-annealing applications. Frequency chirping dynamically changes the detuning between resonance and oscillation frequencies during parametric modulation and reduces unwanted population transfer to excited states caused by pure dephasing and photon loss. We observe that frequency chirping increases the success probability to obtain the solution state and that simulations taking into account pure dephasing reproduce experiments with and without frequency chirping. This study demonstrates the effectiveness and applicability of frequency chirping to a KPO-based quantum annealer.

arXiv:2506.23539•Physical Review Applied•Dec 4, 2025•1 citation

Fast Tunable Coupling Scheme of Kerr Parametric Oscillators Based on Shortcuts to Adiabaticity

Shumpei Masuda, Taro Kanao, Hayato Goto +3 more

Kerr parametric oscillators (KPOs), which can be implemented with superconducting parametrons possessing large Kerr nonlinearity, have been attracting much attention in terms of their applications to quantum annealing, universal quantum computation, and studies of quantum many-body systems. It is of practical importance for these studies to realize fast and accurate tunable coupling between KPOs in a simple manner. We develop a simple scheme of fast tunable coupling of KPOs with high tunability in speed and amplitude using the fast transitionless rotation of a KPO in the phase space based on the shortcuts to adiabaticity. Our scheme enables rapid switching of the effective coupling between KPOs, and can be implemented with always-on linear coupling between KPOs, by controlling the phase of the pump field and the resonance frequency of the KPO without controlling the amplitude of the pump field nor using additional drive fields and couplers. We apply the coupling scheme to a two-qubit gate, and show that our scheme realizes high gate fidelity compared with a purely adiabatic one, by mitigating undesired nonadiabatic transitions.

arXiv:2203.00226•Physical Review Applied•Sep 27, 2022•21 citations

Four-body interactions in Kerr parametric oscillator circuits

Yohei Kawakami, Tomohiro Yamaji, Aiko Yamaguchi +9 more

We theoretically present new unit circuits of Kerr parametric oscillators (KPOs) with four-body interactions, which enable the scalable embedding of all-to-all connected logical Ising spins using the Lechner-Hauke-Zoller (LHZ) scheme. These unit circuits enable four-body interactions using linear couplers, making the circuit fabrication and characterization much simpler than those of conventional unit circuits with nonlinear couplers. Numerical calculations indicate that the magnitudes of the coupling constants can be comparable to those in conventional circuits. On the basis of this theory, we designed a four-KPO circuit and experimentally confirmed the four-body correlation by measuring the pump-phase dependence of the parity of the four-KPO states. We show that the choice of the pump frequencies are important not only to enable the four-body interaction, but to cancel the effects of other unwanted interactions. Using the circuit, we demonstrated the quantum annealing based on the LHZ scheme, where the strength of the interaction between the logical Ising spins is mapped to the local field and controlled by a coherent drive applied to each KPO.

quant-pharXiv:2512.00446•Dec 2, 2025•0 citations

Flux-modulated tunable interaction regimes in two strongly nonlinear oscillators

J. D. Koenig, G. Barbieri, F. Fani Sani +3 more

The ability to efficiently simulate a variety of interacting quantum systems on a single device is an overarching goal for digital and analog quantum simulators. In circuit quantum electrodynamical systems, strongly nonlinear superconducting oscillators are typically realized using transmon qubits, featuring a wide range of tunable couplings that are mainly achieved via flux-dependent inductive elements. Such controllability is highly desirable both for digital quantum information processing and for analog quantum simulations of various physical phenomena, such as arbitrary spin-spin interactions. Furthermore, broad tunability facilitates the study of driven-dissipative oscillator dynamics in previously unexplored parameter regimes. In this work, we demonstrate the ability to selectively activate different dynamical regimes between two strongly nonlinear oscillators using parametric modulation. In particular, our scheme enables access to regimes that are dominated by photon-hopping, two-mode squeezing, or cross-Kerr interactions. Finally, we observe level repulsion and attraction between Kerr-nonlinear oscillators in regimes where the nonlinearities exceed the coupling strengths and decay rates of the system. Our results could be used for realizing purely analog quantum simulators to study arbitrary spin systems as well as for exploring strongly nonlinear oscillator dynamics in previously unexplored interaction regimes.

quant-pharXiv:2511.06533•Physical Review Research•Nov 11, 2025•1 citation

Spectroscopic observation of the crossover from a classical Duffing oscillator to a Kerr parametric oscillator

T. Yamaji, S. Kagami, Aiko Yamaguchi +6 more

We study microwave response of a Josephson parametric oscillator consisting of a superconducting transmission-line resonator with an embedded DC-superconducting quantum interference device (-SQUID). The DC-SQUID allows to control the magnitude of a Kerr nonlinearity over the ranges where it is smaller or larger than the photon loss rate. Spectroscopy measurements reveal the change in the microwave response from a classical Duffing oscillator to a Kerr parametric oscillator in a single device. In the single-photon Kerr regime, we observe parametric oscillations with a well-defined phase of either 0 or $\ensuremath{\pi}$, whose probability can be controlled by an externally injected signal.

arXiv:2010.02621•Physical Review A•Feb 23, 2022•44 citations

Change in bit-flip times of Kerr parametric oscillators caused by their interactions

Yuya Kano, Yohei Kawakami, Shumpei Masuda +8 more

We experimentally investigate how interactions between Kerr parametric oscillators (KPOs) degrade their bit-flip times, where a bit flip is defined as a transition between the two degenerate ground states of a KPO. Interactions between KPOs cause quantum states of KPOs to leak outside the computational subspace, leading to bit flips. Bit flips degrade fidelity and pose a significant problem for KPO-based quantum information processing. We performed an experiment in which a weak microwave signal is injected into one KPO to emulate photon injection from another KPO, and find that the bit-flip time decreases by an order of magnitude due to induced excitations, depending on the frequency and power of the injected signal. Methods to mitigate the decrease in bit-flip times caused by interactions between KPOs are discussed, including adjusting the pump frequencies, coherent-state amplitudes, and couplings between KPOs. These findings provide valuable insights for scaling up KPO-based quantum computers.

quant-pharXiv:2603.29308•Apr 1, 2026•0 citations
We study simultaneous parametric oscillations in a system composed of two distributed-element-circuit Josephson parametric oscillators in the single-photon Kerr regime coupled via a static capacitance. The energy of the system is described by a two-bit Ising Hamiltonian with an effective coupling whose amplitude and sign depend on the relative phase between parametric pumps. We demonstrate that the binary phases of the parametric oscillations are correlated with each other, and that the parity and strength of the correlation can be controlled by adjusting the pump phase. The observed correlation is reproduced in our simulation taking pure dephasing into account. The present result demonstrates the tunability of the Hamiltonian parameters by the phase of external microwave, which can be used in the Ising machine hardware composed of the Kerr parametric oscillator network.
We study parametric oscillations of two capacitively coupled Kerr parametric oscillators (KPOs) with frequency-chirped two- and one-photon drives. The two-KPO system adiabatically evolves from the initial vacuum state to an oscillation state corresponding to a solution state in quantum-annealing applications. Frequency chirping dynamically changes the detuning between resonance and oscillation frequencies during parametric modulation and reduces unwanted population transfer to excited states caused by pure dephasing and photon loss. We observe that frequency chirping increases the success probability to obtain the solution state and that simulations taking into account pure dephasing reproduce experiments with and without frequency chirping. This study demonstrates the effectiveness and applicability of frequency chirping to a KPO-based quantum annealer.
Kerr parametric oscillators (KPOs), which can be implemented with superconducting parametrons possessing large Kerr nonlinearity, have been attracting much attention in terms of their applications to quantum annealing, universal quantum computation, and studies of quantum many-body systems. It is of practical importance for these studies to realize fast and accurate tunable coupling between KPOs in a simple manner. We develop a simple scheme of fast tunable coupling of KPOs with high tunability in speed and amplitude using the fast transitionless rotation of a KPO in the phase space based on the shortcuts to adiabaticity. Our scheme enables rapid switching of the effective coupling between KPOs, and can be implemented with always-on linear coupling between KPOs, by controlling the phase of the pump field and the resonance frequency of the KPO without controlling the amplitude of the pump field nor using additional drive fields and couplers. We apply the coupling scheme to a two-qubit gate, and show that our scheme realizes high gate fidelity compared with a purely adiabatic one, by mitigating undesired nonadiabatic transitions.
We theoretically present new unit circuits of Kerr parametric oscillators (KPOs) with four-body interactions, which enable the scalable embedding of all-to-all connected logical Ising spins using the Lechner-Hauke-Zoller (LHZ) scheme. These unit circuits enable four-body interactions using linear couplers, making the circuit fabrication and characterization much simpler than those of conventional unit circuits with nonlinear couplers. Numerical calculations indicate that the magnitudes of the coupling constants can be comparable to those in conventional circuits. On the basis of this theory, we designed a four-KPO circuit and experimentally confirmed the four-body correlation by measuring the pump-phase dependence of the parity of the four-KPO states. We show that the choice of the pump frequencies are important not only to enable the four-body interaction, but to cancel the effects of other unwanted interactions. Using the circuit, we demonstrated the quantum annealing based on the LHZ scheme, where the strength of the interaction between the logical Ising spins is mapped to the local field and controlled by a coherent drive applied to each KPO.
The ability to efficiently simulate a variety of interacting quantum systems on a single device is an overarching goal for digital and analog quantum simulators. In circuit quantum electrodynamical systems, strongly nonlinear superconducting oscillators are typically realized using transmon qubits, featuring a wide range of tunable couplings that are mainly achieved via flux-dependent inductive elements. Such controllability is highly desirable both for digital quantum information processing and for analog quantum simulations of various physical phenomena, such as arbitrary spin-spin interactions. Furthermore, broad tunability facilitates the study of driven-dissipative oscillator dynamics in previously unexplored parameter regimes. In this work, we demonstrate the ability to selectively activate different dynamical regimes between two strongly nonlinear oscillators using parametric modulation. In particular, our scheme enables access to regimes that are dominated by photon-hopping, two-mode squeezing, or cross-Kerr interactions. Finally, we observe level repulsion and attraction between Kerr-nonlinear oscillators in regimes where the nonlinearities exceed the coupling strengths and decay rates of the system. Our results could be used for realizing purely analog quantum simulators to study arbitrary spin systems as well as for exploring strongly nonlinear oscillator dynamics in previously unexplored interaction regimes.
We study microwave response of a Josephson parametric oscillator consisting of a superconducting transmission-line resonator with an embedded DC-superconducting quantum interference device (-SQUID). The DC-SQUID allows to control the magnitude of a Kerr nonlinearity over the ranges where it is smaller or larger than the photon loss rate. Spectroscopy measurements reveal the change in the microwave response from a classical Duffing oscillator to a Kerr parametric oscillator in a single device. In the single-photon Kerr regime, we observe parametric oscillations with a well-defined phase of either 0 or $\ensuremath{\pi}$, whose probability can be controlled by an externally injected signal.
We experimentally investigate how interactions between Kerr parametric oscillators (KPOs) degrade their bit-flip times, where a bit flip is defined as a transition between the two degenerate ground states of a KPO. Interactions between KPOs cause quantum states of KPOs to leak outside the computational subspace, leading to bit flips. Bit flips degrade fidelity and pose a significant problem for KPO-based quantum information processing. We performed an experiment in which a weak microwave signal is injected into one KPO to emulate photon injection from another KPO, and find that the bit-flip time decreases by an order of magnitude due to induced excitations, depending on the frequency and power of the injected signal. Methods to mitigate the decrease in bit-flip times caused by interactions between KPOs are discussed, including adjusting the pump frequencies, coherent-state amplitudes, and couplings between KPOs. These findings provide valuable insights for scaling up KPO-based quantum computers.