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:2204.03347 · Physical Review Research

Two-qubit gate using conditional driving for highly detuned Kerr nonlinear parametric oscillators

Hiroomi Chono, Taro Kanao, Hayato Goto

Published Oct 21, 2022• 17 citations
arXivHTMLPDF

Abstract

A Kerr nonlinear parametric oscillator (KPO) is one of the promising devices used to realize qubits for universal quantum computing. The KPO can stabilize two coherent states with opposite phases, yielding a quantum superposition called a Schr\"odinger cat state. Universal quantum computing with KPOs requires three kinds of quantum gates: ${R}_{z},{R}_{x}$, and ${R}_{zz}$ gates. We theoretically propose a two-qubit gate ${R}_{zz}$ for highly detuned KPOs. In the proposed scheme, we add a parametric drive for the first KPO. This leads to the ${R}_{zz}$ gate based on the driving of the second KPO depending on the first-KPO state, which we call ``conditional driving.'' First, we perform simulations using a conventional KPO Hamiltonian derived from a superconducting-circuit model under some approximations and evaluate the gate fidelity. Next, we also perform numerical simulations of the two-qubit gate using the superconducting-circuit model without the approximations. The simulation results indicate that the conditional-driving gates can be implemented with high fidelity ($>99.9%$) for rotation angles required for universality.

DOI
10.1103/physrevresearch.4.043054

Related papers

High-performance conditional-driving gate for Kerr parametric oscillator qubits

Hiroomi Chono, Hayato Goto

Kerr parametric oscillators (KPOs), two-photon driven Kerr-nonlinear resonators, can stably hold coherent states with opposite-sign amplitudes and are promising devices for quantum computing. Recently, we have theoretically proposed a two-qubit gate Rzz for highly detuned KPOs and called it a conditional-driving gate [Chono et al., Phys. Rev. Res. 4, 043054 (2022)]. In this study, analyzing its superconducting-circuit model and deriving a corresponding static model, we find that an AC-Zeeman shift due to the flux pulse for the gate operation largely affects the gate performance. This effect becomes a more aggravating factor with shorter gate times, leading to an increase in the error rate. We thus propose a method to cancel this undesirable effect. Furthermore, through the use of shortcuts to adiabaticity and the optimization of flux pulses, we numerically demonstrate a conditional-driving gate with average fidelity exceeding 99.9% twice faster than that without the proposed cancellation method and the shortcuts to adiabaticity.

arXiv:2410.00552•APL Quantum•Jan 23, 2025•2 citations

Quantum Gate for a Kerr Nonlinear Parametric Oscillator Using Effective Excited States

Taro Kanao, Shumpei Masuda, Shiro Kawabata +1 more

A Kerr nonlinear parametric oscillator (KPO) can stabilize a quantum superposition of two coherent states with opposite phases, which can be used as a qubit. In a universal gate set for quantum computation with KPOs, an ${R}_{x}$ gate, which interchanges the two coherent states, is relatively hard to perform owing to the stability of the two states. We propose a method for a high-fidelity ${R}_{x}$ gate by exciting the KPO outside the qubit space with parity-selective transitions, which can be implemented by only adding a driving field. In this method, the utilization of higher effective excited states leads to a faster ${R}_{x}$ gate, rather than states near the qubit space. The proposed method can realize a continuous ${R}_{x}$ gate and thus is expected to be useful for, e.g., recently proposed variational quantum algorithms.

arXiv:2108.03091•Physical Review Applied•Jul 8, 2022•32 citations

Fast elementary gates for universal quantum computation with Kerr parametric oscillator qubits

Taro Kanao, Hayato Goto

Kerr parametric oscillators (KPOs) can stabilize the superpositions of coherent states, which can be utilized as qubits, and are promising candidates for realizing hardware-efficient quantum computers. Although elementary gates for universal quantum computation with KPO qubits have been proposed, these gates are usually based on adiabatic operations and thus need long gate times, which result in errors caused by photon loss in KPOs realized by, e.g., superconducting circuits. In this work we accelerate the elementary gates by experimentally feasible control methods, which are based on numerical optimization of pulse shapes for shortcuts to adiabaticity. By numerical simulations, we show that the proposed methods can achieve speedups compared to adiabatic ones by up to six times with high gate fidelities of 99.9%. These methods are thus expected to be useful for quantum computers with KPOs.

arXiv:2310.20108•Physical Review Research•Feb 22, 2024•7 citations

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

Chaos in coupled Kerr-nonlinear parametric oscillators

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.

arXiv:2110.04019•Physical Review Research•Dec 20, 2021•30 citations

Conditional-squeezing gate in superconducting circuits

Roman Schiaffino, Fernando C. Lombardo, Juan Pablo Paz

We present an implementation of a conditional-squeezing gate that squeezes a SQUID-terminated resonator mode along a direction determined by the state of a dispersively coupled qubit. This gate generalizes the controlled-squeezing gate [Phys. Rev. A \textbf{111}, 042606 (2025)], and relies on a refocusing technique to suppress unwanted effects arising from slowly varying time-dependent terms in the Hamiltonian during the state-dependent parametric resonance required for the operation. As an application, we use the gate to encode an arbitrary qubit state into superpositions of single- and two-mode squeezed states of the resonator. These non-Gaussian states enable error-detectable encoding through parity measurements. We show that refocusing substantially improves the encoding fidelity, which is ultimately limited by Kerr nonlinearities and dissipation in realistic implementations. For experimentally optimistic values of the nonlinearities and decay rates, we obtain encoding fidelities above 0.99 for arbitrary input qubit states. Our results provide a route toward extending this scheme to the generation of higher-order superpositions of squeezed states (a class of rotation-symmetric bosonic codes) using a control qudit.

quant-pharXiv:2609.10655•Sep 10, 2026•0 citations
A Kerr nonlinear parametric oscillator (KPO) is one of the promising devices used to realize qubits for universal quantum computing. The KPO can stabilize two coherent states with opposite phases, yielding a quantum superposition called a Schr"odinger cat state. Universal quantum computing with KPOs requires three kinds of quantum gates: Rz,Rx{R}_{z},{R}_{x}Rz​,Rx​, and Rzz{R}_{zz}Rzz​ gates. We theoretically propose a two-qubit gate Rzz{R}_{zz}Rzz​ for highly detuned KPOs. In the proposed scheme, we add a parametric drive for the first KPO. This leads to the Rzz{R}_{zz}Rzz​ gate based on the driving of the second KPO depending on the first-KPO state, which we call ``conditional driving.'' First, we perform simulations using a conventional KPO Hamiltonian derived from a superconducting-circuit model under some approximations and evaluate the gate fidelity. Next, we also perform numerical simulations of the two-qubit gate using the superconducting-circuit model without the approximations. The simulation results indicate that the conditional-driving gates can be implemented with high fidelity (>99.9>99.9%>99.9) for rotation angles required for universality.
Kerr parametric oscillators (KPOs), two-photon driven Kerr-nonlinear resonators, can stably hold coherent states with opposite-sign amplitudes and are promising devices for quantum computing. Recently, we have theoretically proposed a two-qubit gate Rzz for highly detuned KPOs and called it a conditional-driving gate [Chono et al., Phys. Rev. Res. 4, 043054 (2022)]. In this study, analyzing its superconducting-circuit model and deriving a corresponding static model, we find that an AC-Zeeman shift due to the flux pulse for the gate operation largely affects the gate performance. This effect becomes a more aggravating factor with shorter gate times, leading to an increase in the error rate. We thus propose a method to cancel this undesirable effect. Furthermore, through the use of shortcuts to adiabaticity and the optimization of flux pulses, we numerically demonstrate a conditional-driving gate with average fidelity exceeding 99.9% twice faster than that without the proposed cancellation method and the shortcuts to adiabaticity.
A Kerr nonlinear parametric oscillator (KPO) can stabilize a quantum superposition of two coherent states with opposite phases, which can be used as a qubit. In a universal gate set for quantum computation with KPOs, an Rx{R}_{x}Rx​ gate, which interchanges the two coherent states, is relatively hard to perform owing to the stability of the two states. We propose a method for a high-fidelity Rx{R}_{x}Rx​ gate by exciting the KPO outside the qubit space with parity-selective transitions, which can be implemented by only adding a driving field. In this method, the utilization of higher effective excited states leads to a faster Rx{R}_{x}Rx​ gate, rather than states near the qubit space. The proposed method can realize a continuous Rx{R}_{x}Rx​ gate and thus is expected to be useful for, e.g., recently proposed variational quantum algorithms.
Kerr parametric oscillators (KPOs) can stabilize the superpositions of coherent states, which can be utilized as qubits, and are promising candidates for realizing hardware-efficient quantum computers. Although elementary gates for universal quantum computation with KPO qubits have been proposed, these gates are usually based on adiabatic operations and thus need long gate times, which result in errors caused by photon loss in KPOs realized by, e.g., superconducting circuits. In this work we accelerate the elementary gates by experimentally feasible control methods, which are based on numerical optimization of pulse shapes for shortcuts to adiabaticity. By numerical simulations, we show that the proposed methods can achieve speedups compared to adiabatic ones by up to six times with high gate fidelities of 99.9%. These methods are thus expected to be useful for quantum computers with KPOs.
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.
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.
We present an implementation of a conditional-squeezing gate that squeezes a SQUID-terminated resonator mode along a direction determined by the state of a dispersively coupled qubit. This gate generalizes the controlled-squeezing gate [Phys. Rev. A \textbf{111}, 042606 (2025)], and relies on a refocusing technique to suppress unwanted effects arising from slowly varying time-dependent terms in the Hamiltonian during the state-dependent parametric resonance required for the operation. As an application, we use the gate to encode an arbitrary qubit state into superpositions of single- and two-mode squeezed states of the resonator. These non-Gaussian states enable error-detectable encoding through parity measurements. We show that refocusing substantially improves the encoding fidelity, which is ultimately limited by Kerr nonlinearities and dissipation in realistic implementations. For experimentally optimistic values of the nonlinearities and decay rates, we obtain encoding fidelities above 0.99 for arbitrary input qubit states. Our results provide a route toward extending this scheme to the generation of higher-order superpositions of squeezed states (a class of rotation-symmetric bosonic codes) using a control qudit.