Chaos in coupled Kerr-nonlinear parametric oscillators

Goto, Hayato; Kanao, Taro

doi:10.1103/physrevresearch.3.043196

Cited by 19 publications

(8 citation statements)

References 75 publications

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“…The same authors have shown [47] that the suppression of relative oscillations of infinite-temperature OTOC can reveal the transition to chaos even in a small chain of four spins with OTOC studied on time scales attainable by experiment [48]. The relative oscillations of OTOCs as a qualitative chaos indicator have also been mentioned in other studies [49,50]. Some studies propose that even the asymptotic OTOC mean value can serve as a chaos indicator [17].…”

Section: Introductionmentioning

confidence: 82%

Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator

Novotný¹,

Stránský²

2023

Preprint

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A detailed numerical study reveals that the asymptotic values of the standard deviation-to-mean ratio of the out-of-time-ordered correlator can be successfully used as a measure of the quantum chaoticity of the system. We employ a finite-size fully connected quantum system with two degrees of freedom, namely the algebraic u(3) model, and demonstrate a clear correspondence between the relative oscillations of the correlators and the ratio of the chaotic part of the volume of phase space in the classical limit of the system. We also show how the relative oscillations scale with the system size and conjecture that the scaling exponent can also serve as a robust chaos indicator.

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Section: Introductionmentioning

confidence: 82%

Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator

Novotný¹,

Stránský²

2023

Preprint

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“…Two-qubit gates preserving the biased feature of errors were proposed 21 , and high error-correction performance by concatenating the XZZX surface code 12 with KPOs 22 was numerically presented. Other research subjects on KPOs include fast gate operations and controls 9 , 23 – 26 , spectroscopy 27 , 28 , tomography 9 , 10 , 29 , Boltzmann sampling 30 , effects of strong pump field 31 , quantum phase transitions 6 , 7 , quantum chaos 1 , 32 , and trajectories 33 – 35 .…”

Section: Introductionmentioning

confidence: 99%

Measurement-based preparation of stable coherent states of a Kerr parametric oscillator

Suzuki

Watabe

Kawabata

et al. 2023

Sci Rep

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Kerr parametric oscillators (KPOs) have attracted increasing attention in terms of their application to quantum information processing and quantum simulations. The state preparation and measurement of KPOs are typical requirements when used as qubits. The methods previously proposed for state preparations of KPOs utilize modulation of external fields such as a pump and drive fields. We study the stochastic state preparation of stable coherent states of a KPO with homodyne detection, which does not require modulation of external fields, and thus can reduce experimental efforts and exclude unwanted effects of possible imperfection in control of external fields. We quantitatively show that the detection data, if averaged over an optimal averaging time to decrease the effect of measurement noise, has a strong correlation with the state of the KPO, and therefore can be used to estimate the state (stochastic state preparation). We examine the success probability of the state estimation taking into account the measurement noise and bit flips. Moreover, the proper range of the averaging time to realize a high success probability is obtained by developing a binomial-coherent-state model, which describes the stochastic dynamics of the KPO under homodyne detection.

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“…Since this fourphoton pump cannot be achieved by simple linear driving and must be achieved by parametric modulation of the Josephson junction energy [27,28] (see Supplementary Note 1), we term this system a four-photon Kerr parametric oscillator (KPO). Although a KPO has received much attention very recently because of its use for the generation and stabilization of the cat states [29-36, 38, 72], gate-based quantum computation [30,34,[38][39][40][41][42], measurement-based error correction [43,44], quantum annealing [45][46][47][48][49][50][51], and other physically interesting topics [52][53][54][55][56][57][58][59], little attention has been paid to its applicability to AQEC. Our study reveals that a KPO can be a suitable system for AQEC.…”

Section: Introductionmentioning

confidence: 99%

Autonomous Quantum Error Correction in a Four-Photon Kerr Parametric Oscillator

Kwon,

Watabe,

Tsai

2022

Preprint

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Autonomous quantum error correction has gained considerable attention to avoid complicated measurements and feedback. Despite its simplicity compared with the conventional measurementbased quantum error correction, it is still a far from practical technique because of significant hardware overhead. We propose an autonomous quantum error correction scheme for a rotational symmetric bosonic code in a four-photon Kerr parametric oscillator. Our scheme is the simplest possible error correction scheme that can surpass the break-even point-it requires only a single continuous microwave tone. We also introduce an unconditional reset scheme that requires one more continuous microwave tone in addition to that for the error correction. The key properties underlying this simplicity are protected quasienergy states of a four-photon Kerr parametric oscillator and the degeneracy in its quasienergy level structure. These properties eliminate the need for state-bystate correction in the Fock basis. Our schemes greatly reduce the complexity of autonomous quantum error correction and thus may accelerate the use of the bosonic code for practical quantum computation.

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Chaos in coupled Kerr-nonlinear parametric oscillators

Cited by 19 publications

References 75 publications

Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator

Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator

Measurement-based preparation of stable coherent states of a Kerr parametric oscillator

Autonomous Quantum Error Correction in a Four-Photon Kerr Parametric Oscillator

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