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Abstract Quantum tunneling is the phenomenon that makes superconducting circuits “quantum”. Recently, there has been a renewed interest in using quantum tunneling in phase space of a Kerr parametric oscillator as a resource for quantum information processing. Here, we report a direct observation of quantum interference induced by such tunneling and its dynamics in a planar superconducting circuit through Wigner tomography. We experimentally elucidate all essential properties of this quantum interference, such as mapping from Fock states to cat states, a temporal oscillation due to the pump detuning, as well as its characteristic Rabi oscillations and Ramsey fringes. Finally, we perform gate operations as manipulations of the observed quantum interference. Our findings lay the groundwork for further studies on quantum properties of superconducting Kerr parametric oscillators and their use in quantum information technologies.

Abstract 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.

Abstract Autonomous quantum error correction has gained considerable attention to avoid complicated measurements and feedback. Despite its simplicity compared with the conventional measurement-based 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-by-state 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.