Effective versus Floquet theory for the Kerr parametric oscillator

Abstract

Parametric gates and processes engineered from the perspective of the static effective Hamiltonian of a driven system are central to quantum technology. However, the perturbative expansions used to derive static effective models may not be able to efficiently capture all the relevant physics of the original system. In this work, we investigate the conditions for the validity of the usual low-order static effective Hamiltonian used to describe a Kerr oscillator under a squeezing drive. This system is of fundamental and technological interest. In particular, it has been used to stabilize Schrödinger cat states, which have applications for quantum computing. We compare the states and energies of the effective static Hamiltonian with the exact Floquet states and quasi-energies of the driven system and determine the parameter regime where the two descriptions agree. Our work brings to light the physics that is left out by ordinary static effective treatments and that can be explored by state-of-the-art experiments.

arXiv comment13 pages, 8 Figures. Version accepted in Quantum Journal. (added missing DOI links)

References in corpus (29)

• Charge insensitive qubit design derived from the Cooper pair box
• Anderson Transitions
• Trapped-Ion Quantum Computing: Progress and Challenges
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Dynamically protected cat-qubits: a new paradigm for universal quantum computation
• Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
• Building a fault-tolerant quantum computer using concatenated cat codes
• Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network: Toward quantum soft computing
• 3-Wave Mixing Josephson Dipole Element
• Bias-preserving gates with stabilized cat qubits
• Switching via quantum activation: A parametrically modulated oscillator
• Parametric resonance in tunable superconducting cavities
• Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators
• Kerr-free three-wave mixing in superconducting quantum circuits
• Single-shot Readout of a Superconducting Qubit using a Josephson Parametric Oscillator
• Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation
• Quantum dynamics of a few-photon parametric oscillator
• Quantum interference in the classically forbidden region: a parametric oscillator
• On the static effective Hamiltonian of a rapidly driven nonlinear system
• Observation and manipulation of quantum interference in a superconducting Kerr parametric oscillator
• Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator
• Stabilizing a Bosonic Qubit using Colored Dissipation
• Two-photon driven Kerr quantum oscillator with multiple spectral degeneracies
• Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator
• Impact of chaos on precursors of quantum criticality
• A driven quantum superconducting circuit with multiple tunable degeneracies
• Universal wave functions structure in mixed systems

Cited by in corpus (13)

• High-Coherence Kerr-cat qubit in 2D architecture
• Driving superconducting qubits into chaos
• Symmetries of the squeeze-driven Kerr oscillator
• A Roadmap for Simulating Chemical Dynamics on a Parametrically Driven Bosonic Quantum Device
• Symmetrically Threaded Superconducting Quantum Interference Devices As Next Generation Kerr-cat Qubits
• Asymmetry Control in a Parametric Oscillator for the Quantum Simulation of Chemical Activation
• Impact of chaos on the excited-state quantum phase transition of the Kerr parametric oscillator
• Unraveling the switching dynamics in a quantum double-well potential
• Residual-$ZZ$-coupling suppression and fast two-qubit gate for Kerr-cat qubits based on level-degeneracy engineering
• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators
• Fundamental Limits to Cat-Code Qubits from Chaos-Assisted Tunneling
• Exact amplitudes of parametric processes in driven Josephson circuits
• Degeneracy beyond the parity-symmetry protection in one-dimensional spinless models: The parity-violating Kerr parametric oscillator