Gottesman-Kitaev-Preskill state preparation using periodic driving

Abstract

The Gottesman-Kitaev-Preskill (GKP) code may be used to overcome noise in continuous variable quantum systems. However, preparing GKP states remains experimentally challenging. We propose a method for preparing GKP states by engineering a time-periodic Hamiltonian whose Floquet states are GKP states. This Hamiltonian may be realized in a superconducting circuit comprising a SQUID shunted by a superinductor and a capacitor, with a characteristic impedance twice the resistance quantum. The GKP Floquet states can be prepared by adiabatically tuning the frequency of the external magnetic flux drive. We predict that highly squeezed $>11.9$ dB ($10.8$ dB) GKP magic states can be prepared on a microsecond timescale, given a quality factor of $10^6$ ($10^5$) and flux noise at typical rates.

arXiv commentIncludes main text and supplementary material

References in corpus (45)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Circuit Quantum Electrodynamics
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Encoding a qubit in an oscillator
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Photovoltaic Hall effect in graphene
• The Magnus expansion and some of its applications
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Real-time quantum error correction beyond break-even
• Encoding a qubit in a trapped-ion mechanical oscillator
• Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
• Performance and structure of single-mode bosonic codes
• Implementation of low-loss superinductances for quantum circuits
• Tunable Superconducting Qubits with Flux-Independent Coherence
• Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
• Fault-tolerant bosonic quantum error correction with the surface-GKP code
• Flux Qubits with Long Coherence Times for Hybrid Quantum Circuits
• Quantum Error Correction with the Toric-GKP Code
• Towards Scalable Bosonic Quantum Error Correction
• Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
• Single-Mode Displacement Sensor
• Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
• Floquet States in Open Quantum Systems
• Nanowire Superinductance Fluxonium Qubit
• Simulation of non-Abelian braiding in Majorana time crystals
• Superconducting circuit protected by two-Cooper-pair tunneling
• The superconducting quasicharge qubit
• Circuit quantization in the presence of time-dependent external flux
• Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
• Qubit metrology of ultralow phase noise using randomized benchmarking
• Low overhead fault-tolerant quantum error correction with the surface-GKP code
• Quantum electrodynamics of a superconductor-insulator phase transition
• Surpassing the resistance quantum with a geometric superinductor
• Modular Bosonic Subsystem Codes
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
• AC flux sweet spots in parametrically-modulated superconducting qubits
• Floquet Many-body Engineering: Topological and Many-body Physics in Phase Space Lattices
• Stabilizing a Bosonic Qubit using Colored Dissipation
• Kicked-Harper model vs On-Resonance Double Kicked Rotor Model: From Spectral Difference to Topological Equivalence
• Inelastic scattering of a photon by a quantum phase-slip
• Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
• Magnifying quantum phase fluctuations with Cooper-pair pairing
• Stabilizer subsystem decompositions for single- and multi-mode Gottesman-Kitaev-Preskill codes

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• Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian
• Clifford operations and homological codes for rotors and oscillators
• Engineering Bosonic Codes with Quantum Lattice Gates
• The complexity of Gottesman-Kitaev-Preskill states
• Protected phase gate for the $0$-$\pi$ qubit using its internal modes
• Quantum data generation in a denoising model with multiscale entanglement renormalization network
• Fault-Tolerant Non-Clifford GKP Gates using Polynomial Phase Gates and On-Demand Noise Biasing
• Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits
• Single-Period Floquet Control of Bosonic Codes with Quantum Lattice Gates