Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian
arXiv:2410.10467 · doi:10.1088/1361-6633/adb072
Abstract
We develop a systematic perturbative framework to engineer an arbitrary target Hamiltonian in the Floquet phase space of a periodically driven oscillator based on Floquet-Magnus expansion. The high-order errors in the engineered Floquet Hamiltonian are mitigated by adding high-order driving potentials perturbatively. We introduce a transformation method that allows us to obtain an analytical expression of the leading-order correction drive for engineering a target Hamiltonian with discrete rotational and chiral symmetries in phase space. We also provide a numerically efficient procedure to calculate high-order correction drives and apply it to engineer the target Hamiltonian with degenerate eigenstates of multi-component cat states that are important for fault-tolerant hardware-efficiency bosonic quantum computation.
23 pages, 5 figures; a new subsection and a new figure are added in the 2nd version
References in corpus (63)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- On the Measurement of Qubits
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Atomic quantum gases in periodically driven optical lattices
- The Magnus expansion and some of its applications
- Observation of a Discrete Time Crystal
- Floquet Time Crystals
- State preservation by repetitive error detection in a superconducting quantum circuit
- Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
- High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
- Dynamically protected cat-qubits: a new paradigm for universal quantum computation
- Discrete time crystals: rigidity, criticality, and realizations
- Long-time behavior of periodically driven isolated interacting lattice systems
- Exciting Collective Oscillations in a Trapped 1D Gas
- Time crystals: a review
- New class of quantum error-correcting codes for a bosonic mode
- Encoding a qubit in a trapped-ion mechanical oscillator
- Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators
- Modeling spontaneous breaking of time-translation symmetry
- Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator
- Performance and structure of single-mode bosonic codes
- Hardware-efficient autonomous quantum error correction
- Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
- Equilibration and Order in Quantum Floquet Matter
- Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements
- Many-body energy localization transition in periodically driven systems
- Interference of an array of independent Bose-Einstein condensates
- Bosonic quantum error correction codes in superconducting quantum circuits
- Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes
- Fault-tolerant detection of a quantum error
- Quantum computing with rotation-symmetric bosonic codes
- The Bright Side of Coulomb Blockade
- Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
- Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
- Widely tunable, non-degenerate three-wave mixing microwave device operating near the quantum limit
- Quantum information processing with bosonic qubits in circuit QED
- Towards Scalable Bosonic Quantum Error Correction
- Measurement of a topological edge invariant in a microwave network
- Quantum heat engine based on photon-assisted Cooper pair tunneling
- Phase Space Crystals: A New Way to Create a Quasienergy Band Structure
- From Coulomb blockade to nonlinear quantum dynamics in a superconducting circuit with a resonator
- Sufficient conditions for the convergence of the Magnus expansion
- Universal quantum fluctuations of a cavity mode driven by a Josephson junction
- A Single-Cooper-Pair Josephson Laser
- Preparing encoded states in an oscillator
- Nonclassical photon pair production in a voltage-biased Josephson junction
- Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
- Josephson photonics with a two-mode superconducting circuit
- Antibunched photons from inelastic Cooper-pair tunneling
- Floquet Many-body Engineering: Topological and Many-body Physics in Phase Space Lattices
- Introduction of a DC Bias into a High-Q Superconducting Microwave Cavity
- Photon cross-correlations emitted by a Josephson junction in two microwave cavities
- Systematic Magnus-based approach for suppressing leakage and non-adiabatic errors in quantum dynamics
- Correlated Cooper pair transport and microwave photon emission in the dynamical Coulomb blockade
- Synthesizing Lattice Structure in Phase Space
- Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
- Non-classical light from superconducting resonators coupled to voltage-biased Josephson junctions
- Generating entangled quantum microwaves in a Josephson-photonics device
- Multi-Photon Resonances in Josephson Junction-Cavity Circuits
- Gottesman-Kitaev-Preskill state preparation using periodic driving
- Phase Space Crystal Vibrations: Chiral Edge States with Preserved Time-reversal Symmetry
- Engineering Arbitrary Hamiltonians in Phase Space
- Universal time-dependent control scheme for realizing arbitrary linear bosonic transformations