Photon-number dependent Hamiltonian engineering for resonators

Inventors

Wang, Chiao-Hsuan • Noh, Kyungjoo • Lebreuilly, José • Girvin, Steven M. • Jiang, Liang

Assignees

University of Chicago • Yale University

Abstract

Cavity resonators are promising resources for quantum technology, while native nonlinear interactions for cavities are typically too weak to provide the level of quan¬ tum control required to deliver complex targeted operations. Here we investigate a scheme to engineer a target Hamiltonian for photonic cavities using ancilla qubits. By off-resonantly driving dispersively coupled ancilla qubits, we develop an optimized approach to engineering an arbitrary photon-number dependent (PND) Hamiltonian for the cavities while minimizing the operation errors. The engineered Hamiltonian admits various applications including canceling unwanted cavity self-Kerr interac¬ tions, creating higher-order nonlinearities for quantum simulations, and designing quantum gates resilient to noise. Our scheme can be implemented with coupled microwave cavities and transmon qubits in superconducting circuit systems.

Core Innovation

The invention provides a method and system for controlling a quantum interaction in a cavity system by using an external electromagnetic field to drive a first ancilla qubit. The method determines a target Hamiltonian associated with the cavity system that is dependent on one or more photon-number states of a first electromagnetic resonator, and the external electromagnetic field is designed to make the interaction between the external field and the cavity system emulate the target Hamiltonian while minimizing decoherence of the one or more photon-number states due to excitation of the first ancilla qubit by the external electromagnetic field.

After the external electromagnetic field is designed to emulate the target Hamiltonian with reduced ancilla-induced decoherence, the method drives the first ancilla qubit with the external electromagnetic field to induce a quantum evolution of the cavity system to a quantum state. The drive is selected to emulate arbitrary photon-number dependent Hamiltonians within cavity/resonator systems by suppressing effects that include ancilla excitation and micromotion, and by reducing qubit-induced cavity errors.

The disclosed approach is extended to include photon-photon interaction features in the target Hamiltonian, including engineered three-photon interactions and parity-dependent energies for bosonic error-syndrome use, as well as error-transparent continuous logical Z-rotations including a π/8 gate for cat/binomial bosonic codes. It also includes cavity Kerr terms, including cancellation of unwanted self-Kerr, and generalizes to coupled cavities for error-transparent controlled-phase and controlled-Z type rotations, with modeling that includes decoherence processes.

Claims Coverage

The provided material includes two independent claims, each centered on determining a photon-number dependent target Hamiltonian and driving a coupled ancilla qubit with an external electromagnetic field to emulate the target Hamiltonian while minimizing ancilla-induced decoherence.

Across the independent claims, the main inventive coverage is the use of an externally generated electromagnetic field to drive a coupled ancilla qubit so the cavity-system interaction emulates a photon-number dependent target Hamiltonian, with explicit minimization of decoherence of the photon-number states caused by excitation of the ancilla qubit, and with the resulting induced quantum evolution to a quantum state.

Stated Advantages

Documented Applications