Accurate methods for the analysis of strong-drive effects in parametric gates

Abstract

The ability to perform fast, high-fidelity entangling gates is an important requirement for a viable quantum processor. In practice, achieving fast gates often comes with the penalty of strong-drive effects that are not captured by the rotating-wave approximation. These effects can be analyzed in simulations of the gate protocol, but those are computationally costly and often hide the physics at play. Here, we show how to efficiently extract gate parameters by directly solving a Floquet eigenproblem using exact numerics and a perturbative analytical approach. As an example application of this toolkit, we study the space of parametric gates generated between two fixed-frequency transmon qubits connected by a parametrically driven coupler. Our analytical treatment, based on time-dependent Schrieffer-Wolff perturbation theory, yields closed-form expressions for gate frequencies and spurious interactions, and is valid for strong drives. From these calculations, we identify optimal regimes of operation for different types of gates including $i$SWAP, controlled-Z, and CNOT. These analytical results are supplemented by numerical Floquet computations from which we directly extract drive-dependent gate parameters. This approach has a considerable computational advantage over full simulations of time evolutions. More generally, our combined analytical and numerical strategy allows us to characterize two-qubit gates involving parametrically driven interactions, and can be applied to gate optimization and cross-talk mitigation such as the cancellation of unwanted ZZ interactions in multi-qubit architectures.

20 pages, 9 figures, 62 references

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Cited by in corpus (20)

• Mitigating off-resonant error in the cross-resonance gate
• Tunable coupler to fully decouple and maximally localize superconducting qubits
• Optimization of the resonator-induced phase gate for superconducting qubits
• Cavity-mediated entanglement of parametrically driven spin qubits via sidebands
• Fast parametric two-qubit gate for highly detuned fixed-frequency superconducting qubits using a double-transmon coupler
• A high-efficiency plug-and-play superconducting qubit network
• Lecture Notes on Quantum Electrical Circuits
• Dissipative protection of a GKP qubit in a high-impedance superconducting circuit driven by a microwave frequency comb
• Pymablock: an algorithm and a package for quasi-degenerate perturbation theory
• High-performance multiqubit system with double-transmon couplers: Toward scalable superconducting quantum computers
• Parity-dependent state transfer for direct entanglement generation
• Parametric multi-element coupling architecture for coherent and dissipative control of superconducting qubits
• Frozonium: Freezing Anharmonicity in Floquet Superconducting Circuits
• GPU-accelerated Effective Hamiltonian Calculator
• Parametric phase modulation in superconducting circuits
• Concurrent Fermionic Simulation Gate
• Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits
• Engineered Robustness for Nonadiabatic Geometric Quantum Gates
• The perfect entangler spectrum as a tool to analyze crosstalk
• Exact amplitudes of parametric processes in driven Josephson circuits