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 iSWAP, 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.

Optimization of the resonator-induced phase gate for superconducting qubits

“…where we expand the generator Ĝ(t) and the resulting effective Hamiltonian up to an arbitrary order in the interaction [37,38,42,43,50,51,62]. Here, we implement the perturbation up to the second order.…”

Engineering, control and longitudinal readout of Floquet qubits

“…We extend the principle of the Floquet spectrum to driven Floquet qubits, widely used in static systems with a single drive frequency. This approach has recently been used by Petrescu et al [26] to extract gate parameters maximizing the gate rate while minimizing higher order ZZ-terms. The generalized Floquet spectrum is defined with respect to the second drive frequency acting on the periodic Floquet System, typically the drive inducing a X-Gate on a Floquet qubit.…”

“…Here, a transmon qubit ( b) is interaction with a readout cavity (â) via a flux-tunable coupler (ĉ). This system can be modeled as a triplet of coupled Kerr oscillators [26]…”

Quantum crosstalk analysis for simultaneous gate operations on superconducting qubits

“…1(a), where fixed-frequency transmon qubits [44] are coupled via a tunable bus [45]. We note that although several works have previously examined various quantum crosstalk effects, such as ZZ crosstalk for singlequbit gates [21,46,56], two-qubit gates [10,11,33,[46][47][48][49][50][51][52][53][54][55][56] and spectator-qubit induced crosstalk in multi-qubit systems [30][31][32][33][57][58][59], but restricted mainly on isolated two-qubit gates. Giving crosstalk analysis in the context of simultaneous gate operations on a multi-qubit lattice could give more physical insight into the nature of crosstalk effect [18,60] on practically implemented quantum processors [15,16].…”