Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform

Abstract

The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of 0.9 ± 0.03 and 1.3 ± 0.4% for the CZ and the iSWAP gate, respectively. We argue that spurious ZZ-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance. Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.

Numerical analysis of effective models for flux-tunable transmon systems

“…( 1) was analytically discussed by Koch et al [10]. This work motivated several studies [4,[6][7][8]14] where transmons (fixed-frequency and/or flux-tunable) are modelled as anharmonic oscillators with fixed or tunable frequencies. The anharmonic oscillator is defined in terms of the harmonic basis…”

“…Architecture I, which is discussed in Refs. [4,8,9,12], is described by the circuit Hamiltonian ĤI = ĤTun,2 + ĤFix,1 + ĤFix,0 + V2,1 + V2,0 , (7) and architecture II, which is discussed in Refs. [5,13], is described by…”

“…( 1) and ( 13) have the same form, it is usually argued, see Refs. [4,[6][7][8][9], that only the Josephson energy E J in the expression for the qubit frequency ω ≃ √ 2E C E J has to be replaced by the effective Josephson energy E J,eff . This leads then to the time-dependent qubit frequency…”

“…Since the number of different superconducting circuits is vast, we will focus on three different circuit Hamiltonians (two of them correspond to experimental systems; see Refs. [4,5])) and their corresponding effective Hamiltoni-ans. Note that for a particular circuit Hamiltonian there might exist a vast amount of different effective models.…”

“…Here we fo-cus on the often made approximation (see Ref. [4,[6][7][8][9]) that the effective interaction strength is of static nature. A summary and conclusions drawn from our analysis are presented in Sec.…”