Implementing High-fidelity Two-Qubit Gates in Superconducting Coupler Architecture with Novel Parameter Regions

Abstract

Superconducting circuits with coupler architecture receive considerable attention due to their advantages in tunability and scalability. Although single-qubit gates with low error have been achieved, high-fidelity two-qubit gates in coupler architecture are still challenging. This paper pays special attention to examining the gate error sources and primarily concentrates on the related physical mechanism of ZZ parasitic couplings using a systematic effective Hamiltonian approach. Benefiting from the effective Hamiltonian, we provide simple and straightforward insight into the ZZ parasitic couplings that were investigated previously from numerical and experimental perspectives. The analytical results obtained provide exact quantitative conditions for eliminating ZZ parasitic couplings, and trigger four novel realizable parameter regions in which higher fidelity two-qubit gates are expected. Beyond the numerical simulation, we also successfully drive a simple analytical result of the two-qubit gate error from which the trade-off effect between qubit energy relaxation effects and ZZ parasitic couplings is understood, and the resulting two-qubit gate error can be estimated straightforwardly. Our study opens up new opportunities to implement high-fidelity two-qubit gates in superconducting coupler architecture. I. BACKGROUND AND MOTIVATION

Non-perturbative analytical diagonalization of Hamiltonians with application to coupling suppression and enhancement in cQED

“…Summing all the contributions gives the 4th-order perturbation ζ (4) in Eq. (37). Notice that virtual interactions that only involve the first excited state have no contribution to the ZZ interaction at this perturbation level, i.e., ζ (4) = ζ t + ζ t .…”

“…The Hamiltonian interaction term is written as ζσ z1 σ z2 , acting on the two qubits. Typically, in superconducting systems, it arises from the interaction of the |11 state with the non-computational state in the physical qubits, and can both be used as a resource for entangling gates [21][22][23][24] or viewed as cross-talk noise that needs to be suppressed [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

“…( 36) is only valid when ignoring the higher level of the resonator. If we reduce the qubit detuning ∆ j so that it becomes comparable with the anharmonicity α j , the second excited state of the resonator comes into the picture and can be used to suppress the ZZ interaction, also known as the quasidisq regime [10,37]. We identify this regime as the quasidispersive regime because g/∆ j is usually larger than 0.1 in superconducting qubits with weak anharmonicity (e.g., Transmons), though we show the same analysis can also hold for stronger anharmonicities.…”

“…The expression has also been computed using diagrammatic techniques within the strong dispersive regime [25,50]. A more general expression, including an additional direct coupling between the qubits and an anharmonicity in the resonator, is derived in [37]. Here, we stay with this model for simplicity and investigate the degrees of freedom one has in this energy landscape.…”

“…In the first regime, where the leakagelevel-mediated ZZ interaction can be used to generate CZ gates [21][22][23][24], we consider the two-excitation manifold and compute accurate approximations of the ZZ interaction strength applicable to the full parameter regime for gate implementation. In the second scenario, we study the suppression of ZZ interactions [10,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] in the traditional setup of resonator mediated coupling without direct qubit-qubit interaction. We compute the perturbative expansion of the ZZ interaction up to the 8th order perturbation as parametric expressions.…”