Impact of Spectators on a Two-Qubit Gate in a Tunable Coupling Superconducting Circuit

Cross-resonance (CR) gates have emerged as a promising scheme for fault-tolerant quantum computation with fixed-frequency qubits. We experimentally implement an entangling CR gate by using a microwave-only control in a tunable coupling superconducting circuit, where the tunable coupler provides extra degrees of freedom to verify optimal conditions for constructing a CR gate. By developing a three-qubit Hamiltonian tomography protocol, we systematically investigate the dependency of gate fidelities on spurious qubit interactions and present the first experimental approach to the evaluation of the perturbation impact arising from spectator qubits. Our results reveal that the spectator qubits lead to reductions in CR gate fidelity dependent on ZZ interactions and particular frequency detunings between spectator and gate qubits. The target spectator demonstrates a more serious impact than the control spectator under a standard echo pulse scheme, whereas the degradation of gate fidelity is observed up to 22.5% as both the spectators are present with a modest ZZ coupling to the computational qubits. Our experiments uncover an optimal CR operation regime, and the method we develop here can readily be applied to improving other kinds of two-qubit gates in large-scale quantum circuits.