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  1. We describe the generation of entangling gates on superconductor-semiconductor hybrid qubits by ac voltage modulation of the Josephson energy. Our numerical simulations demonstrate that the unitary error can be below 10−5 in a variety of 75-ns-long two-qubit gates (CZ, 𝑖⁢SWAP, and √𝑖⁢SWAP) implemented using parametric resonance. We analyze the conditional 𝑍⁢𝑍 phase and demonstrate that the CZ gate needs no further phase-correction steps, while the 𝑍⁢𝑍 phase error in swap-type gates can be compensated by choosing pulse parameters. With decoherence considered, we estimate that qubit relaxation time needs to exceed 70μ⁢s to achieve the 99.9% fidelity threshold. 
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