Limits to two-spin-qubit gate fidelity from vacuum and thermal fluctuations*

The basic building block in a quantum circuit is the logical qubit which requires high fidelity of physical qubit operation. In spin qubit quantum computing systems, metallic gates and antennas are necessary for qubit operation, initialization, and readout. Thermal and vacuum fluctuations are enhanced in the vicinity of metallic gates, and the gate fidelity is limited by corresponding evanescent wave Johnson noise (EWJN). Here, we use an open quantum system model to describe Markovian spin qubit relaxation and decoherence processes using Lindblad master equation. We study the fundamental limits to two spin-qubit gate fidelity from EWJN in two promising quantum computing systems: NV centers in diamond and silicon quantum dot system. We first consider optimization of control pulse design where we propose an open qubit driving protocol that is more robust against Markovian relaxation and decoherence processes. Then, we perform geometry optimization of metallic gates and antennas to obtain the optimal gate fidelity. Our work provides a rigorous treatment to reach the limits of two-spin-qubit gate fidelity overcoming the effects of vacuum and thermal fluctuations.