Fast high-fidelity entangling gates for silicon quantum dot spin qubits from geometric space curves

Most demonstrations of entangling gates between spin qubits in silicon quantum dots have focused on a restricted set of gates generated by non-optimal pulse waveforms. We will present a general method for designing any type of two-qubit gate implemented with pulses that approach the quantum speed limit while respecting experimental constraints. These pulses are obtained from geometric space curves whose boundary conditions dictate the entanglement class of the resulting gate. Our framework yields fast CNOT-equivalent gates with fidelities exceeding 99% for typical experimental parameters. We show that the fidelity can be further improved by applying numerical pulse optimization algorithms on our analytically designed pulses.