Dissipation and gate timing errors in SWAP operations of qubits

Abstract

We investigate the fidelity of a sequence of SWAP gates on a Si-based quantum dot (QD) spin qubit chain. We particularly examine how valley leakage and gate timing error affect the gate fidelity compared to charge noise, which is always present. In our Hamiltonian, each qubit is coupled via Heisenberg exchange to every other qubit in the chain, with the strength of the exchange interaction decreasing exponentially with qubit distance. Valley leakage is modeled through a dissipation term γ as appropriate for the experimentally observed intervalley tunneling effect. We show that randomness in the valley leakage parameter has little to no effect on the SWAP gate fidelity in the currently fabricated Si circuits. We introduce disorder in the forms of charge noise and gate timing error and average the fidelities of 10,000 calculations for each set of parameters. The fidelities are then plotted against JSWAP, the strength of the exchange coupling corresponding to the SWAP gate. We find that valley leakage decreases the fidelity of the SWAP operation-though the effect is small compared to that of the known charge noise-and that gate timing error creates an effective optimal value of JSWAP, beyond which infidelity begins to increase.