Design and Dynamics of Two-Qubit Gates with Motional States of Electrons on Helium
Systems of individual electrons electrostatically trapped on condensed noble gas surfaces have recently attracted considerable interest as potential platforms for quantum computing. The electrons serve as charge qubits in the system, and the purity of the noble gas surface protects the relevant quantum properties of each electron. Previous work has indicated that manipulation of a confining double-well potential for electrons on superfluid helium can generate entanglement suitable for two-qubit gate operations. In this work, we incorporate a time-dependent tuning of the potential shape to further explore operation of two-qubit gates with the superfluid helium system. Through numerical time evolution of the closed system (without decoherence), we show that control-induced errors can be minimized to allow for fast, high-fidelity two-qubit gates. In particular, we simulate operation of the $\sqrt{i\mathrm{SWAP}}$ and CZ gates and obtain estimated fidelities of 0.999 and 0.996 with execution times of 2.9 ns and 9.4 ns, respectively. Furthermore, we examine the stability of these gate fidelities under non-ideal execution conditions, which reveals new properties to consider in the device design. Finally, we reflect on the impact of screening and decoherence on our results. The methodology presented here enables future efforts to isolate control-induced effects from environmental noise, which is an important step towards the realization of high-fidelity two-qubit gates with electrons on helium.