We study how to use the surface states in a Bi₂Se₃ topological insulator ultra-thin film that are affected by finite size effects for the purpose of quantum computing. We demonstrate that: (i) surface states under the finite size effect can effectively form a two-level system where their energy levels lie in between the bulk energy gap and a logic qubit can be constructed, (ii) the qubit can be initialized and manipulated using electric pulses of simple forms, (iii) two-qubit entanglement is achieved through a \(\sqrt {{\rm{SWAP}}} \) operation when the two qubits are in a parallel setup, and (iv) alternatively, a Floquet state can be exploited to construct a qubit and two Floquet qubits can be entangled through a Controlled-NOT operation. The Floquet qubit offers robustness to background noise since there is always an oscillating electric field applied, and the single qubit operations are controlled by amplitude modulation of the oscillating field, which is convenient experimentally.

我们研究如何利用Bi ₂ Se ₃拓扑绝缘体超薄膜中受有限尺寸效应影响的表面态进行量子计算。我们证明：（i）有限尺寸效应下的表面态可以有效地形成一个两能级系统，其能级位于体能隙之间，并且可以构造逻辑量子位，（ii）可以初始化量子位，并且使用简单形式的电脉冲进行操纵，(iii)当两个量子位处于并行设置时，通过\(\sqrt {{\rm{SWAP}}} \)操作实现两个量子位纠缠，并且 (iv) 或者，可以利用 Floquet 状态来构造一个量子位，并且可以通过受控非操作来纠缠两个 Floquet 量子位。 Floquet 量子位对背景噪声具有鲁棒性，因为始终施加振荡电场，并且单量子位操作由振荡场的幅度调制控制，这在实验上很方便。