Figure 1

(Color online) (a) Schematic of the basic building block of a Kitaev lattice, consisting of four superconducting charge qubits (labeled 1–4): (i) qubits 1 and 2 are inductively coupled via a mutual inductance $M$; (ii) qubits 1 and 3 are coupled via an LC oscillator; and (iii) qubits 1 and 4 are capacitively coupled via a mutual capacitance $C_m$. Inset: the three types of interqubit couplings are denoted as $x$-, and $y$- or $z$-type bonds. Here each charge qubit consists of a Cooper-pair box (green dot online or gray dot in print) that is linked to a superconducting ring via two identical Josephson junctions (each with coupling energy $E_J$ and capacitance $C_J$), to form a SQUID loop. Also, each qubit is controlled by both a voltage $V_i$ (applied to the qubit via the gate capacitance $C_g$) and a magnetic flux ${\Phi }_i$ (piercing the SQUID loop). (b) A partial Kitaev lattice (honeycomb lattice) constructed by repeating the building block in (a), where a charge qubit is placed at each site. A plaquette is defined as a hexagon in the lattice. The plaquette operator is defined as $W_p={\sigma }_1^x{\sigma }_2^y{\sigma }_3^z{\sigma }_4^x{\sigma }_5^y{\sigma }_6^z$ and is shown for a given plaquette $p$.Reuse & Permissions

Figure 2

(Color online) (a) Two types of vortex excitations $w_1$ and $w_2$. A pair of vortices are generated along the horizontal direction for $w_1$ (vertical direction for $w_2$) by the spin-pair operator ${\tilde{\sigma }}^z\equiv {\sigma }^{z}I$ $\left({\tilde{\sigma }}^y\equiv {\sigma }^y{\sigma }^x\right)$ acting on a $z$ link. (b) Two bond-state excitations $b_1$ and $b_2$, which are also generated by the spin-pair operators ${\tilde{\sigma }}^z$ and ${\tilde{\sigma }}^y$ on a $z$ link.Reuse & Permissions

Figure 3

(Color online) Schematic of the procedures for braiding excitations. (a) The operations $U_h$ and $U_v$ for creating excitations, which are achieved by successively applying spin-pair operators at $z$ bonds along the horizontal $\left(P_h\right)$ and vertical $\left(P_v\right)$ paths. Here the paths $P_v$ and $P_h$ intersect at a $z$ bond. (b) A combined operation $U_h^{-1}{U}_v^{-1}{U}_h{U}_v$ for both, braiding the excitations created in (a), and fusing them to the vacuum. (c) The operations $U_h$ and $U_v$ for creating excitations, which are also achieved by successively applying spin-pair operators at $z$ bonds along $P_h$ and $P_v$ but the paths $P_v$ and $P_h$ do not intersect at a $z$ bond.Reuse & Permissions