Strategy for implementing stabilizer-based codes on solid-state qubits

We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the “standard” five-qubit and CSS codes, on solid-state qubits with Ising or $XY$-type interactions. Using pulse sequences, we show how to dynamically generate the effective dynamics of the stabilizer Hamiltonian, the sum of an appropriate set of stabilizer operators for a given code. Within this approach, the encoded states (ground states of the stabilizer Hamiltonian) can be prepared without measurements and preserved against both the time evolution governed by the original qubit Hamiltonian, and errors caused by local sources.

Figure 1

Four types of surface-code generation on the $2\times 3$ lattice in Ref. [3] starting from a single-qubit Hamiltonian that includes $Y$ operators. All operators in (a) and (b) are transformed to $X$ and those in (c) and (d) to $Z$. Subsequently, the four types of stabilizer operators are combined into the topological Hamiltonian in the manner discussed in the text.