Figure 1

(Color online) The evolution of a local Pauli observable $Z_3$ for a qubit chain of length $N=8$. The color-coded boxes denote Pauli operators $X_i$ and $Z_i$, respectively, and each row of boxes represents a tensor product of such Pauli operators. Within the cycle that leads to reflection of the chain, each local observable undergoes the phases of expansion, transmission, and contraction. When expanding or contracting, the operators pick up a sign factor of $-1$ under conjugation by a $Y$ pulse.Reuse & Permissions

Figure 2

(Color online) Arrangement of logical qubits within the chain (a) and pulse sequences for gates (b), for $n=3$. (a) Only every second physical qubit in the chain (●) is used as a logical qubit. The qubits in between (엯) are ancillas. (b) Pulse sequences for the implementation of the universal gates, during the first half of a clock cycle. The second half-cycle is analogous, with $\alpha \to -\alpha$. The symbol ∎ denotes application of the elementary transition function $T$. The vertical bars denote pulses (2).Reuse & Permissions

Figure 3

(Color online) The solution for the recursion relations (A3) in free space. Each vertex in the lattice denotes a space-time point $(i,t)$. The symbol ● indicates $v_i\left(t\right)=1$ and + $v_i\left(t\right)=0$. To obtain the solution for the case with boundary from the free space solution, the lattice is “folded back” to the space interval $[0,N+1]$.Reuse & Permissions