Figure 4: Scaling of the dynamical correlation length .

For all sizes and cases, 2,000 realizations of the boundary states were used. The data-point code used in a applies to all other panels. When not visible, the error bars are smaller than the size of the data points. (a–c) Fixed input and output; (d–f) mixed boundary conditions; (a,d) 20% TOFFOLI; (b,e) 40% TOFFOLI; and (c,f) 100% TOFFOLI. For systems with the smallest depth W studied, 16 × 42, and for circuits with few TOFFOLI gates (20%) and fixed-input and output boundary conditions, tends to saturate, indicating that complete solutions have been reached. Notice that the functional form of the scaling does not depend on the boundary conditions, and depends solely on the concentration of TOFFOLI gates.