Landscape of the best TDS algorithm, as measured by the worst-case error U - U exact , as a function of the relative field strength α = J / h and evolution time T at identical circuit depth for a 1x8 Heisenberg chain. The circuit depth is fixed to one step of optimised THRIFT 8 evolution. For the other algorithms, the number of steps is chosen to match the 2-qubit depth as closely as possible according to the 2-qubit depths shown in Table 3. The colour of each point represents the algorithm that achieves the lowest error at those values of J and T, while the brightness indicates the magnitude of the error. The isolated purple and red pixels in the THRIFT 4 and THRIFT 2 regions are artifacts of the randomness in the field strengths and running the optimised small A and eighth-order simulations with different random fields, but do not seem indicative of the general relative performance of the algorithms at these ( α , T )-points.
