Fig. 2: 2-qubit gate depth scaling as a function of system size and simulation time for the 1D and 2D transverse-field Ising model (TFIM).
From: Efficient and practical Hamiltonian simulation from time-dependent product formulas
a 2-qubit gate depth to achieve \(\left\Vert U-{U}_{{{\rm{exact}}}}\right\Vert \le 0.01\) for the different TDS algorithms for a field strength of J = 1/8 and evolution time T = L, for a 1 × L Ising chain with transverse field. The depths follow a power law of the form d = aLk whose parameters a and k we determine via a least-squares fit and report, also for different values of α, in Supplementary Fig. 4. b Similar simulation for a 3 × 3 transverse-field Ising model. Because the 2D transverse-field Ising model is not integrable and hence large system sizes are not classically simulable, we fix the system size to 3 × 3 and only scale the evolution time T. Error bars (mostly barely visible) are ±1, i.e., the minimal possible depth resolution.
