A new method of simulations for the propagators of multi-qubit registers

A numerical method of simulations for the evolution operators (propagators) of coupled qubits was developed on the basis of Magnus representation. The propagator of a multi-qubit system can be expressed by a N × N matrix whose size increases as N = 2ⁿ with the number of qubits n . Therefore, the standard approach to the propagator calculation requires the involvement of numerically expensive procedures. We have shown that the calculations of the propagator at the current time can be reduced to the inversion of the Vandermonde matrix, which occurs when constructing interpolation polynomials. In this case, due to the recurrence relations, the number of required flops increases only as ∼ O(N ²) (in opposite to ∼ O (N ³) flops for the matrix of the general form). This fact allows us to speed up the calculation of the propagator for multi-qubit systems. (paper)