trapdiff.m

Directional derivatives for the trapezium product quadrature published by Iserles and Norsett (see Corollary 3.3) in (https://doi.org/10.1098/rsta.1999.0362). The derivatives are of the following propagator:

         expm(-i*((HL+HR)/2+i*dt*(sqrt(3)/12)*[HL,HR])*dt)

with respect to the coefficients cL, cR in the evolution generators HL and HR on the left and the right side of the interval respectively. Evolution generators HL and HR are split into the drift part Ho and the control part Hc, such that HL=Ho+cL*Hc and HR=Ho+cR*Hc on the left and the right edge of the interval. The derivatives are calculated using Eq 16 of Goodwin and Kuprov (https://doi.org/10.1063/1.4928978).

Syntax

    [DL,DR]=trapdiff(spin_system,Hd,Hc,dt,cL,cR)

Arguments

    Hd - a cell array of two matrices containing drift 
         generators at the left (first element) and the
         right (second element) edge of the interval

    Hc - control operator or superoperator
         
    dt - interval duration, seconds

    cL - control operator coefficient at the
         left edge of the interval

    cR - control operator coefficient at the
         right edge of the interval

Outputs

    DL - derivative of the interval propagator
         with respect to cL

    DR - derivative of the interval propagator
         with respect to cR

See also

Numerical Infrastructure Optimal control module

Version 2.7, authors: Uluk Rasulov, Ilya Kuprov