BQP-completeness conjecture for CFT unitary evolution

For finite-Fourier-series functions $f^{(1)},\ldots,f^{(k)}$, with coefficients supplied as inputs and with $n_j$ denoting the largest nonzero Fourier index of $f^{(j)}$, define the CFT unitary evolution problem as approximating

$$\left|(1,\prod_{j=1}^k e^{iL(f^{(j)})}1)\right|$$

to error $\epsilon$. CFT unitary evolution conjecture. This problem is in $\mathbf{BQP}$, meaning that a quantum algorithm runs in polynomial time in the inputs ${n_j}_j\cup{(\hat{f^{(j)}})_l}_{j,l}\cup{k,1/\epsilon}$; generically, it is $\mathbf{BQP}$-complete. This is proposed as the quantum-computational formulation of CFT unitary evolution; no proof is given in the source.