Figure 1

The circuit to implement the quasiextreme channel ${\mathcal{E}}^{\mathrm{qe}}$. The unitary operators $U(\mathit{\delta })$ and $U(\mathit{\phi })$ serve to diagonalize the channel.Reuse & Permissions

Figure 2

Schematic diagram for the SKDN algorithm. (a) Representation of the algorithm on the Bloch ball. The SKDN algorithm finds a polynomial-length gate sequence to approximate an arbitrary single-qubit unitary operator $U$ by starting with an initial approximation $U_0$ with initial error bound ${ϵ}_0<1/32$ followed by iteratively constructing operators to produce decreasing errors. (b) Action of gates $G_n$ in the lookup database represented as rotations of the sphere. (c) The radius $\pi /2$ ball of single-qubit unitary operations (note that this is different than the Bloch ball). Each lookup database gate element $G_n$ is located within one cube of a period $1/32\sqrt{3}$ cubic lattice. At the boundary, a cube’s center can lie outside the ball but still must be a legitimate domain for the search algorithm.Reuse & Permissions