quantum gate directory

Virtual distillation is an error-mitigation technique that improves expectation-value estimates by effectively amplifying the contribution of the dominant eigenstate of a noisy quantum state. The gate $B^{(2)}_i$ is a the two-qubit case of a more general entangling gate. In the two-qubit case it on the $i$th qubit of two copies of a prepared state $\rho$ before measurement to extract information about higher moments of $\rho$ (such as $\mathrm{Tr}(\rho^2 O)$) using standard quantum hardware.

$$ B^{(2)}_i = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 0 \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} $$

See arXiv:2011.07064 for the full protocol.