quantum gate directory
Virtual Distillation
Symbol
$B^{(2)}_i$
Description:
A two-qubit entangling gate used in virtual distillation error-mitigation protocols.
Groups
This gate is contained in the following groups:
Virtual distillation is an error-mitigation technique that amplifies the dominant eigenstate of a noisy density matrix. The gate $B^{(2)}_i$ is the two-qubit case of a more general entangling gate applied to two copies of a state.
$$ B^{(2)}_i = \begin{bmatrix} 1 & 0 & \phantom{+}0 & 0 \\ 0 & \frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 0 \\ 0 & \frac{\sqrt{2}}{2} & \phantom{+}\frac{\sqrt{2}}{2} & 0 \\ 0 & 0 & \phantom{+}0 & 1 \end{bmatrix} $$
Properties
- Unitary and entangling.
- Implements a partial swap between two copies of a state on qubit $i$.
Usage
- Estimating nonlinear functionals like $\mathrm{Tr}(\rho^2 O)$ with hardware.
- Error mitigation in near-term experiments.
See arXiv:2011.07064 for the full protocol.
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