circuit-level 2 qubits
Virtual Distillation
A two-qubit entangling gate used in virtual distillation error-mitigation protocols.
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.
The unitary, drawn
Every entry of the matrix as a disc. The area is the transition probability $|U_{jk}|^2$; the colour and the hand are the phase. Rows are outputs $\langle j|$, columns inputs $|k\rangle$, in the computational basis.
Phase
Disc area $= |U_{jk}|^2$. Hover an entry for its value, or take the JSON.
Weyl chamber
Where this gate sits among all two-qubit gates, up to single-qubit rotations before and after.
Coordinates:
not entangling entangling perfect entangler
$(a, b, c)$ means the gate equals $e^{i(a\,XX + b\,YY + c\,ZZ)}$ up to single-qubit gates, reduced to the chamber $\pi/4 \ge a \ge b \ge |c|$ (the convention of the canonical gate, Qiskit and Cirq). The $a = \pi/4$ face is a mirror: $(\pi/4, b, c)$ and $(\pi/4, b, -c)$ are the same gate. Drag the figure to rotate it, double-click to reset.