Fig. 2: Visual representation of Eq. (4) for the 2-qubit 2-SAT problem, with each qubit located in the xz-plane of its Bloch sphere.

The three projectors corresponding to the three clauses in the 2-qubit 2-SAT defined by Eq. (33b) are shown as tensor products of \(\left\vert {\theta }^{\perp }\right\rangle =\hat{R}(\pi +\theta )\left\vert +\right\rangle\) (indicated as a red dot) and \(\vert {\bar{\theta }}^{\perp }\rangle =\hat{R}(\pi -\theta )\vert + \rangle\) (indicated as a blue dot). Upon measuring the observable corresponding to each \({\hat{P}}_{j}(\theta )\), an outcome +1 heralds success (and corresponds to the ±θ states), while an outcome −1 heralds failure (and corresponds to the ±θ^⊥ states). Thus, each measurement serves to rule out a possible final solution, shown to the right of drawings of each projector. The unique solution that remains is the solution to this 2-SAT problem.