After seeing a talk on counterfactual computation by Jozsa at the Isaac Newton Institute, Keith Bowden of the Theoretical Physics Research Unit at Birkbeck College, University of London published a paper[2] in 1997 describing a digital computer that could be counterfactually interrogated to calculate whether a light beam would fail to pass through a maze[3] as an example of this idea.
[4] The quantum computer may be physically implemented in arbitrary ways[5] but, to date, the common apparatus considered features a Mach–Zehnder interferometer.
After many repetitions of very rapid projective measurements, the "not running" state evolves to a final value imprinted into the properties of the quantum computer.
(iii) After cancelling the terms (if any) whose complex amplitudes together add to zero, the set m of measurement outcomes is a counterfactual outcome if (iv) there are no terms left with the computer-running label in their history labels, and (v) there is only a single possible computer output associated to m. In 1997, after discussions with Abner Shimony and Richard Jozsa, and inspired by the idea of the (1993) Elitzur-Vaidman bomb tester, Keith Bowden (Birkbeck College) published a paper[2] describing a digital computer that could be counterfactually interrogated to calculate whether a photon would fail to pass through a maze of mirrors.
In 2015, counterfactual quantum computation was demonstrated in the experimental context of "spins of a negatively charged nitrogen-vacancy color center in a diamond".