“Due to quantum effects, it’s possible to build a quantum computer that computes without running—or as the scientists explain, “the result of a computation may be learned without actually running the computer.” So far, however, the efficiency of this process, which is called counterfactual computation (CFC), has had an upper limit of 50%, limiting its practical applications.

Now in a new paper, scientists have experimentally demonstrated a slightly different version called a “generalized CFC” that has an efficiency of 85% with the potential to reach 100%. This improvement opens the doors to realizing a much greater variety of applications, such as low-light medical X-rays and the imaging of delicate biological cells and proteins—in certain cases, using only a single photon.” said *Phys.org*

The researchers, led by Prof. Jiangfeng Du at the University of Science and Technology of China and Prof. Liang Jiang at Yale University in the US, have published a paper on the high-efficiency counterfactual computing method in a recent issue of *Physical Review Letters*.

“The main keys to achieving high-efficiency CFC include the utilization of exotic quantum features (quantum superposition, quantum measurement, and the quantum Zeno effect), as well as the use of a generalized CFC protocol,” Du told *Phys.org*.

**How counterfactual computing works**

By “not running,” the scientists mean that the computer—which can operate in either an “on” subspace or an “off” subspace—stays in its “off” subspace for the entire computation. Physically maintaining the computer in the “off” subspace, in this scheme, involves controlling the spin properties of a diamond system, which acts as a quantum switch. Some of the spins must be kept in a superposition state, in which they occupy two states at the same time.

“To control the spin superposition, the physicists took advantage of the quantum Zeno effect, in which frequent measurements on a system can “freeze” the system in its current state. By applying a sequence of pulses to the system, the scientists could keep the system in its “off” subspace, and so keep it from running.” said *Phys.org*

“The procedure comprises a quantum switch and a quantum register,” Jiang explained. “For each repetition, we prepare the quantum switch into a quantum superposition state, including two coherent parts (‘on’ and ‘off’). Then the ‘algorithm,’ a NOT gate on the quantum register in our case, is performed in the ‘on’ subspace. Although it seems the computer has run in this step, a consequent projective measurement will remove all the changes in the ‘on’ subspace, since the probability of the whole system collapsing into the ‘off’ subspace during the measurement is very large (approaches 100% as the number of repetitions tends to infinity utilizing the quantum Zeno effect).”

The researchers explain that the “on” and “off” states can be thought of as the two paths of an interferometer, where a photon may take one path or the other, but not both.

“Such a situation is very similar to the case of a photon passing through a two-way interferometer,” Jiang said. “When a detector on one of the paths catches the photon, then one says the photon does not go on the other path. Similarly, when the whole system collapses into the ‘off’ subspace, one can conclude that the computer does not run. After each repetition, the state changes slightly. It finally evolves to a certain value after N repetitions from its initial value. By detecting its state, we get the information that is ‘programmed’ in the computer, although the computer has not run.”

**Breaking the efficiency limit**

Previous experimental CFC protocols have faced a counterfactual efficiency limit of 50%, where the counterfactual efficiency is defined as “the average probability of learning the result of a computation without running the computer.” But the generalized CFC (first proposed by G. Mitchison and R. Jozsa in 2001) does not face this limit, which allowed the researchers in the new study to experimentally demonstrate an efficiency of 85% at 17 pulse repetitions.

“The key difference between the two protocols is that the ‘off’ subspace of the generalized CFC is dependent on the choice of the ‘algorithm’ (U_{r}), whereas it is independent in the controlled-U_{r} CFC,” said coauthor Chenyong Ju at the University of Science and Technology of China. “As a consequence of this fact, the sum of the ‘volume’ of each ‘off’ subspace, which has a direct relation to the counterfactual efficiency, is much larger for the generalized CFC than the controlled-U_{r} CFC.”

The higher efficiency opens up the possibility of developing highly efficient yet very low-light imaging technology. This technology could be useful in any situation in which light may damage or destroy the illuminated sample, which makes the method particularly relevant for biological imaging. Applications may include imaging green fluorescent proteins that might be bleached under laser light, as well as UV imaging of cells and safe X-ray imaging. In some situations, these applications might be performed using only a single photon.

“The use of one photon is just for the special case that the object to be imaged has only one pixel being transparent, whereas the other pixels are opaque,” said coauthor Fei Kong at the University of Science and Technology of China. “To image the object with our protocol, one may imagine that the situation in which a photon is absorbed by an opaque pixel is just like the computer evolving into the ‘on’ subspace. Such a process is effectively avoided in our protocol. The photon will eventually ‘find’ the transparent pixel and pass through it. Through a detector below, one can locate this pixel and hence accomplish the imaging with just one photon. The number of photons needed is proportional to the number of transparent pixels, whereas normal imaging methods need [many more] photons.”

In the future, the researchers also plan to investigate potential applications of counterfactual computing for secure communication.

“We are looking forward to exploring more realistic applications of the generalized CFC,” Du said. “There are several recent works on the topic of counterfactual quantum cryptography and communication. Employing the counterfactual quantum phenomenon, several groups have proposed and demonstrated a new model of secret communication in which no physical signal particles are transmitted, which provides practical security advantages. We wonder what the potential of the generalized CFC is in this area.”