Counterfactual Quantum Computation

Counterfactual Quantum Computation is a method of inferring the result of a computation without actually running a quantum computer otherwise capable of actively performing that computation.

Conceptual Origin

Physicists Graeme Mitchinson and Richard Jozsa introduced the notion of counterfactual computing^[1] as an application of quantum computing, founded on the concepts of Counterfactual Definiteness, on a re-interpretation of the Elitzur–Vaidman bomb tester thought experiment, and making theoretical use of the phenomenon of interaction-free measurement.

Outline of Method

The quantum computer may be physically implemented in arbitrary ways^[2] but the common apparatus considered to date features a Mach–Zehnder interferometer. The quantum computer is set in a superposition of "not running" and "running" states by means such as the Quantum Zeno Effect. Those state histories are quantum interfered. 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. Measuring that value allows for learning the result of some types of computations^[3] such as Grover's algorithm even though the result was derived from the non-running state of the quantum computer.

Definition

The original formulation^[1] of Counterfactual Quantum Computation stated that a set m of measurement outcomes is a counterfactual outcome if (1) there is only one history associated to m and that history contains only "off" (non-running) states, and (2) there is only a single possible computational output associated to m.

A refined definition^[4] of counterfactual computation expressed in procedures and conditions is: (i) Identify and label all histories (quantum paths), with as many labels as needed, which lead to the same set m of measurement outcomes, and (ii) coherently superpose all possible histories. (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.

Experimental Demonstration

In 2015, Counterfactual Quantum Computation was demonstrated in the experimental context of "spins of a negatively charged Nitrogen-vacancy color center in a diamond".^[5] Previously suspected limits of efficiency were exceeded, achieving counterfactual computational efficiency of 85% with the higher efficiency foreseen in principle.^[6]

References

1 2 Mitchison, Graeme; Jozsa, Richard (May 8, 2001). "Counterfactual computation". Proceedings of Royal Society London A 457: 1175–1193. doi:10.1098/rspa.2000.0714.
↑ Hosten, Onur; Rakher, Matthew T.; Barreiro, Julio T.; Peters, Nicholas A.; Kwiat, Paul G. (December 14, 2005). "Counterfactual quantum computation through quantum interrogation". Nature 439: 949–952. doi:10.1038/nature04523.
↑ Mitchison, Graeme; Jozsa, Richard (February 1, 2008). "The limits of counterfactual computation". arXiv:quant-ph/0606092.
↑ Hosten, Onur; Rakher, Matthew T.; Barreiro, Julio T.; Peters, Nicholas A.; Kwiat, Paul (Jun 26, 2006). "Counterfactual computation revisited". arXiv:quant-ph/0607101.
↑ Kong, Fei; Ju, Chenyong; Huang, Pu; Wang, Pengfei; Kong, Xi; Shi, Fazhan; Jiang, Liang; Du, Jiangfeng (August 21, 2015). "Experimental Realization of High-Efficiency Counterfactual Computation". Physical Review Letters 115 (8): 080501. doi:10.1103/PhysRevLett.115.080501.
↑ Zyga, Lisa. "Quantum computer that 'computes without running' sets efficiency record". Phys.org. Omicron Technology Limited. Retrieved 6 September 2015.

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