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Counterfactual quantum computation through quantum interrogation


The logic underlying the coherent nature of quantum information processing often deviates from intuitive reasoning, leading to surprising effects. Counterfactual computation constitutes a striking example: the potential outcome of a quantum computation can be inferred, even if the computer is not run1. Relying on similar arguments to interaction-free measurements2 (or quantum interrogation3), counterfactual computation is accomplished by putting the computer in a superposition of ‘running’ and ‘not running’ states, and then interfering the two histories. Conditional on the as-yet-unknown outcome of the computation, it is sometimes possible to counterfactually infer information about the solution. Here we demonstrate counterfactual computation, implementing Grover's search algorithm with an all-optical approach4. It was believed that the overall probability of such counterfactual inference is intrinsically limited1,5, so that it could not perform better on average than random guesses. However, using a novel ‘chained’ version of the quantum Zeno effect6, we show how to boost the counterfactual inference probability to unity, thereby beating the random guessing limit. Our methods are general and apply to any physical system, as illustrated by a discussion of trapped-ion systems. Finally, we briefly show that, in certain circumstances, counterfactual computation can eliminate errors induced by decoherence.

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Figure 1: An optical realization of counterfactual computation.
Figure 2: Experimentally determined probabilities for the output state of 670-nm single photons conditionally prepared through downconversion17.
Figure 3: Proposed set-up for the ‘chained Zeno effect’.

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  1. Jozsa, R. in Lecture Notes in Computer Science (ed. Williams, C. P.) Vol. 1509, 103–112 (Springer, London, 1998)

    Google Scholar 

  2. Elitzur, A. C. & Vaidman, L. Quantum-mechanical interaction-free measurements. Found. Phys. 23, 987–997 (1993)

    Article  ADS  Google Scholar 

  3. Kwiat, P. G. et al. High-efficiency quantum interrogation measurements via the quantum Zeno effect. Phys. Rev. Lett. 83, 4725–4728 (1999)

    Article  ADS  CAS  Google Scholar 

  4. Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)

    Article  ADS  CAS  Google Scholar 

  5. Mitchison, G. & Jozsa, R. Counterfactual computation. Proc. R. Soc. Lond. A 457, 1175–1193 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  6. Misra, B. & Sudarshan, E. C. G. The Zeno's paradox in quantum theory. J. Math. Phys. 18, 756–763 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  7. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information 248–276 (Cambridge Univ. Press, Cambridge, UK, 2000)

    MATH  Google Scholar 

  8. Kwiat, P. G., Mitchell, J. R., Schwindt, P. D. D. & White, A. G. Grover's search algorithm: an optical approach. J. Mod. Opt. 47, 257–266 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  9. Kwiat, P. G. et al. Interaction-free measurement. Phys. Rev. Lett. 74, 4763–4766 (1995)

    Article  ADS  CAS  Google Scholar 

  10. Franson, J. D., Jacobs, B. C. & Pittman, T. B. Quantum computing using single photons and the Zeno effect. Phys. Rev. A 70, 062302 (2004)

    Article  ADS  Google Scholar 

  11. Rudolph, T. & Grover, L. Quantum searching a classical database (or how we learned to stop worrying and love the bomb). Preprint at (2002).

  12. Dhar, D., Grover, L. K. & Roy, S. M. Preserving quantum states: A Super-Zeno effect. Preprint at (2005).

  13. Viola, L. & Lloyd, S. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733–2744 (1998)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  14. Monroe, C., Meekhof, D. M., King, B. E. & Wineland, D. J. A “Schrodinger Cat” superposition state of an atom. Science 272, 1131–1136 (1996)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  15. Brickman, K. A. et al. Implementation of Grover's quantum search algorithm in a scalable system. Phys. Rev. A 72, 050306 (R) (2005).

  16. Rowe, M. A. et al. Experimental violation of a Bell's inequality with efficient detection. Nature 409, 791–794 (2001)

    Article  ADS  CAS  Google Scholar 

  17. Hong, C. K. & Mandel, L. Experimental realization of a localized one-photon state. Phys. Rev. Lett. 56, 58–60 (1986)

    Article  ADS  CAS  Google Scholar 

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We acknowledge discussions with B. DeMarco, and partial support from the National Science Foundation, Disruptive Technologies Office, and the US Army Research Office.

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Correspondence to Onur Hosten.

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Reprints and permissions information is available at The authors declare no competing financial interests.

Supplementary information

Supplementary Methods

This file contains details on the algorithm and the experimental encoding; the experiment; clarifications; and the high-efficiency qubit-by-qubit-interrogation technique. This file also presents a method to interrogate all database elements simultaneously.

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Hosten, O., Rakher, M., Barreiro, J. et al. Counterfactual quantum computation through quantum interrogation. Nature 439, 949–952 (2006).

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