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Counterfactual quantum computation through quantum interrogation

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Abstract

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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Acknowledgements

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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Author notes

  1. Matthew T. Rakher

    Present address: Department of Physics, University of California Santa Barbara, Santa Barbara, California, 93106, USA

Authors and Affiliations

  1. Department of Physics, University of Illinois at Urbana-Champaign, Illinois, 61801, Urbana, USA

    Onur Hosten, Matthew T. Rakher, Julio T. Barreiro, Nicholas A. Peters & Paul G. Kwiat

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  1. Onur Hosten
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  2. Matthew T. Rakher
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Correspondence to Onur Hosten.

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Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. 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). https://doi.org/10.1038/nature04523

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