Letter

Nature 439, 949-952 (23 February 2006) | doi:10.1038/nature04523

Counterfactual quantum computation through quantum interrogation

Onur Hosten1, Matthew T. Rakher1,2, Julio T. Barreiro1, Nicholas A. Peters1 and Paul G. Kwiat1

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.

  1. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  2. †Present address: Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA

Correspondence to: Onur Hosten1 Correspondence and requests for materials should be addressed to O.H. (Email: hosten@uiuc.edu).

Received 4 August 2005; Accepted 14 December 2005

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