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International Workshop on Quantum Information Processing
 
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QIP 2010 at

ETH Life

The daily web-journal of ETH Zurich:

"Lifting the big veil"

"Nach dem grossen Schleier lüften"

18.01.2010

QIP 2010 at the

Swiss Radio DRS

Echo der Zeit

from Monday Jan 18, 2010

in German, Link >>

(Real Player recommended)

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pdf files of
Programme Booklet >>
and
Abstracts of all Talks >>

You will receive a hard copy of these files at the registration desk.

Sponsors

Pauli Center for Theoretical Studies

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The Swiss National Science Foundation

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ETH Zurich (Computer Science and Physics Department)

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Quantum Science and Technology

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CQT Singapore

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QAP European Project

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Sandia National Laboratories

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Institute for Quantum Computing

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id Quantique

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On the power of a unique quantum witness

Iordanis Kerenidis, CNRS - LRI, Universite Paris-Sud and CQT Singapore
joint work with Rahul Jain, Greg Kuperberg, Miklos Santha, Or Sattath, and Shengyu Zhang

In a celebrated paper, Valiant and Vazirani raised the question of whether the difficulty of NP-complete problems was due to the wide variation of the number of witnesses of their instances. They gave a strong negative answer by showing that distinguishing between instances having zero or one witnesses is as hard as recognizing NP, under randomized reductions.

We consider the same question in the quantum setting and investigate the possibility of reducing quantum witnesses in the context of the complexity class QMA, the quantum analogue of NP. The natural way to quantify the number of quantum witnesses is the dimension of the witness subspace W in some appropriate Hilbert space H. We present an efficient deterministic procedure that reduces any problem where the dimension d of W is bounded by a polynomial to a problem with a unique quantum witness. The main idea of our reduction is to consider the Alternating subspace of the d-th tensor power of H. Indeed, the intersection of this subspace with the d-th tensor power of H is one-dimensional, and therefore can play the role of the unique quantum witness.

 

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