7,652 research outputs found
Exponential Quantum Speed-ups are Generic
A central problem in quantum computation is to understand which quantum
circuits are useful for exponential speed-ups over classical computation. We
address this question in the setting of query complexity and show that for
almost any sufficiently long quantum circuit one can construct a black-box
problem which is solved by the circuit with a constant number of quantum
queries, but which requires exponentially many classical queries, even if the
classical machine has the ability to postselect.
We prove the result in two steps. In the first, we show that almost any
element of an approximate unitary 3-design is useful to solve a certain
black-box problem efficiently. The problem is based on a recent oracle
construction of Aaronson and gives an exponential separation between quantum
and classical bounded-error with postselection query complexities.
In the second step, which may be of independent interest, we prove that
linear-sized random quantum circuits give an approximate unitary 3-design. The
key ingredient in the proof is a technique from quantum many-body theory to
lower bound the spectral gap of local quantum Hamiltonians.Comment: 24 pages. v2 minor correction
Anderson localization of entangled photons in an integrated quantum walk
Waves fail to propagate in random media. First predicted for quantum
particles in the presence of a disordered potential, Anderson localization has
been observed also in classical acoustics, electromagnetism and optics. Here,
for the first time, we report the observation of Anderson localization of pairs
of entangled photons in a two-particle discrete quantum walk affected by
position dependent disorder. A quantum walk on a disordered lattice is realized
by an integrated array of interferometers fabricated in glass by femtosecond
laser writing. A novel technique is used to introduce a controlled phase shift
into each unit mesh of the network. Polarization entanglement is exploited to
simulate the different symmetries of the two-walker system. We are thus able to
experimentally investigate the genuine effect of (bosonic and fermionic)
statistics in the absence of interaction between the particles. We will show
how different types of randomness and the symmetry of the wave-function affect
the localization of the entangled walkers.Comment: 7 pages, 5 figures, revised version published on Nature Photonics 7,
322-328 (2013
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