et al.

PERSPECTIVES
768
A Start B
Start
Finish X Finish X
Calculating with quantum random walks. (A) A
classical random walk process in which M particles
are initially located in N paths or channels. There is
some probability that a particle will hop to an adjacent
channel at any moment in time. (B) A quantum
random walk process in which the wavelike nature
of each particle spreads out among many channels.
Nonetheless, each particle will be found in a
single channel when its position is measured at the
end of the process, as indicated by the two Xs at the
bottom in this example. The probability of detecting
the photons is proportional to the output of certain
matrix calculations (the permanent) and allows
these calculations to be performed much faster than
with classical algorithms for large N.
The output probability distribution from
a quantum random walk process does not
simply correspond to a sum of the independent
probabilities for the individual particles
even if there is no physical interaction
between the particles (panel B of the
fi gure). The extra interactions arise because
the state of the system must obey the rule
that Ψ(x 1, x 2) = ±Ψ(x 2, x 1) when two indistinguishable
particles are swapped or interchanged.
The plus sign applies to particles
that are known for historical reasons as
bosons, whereas the minus sign applies to
particles known as fermions. Applying this
rule to the wave function produces an effective
attraction between identical bosons and
an effective repulsion between identical fermions.
For example, the probability of fi nding
two identical fermions at the same location
x 1 = x 2 is zero because that corresponds
to Ψ(x 1, x 1) = –Ψ(x 1, x 1). These effects are
commonly referred to as exchange forces,
even though there is no physical interaction
between the particles. Roughly speaking,
the exchange forces provide an effective
interaction that can be used to perform
certain calculations.
Spring et al., Broome et al., and Tillmann
et al. used indistinguishable particles of light
(photons) to implement a quantum random
walk of this kind called boson sampling.
The photons propagated through a series of
conducting channels known as waveguides
that were fabricated on the surface of a chip.
Neighboring channels were coupled to each
other by bringing them sufficiently close
together that a photon had some probability
of hopping to the adjacent waveguide. The
probabilities of detecting the photons in the
various output channels were then measured
with single-photon detectors. It is possible
to fabricate a much larger number of waveguides
on the surface of a chip than were
used in these examples, so full-scale implementations
should be possible in the future.
The probability of detecting a photon
(a boson) in each of the output channels is
proportional to the so-called permanent of
a matrix ( 5). The permanent of an N × N
matrix is defi ned as the sum of all products
of N elements of the matrix chosen in such
a way that each row and column appears
only once. The permanent is similar to the
more familiar determinant aside from the
minus signs that appear in the determinant.
There are effi cient methods for calculating
the determinant of a matrix that use classical
computers, but the best-known classical
algorithm for calculating the permanent
requires an exponentially large number of
computational steps and is not feasible for
large N. The relevant matrices are related
to the coupling coeffi cients between the N
input and output channels, which can be
controlled experimentally.
Experiments of this kind provide a simple
demonstration of the ability of a quantum
system to perform a potentially useful
MOLECULAR BIOLOGY
New Tool for Genome Surgery
John van der Oost
A bacterial system that uses RNA to edit DNA is harnessed for engineering mammalian genomes.
Gene therapy is the holy grail of
human medicine. Many diseases
are caused by a defective gene,
sometimes with a mutation as subtle as a
single-nucleotide variation. Before restoration
of such a mutation in a patient’s
genome can take place, the target nucleotide
sequence has to be cleaved at a single
position, out of 3 billion possibilities.
This degree of precise surgery requires an
enzyme with highly selective target recognition.
Successful editing of eukaryotic
genomes has been accomplished with
DNA nucleases designed to bear a unique
site that binds to a specifi c DNA sequence.
Laboratory of Microbiology, Wageningen University, 6703 HB
Wageningen, Netherlands. E-mail: john.vanderoost@wur.nl
15 FEBRUARY 2013 VOL 339 SCIENCE www.sciencemag.org
Published by AAAS
computation without the need for the quantum
logic operations required for a generalpurpose
quantum computer. For larger values
of N, this approach may eventually provide
the fi rst demonstration of an actual calculation
that can be done faster using quantum techniques
than could be achieved with a classical
computer. In addition, Childs et al. ( 6) have
shown that any calculation can be performed
using quantum random walks if quantum logic
operations ( 7, 8) between the photons are also
included. The combination of these two techniques
may eventually lead to the building of a
full-scale quantum computer.
References
1. J. B. Spring et al., Science 339, 798 (2013);
10.1126/science.1231692.
2. M. A. Broome et al, Science 339, 794 (2013);
10.1126/science.1231440.
3. M. Tillmann et al., http://arxiv.org/abs/1212.2240
(2012).
4. Y. Aharonov, L. Davidovich, N. Zagury, Phys. Rev. A 48,
1687 (1993).
5. S. Aaronson, A. Arkhipov, in Proceedings of ACM Symposium
on the Theory of Computing, STOC (Association for
Computing Machinery, New York, 2011), pp. 333–342,
http://dl.acm.org/citation.cfm?id=1993682.
6. A. M. Childs, D. Gosset, Z. Webb, Science 339, 791
(2013).
7. E. Knill, R. Lafl amme, G. J. Milburn, Nature 409, 46
(2001).
8. T. B. Pittman, M. J. Fitch, B. C. Jacobs, J. D. Franson,
Phys. Rev. A 68, 032316 (2003).
10.1126/science.1234061
A major drawback of these protein-guided
systems to “engineer” genomes, however,
is that each new target sequence requires
laboriously adjusting the specifi city of the
nuclease’s DNA binding site. On pages 819
and 823 of this issue, Cong et al. ( 1) and
Mali et al. ( 2) describe effi cient genome
editing in human cells based on an RNAguided
system.
Upon identifying the exact genomic
target site, an endonuclease will cleave
the DNA. Depending on the nature of the
consequential DNA damage (single-strand
nicks or double-strand breaks) and on the
type of DNA repair system that is activated
in response to the damage (homologous
or nonhomologous recombination), strand
religation may either seamlessly revert to
on February 14, 2013
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