Quantum
data compares faster
By
Kimberly Patch,
Technology Research News
Although computers that use quantum particles
like atoms or electrons to represent the ones and zeros of computing are
at least two decades from practical reality, researchers are finding that
quantum computers can theoretically compute exponentially faster than
the fastest possible electronic computer  at least for some tasks.
Researchers from Canada and the Netherlands have found a mathematical
fingerprinting scheme that would allow quantum computers to compare two
sets of data much more efficiently than is possible with the classical
computers we use today.
This quantum fingerprinting scheme increases the list of mathematical
problems that quantum computers would be able to solve much faster than
classical computers. "It gives an example of a fairly natural problem
where quantum communication is exponentially more efficient than classical
communication," said Ronald de Wolf, who was a researcher at the Center
for Mathematics and Computer Science in the Netherlands when the work
was done, but is now at the University of California at Berkeley. Other
examples include factoring large numbers to crack secret codes and searching
large databases.
The fingerprinting scheme could eventually be used to produce efficient
communications among quantum computers, and also in quantum cryptography,
said de Wolf.
Quantum computers use different states of quantum particles like atoms
or electrons to represent the ones and zeros of computing as quantum bits,
or qubits. For example, an electron can be spin up, or spin down in a
way similar to a top which spins either clockwise or counterclockwise.
The fingerprinting scheme essentially allows researchers to make a much
smaller mathematical fingerprint of a set of data. It takes less computing
power and communications bandwidth to work with the fingerprints rather
than the full data sets to, for instance, compare them. The quantum scheme
allows a mathematical fingerprint of a set of data to be more than an
order of magnitude smaller than would be possible using today's classical
computers.
The mathematics involves three steps. First, the data is plotted in an
imaginary, manydimensional space.
Second, the information in the manydimensional space is boiled down,
or fingerprinted, using only a small number of qubits. The number of qubits
needed is equal to the logarithm of the number of dimensions involved.
The logarithm of a number, which is the number of times 10 must be multiplied
together to equal that number, increases very slowly relative to the size
of the number. For example, the logarithm of 10 is 1 and the logarithm
of 100 is 2.
Third, it is possible to test whether two given quantum states are equal,
which allows two data sets plotted and fingerprinted this way to be compared.
"There is no classical analog to the second or third [steps]," making
it impossible for classical computers to do this,just delete" said de
Wolf.
Instead, today's computers require a number of bits equal to the square
root of the number of dimensions, which is a much larger number than the
logarithm. For example, the square root of 10 is 3.16 and the square root
of 100 is 10.
For a 1megabyte set of data, a classical computer fingerprint would require
3,000 bits, while the quantum fingerprint would be only 25 quantum bits
long. The gap widens as the data set grows. For a 1,000gigabyte set of
data, a classical fingerprint would take up 3 million bits, and the quantum
scheme only 45 quantum bits. There are eight bits in one byte of data.
What makes qubits mathematically more flexible has to do with the weird
quantum properties of particles. Rather than simply representing a 1 or
a 0, a qubit is a superposition of both, meaning it has a certain probability
of being a 0 and a certain probability of being a 1. The two possibilities
are complex numbers whose squared values add up to the total of both.
"The point of quantum bits... is that their state can be partly zero and
partly one at the same time. Mathematically... it's this superposition
of things that would exclude each other in the classical world that matters,"
said de Wolf.
What the mathematics boils down to is the quantum fingerprinting scheme
exponentially reduces the amount of communication required for comparing
sets of data, said de Wolf.
For example, if Alice and Bob were on distance spaceships that could not
communicate with each other, but could only send messages to a command
center on earth, in order to compare two large sets of data from Alice
and Bob, the command center would only require Alice and Bob to send the
fingerprints rather than the full data set, de Wolf said.
It's exciting work, said Emanuel Knill, a mathematician at Los Alamos
National Laboratory. It is "one way in which two people with large documents
but limited communication can efficiently determine whether the documents
or the same are not." The work establishes that quantum computing could
be exponentially more efficient in this type of communications than today's
computers, he added.
The researchers could implement the work in the laboratory within a few
years, according to de Wolf. The quantum computers that would use the
scheme, however, are further off. Most researchers agree it will be at
least 20 years before practical quantum computers could be built.
De Wolf's research colleagues were Harry Berman of the University of Amsterdam
and the Center for Mathematics and Computer Science (CWI) in the Netherlands,
and Richard Cleve and John Watrous of the University of Calgary in Canada.
They published the work in Physical Review Letters, September 26, 2001.
The research was funded by the European Union and Natural Sciences and
Engineering Research Council of Canada (NSERC).
Timeline: 3 years, > 20 years
Funding: Government
TRN Categories: Quantum Computing
Story Type: News
Related Elements: Technical paper, "Quantum Fingerprinting,"
Physical Review Letters, September 2001, also posted in the arXiv physics
archive at http://arXiv.org/abs/quantph/0102001.
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January
23, 2002
Page
One
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Quantum data compares
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