Download Executive Summary Last modified October 13

Abdullah Hakmi
ID: 20122
Prof: AC
Quantum computing
MIS 201
Project 3
Sunday, July 19, 2009
Executive Summary:
A quantum computer is a device for computation that makes direct use
of quantum mechanical phenomena, such as superposition and entanglement, to
perform operations on data. The basic principle behind quantum computation is
that quantum properties can be used to represent data and perform operations
on these data.
Introduction:
The massive amount of processing power generated by computer
manufacturers has not yet been able to quench our thirst for speed and
computing capacity. In 1947, American computer engineer Howard Aiken said
that just six electronic digital computers would satisfy the computing needs of
the United States. Others have made similar errant predictions about the
amount of computing power that would support our growing technological
needs1. Of course, Aiken didn't count on the large amounts of data generated by
scientific research, the proliferation of personal computers or the emergence of
the Internet, which have only fueled our need for more, more and more
computing power.
Will we ever have the amount of computing power we need or want? If,
as Moore's Law states, the number of transistors on a microprocessor continues
to double every 18 months, the year 2020 or 2030 will find the circuits on a
1
University of Illinois at Urbana-Champaign
microprocessor measured on an atomic scale. And the logical next step will be
to create quantum computers, which will harness the power of atoms and
molecules to perform memory and processing tasks. Quantum computers have
the potential to perform certain calculations significantly faster than any
silicon-based computer.
Although quantum computing is still in its immaturity, experiments
have been carried out in which quantum computational operations were
executed on a very small number of qubits (quantum binary digits). Both
practical and theoretical research continues with interest, and many national
government and military funding agencies support quantum computing
research to develop quantum computers for both civilian and national security
purposes, such as cryptanalysis.
If large-scale quantum computers can be built, they will be able to solve
certain problems much faster than any of our current classical computers (for
example Shor's algorithm). Quantum computers are different from other
computers such as DNA computers and traditional computers based on
transistors. Some computing architectures such as optical computers may use
classical superposition of electromagnetic waves. Without some specifically
quantum mechanical resources such as entanglement, it is conjectured that an
exponential advantage over classical computers is not possible.
Methodology:
While a classical three-bit state and a quantum three-qubit state are both
eight-dimensional vectors, they are manipulated quite differently for classical
or quantum computation, respectively. For computing in either case, the system
must be initialized, “for example into the all-zeros string, corresponding to the
vector (1,0,0,0,0,0,0,0). In classical randomized computation, the system
evolves according to the application of stochastic matrices, which preserve that
the probabilities add up to one (i.e., preserve the L1 norm). In quantum
computation, on the other hand, allowed operations are unitary matrices, which
are effectively rotations (they preserve that the sum of the squares add up to
one, the Euclidean or L2 norm). (Exactly what unitaries can be applied depend
on the physics of the quantum device.) “2Consequently, since rotations can be
undone by rotating backward, quantum computations are reversible.
Technically, quantum operations can be probabilistic combinations of unitaries,
so quantum computation really does generalize classical computation.
Finally, upon termination of the algorithm, the result needs to be read
off. In the case of a classical computer, it is sampled from the probability
distribution on the three-bit register to get one distinct three-bit string, say 000.
Quantum mechanically measures the three-qubit state, which is equivalent to
collapsing the quantum state down to a classical distribution (with the
coefficients in the classical state being the squared magnitudes of the
Quantum Computing with Molecules" article in Scientific American
by Neil Gershenfeld and Isaac L. Chuang - a generally accessible
overview of quantum computing and so on.
2
coefficients for the quantum state, as described above) 3followed by sampling
from that distribution. Many algorithms will only give the correct answer with
a certain probability, however by repeatedly initializing, running and
measuring the quantum computer, the probability of getting the correct answer
can be increased.
Limitations of the technology:
Scientists have already built basic quantum computers that can perform
certain calculations; but a practical quantum computer is still years away.
Quantum computing is still in theory and this is the main limitation that it has
so far. There are future problems and challenges that are expected to happen if
scientists have reached this technology and wanted to implement it into use.
One of the greatest challenges is controlling or removing decoherence. This
usually means isolating the system from its environment as the slightest
interaction with the external world would cause the system to decohere. This
effect is irreversible, as it is non-unitary, and is usually something that should
be avoided, if not highly controlled. Decoherence times for candidate systems,
in particular the transverse relaxation time T2, typically range between
nanoseconds and seconds at low temperature.
3
M. I. Dyakonov, Université Montpellier (2006-10-14). "Is Fault-Tolerant Quantum
Computation Really Possible?". Retrieved on 2007-02-16.
These issues are more difficult for optical approaches as the timescales
are orders of magnitude lower and an often cited approach to overcoming them
is optical pulse shaping. Error rates are typically proportional to the ratio of
operating time to decoherence time, hence any operation must be completed
much more quickly than the decoherence time.
If the error rate is small enough, it is thought to be possible to use
quantum error correction, which corrects errors due to decoherence, thereby
allowing the total calculation time to be longer than the decoherence time. An
often-cited figure for required error rate in each gate is 10−4. This implies that
each gate must be able to perform its task 10,000 times faster than the
decoherence time of the system.
Meeting this scalability condition is possible for a wide range of
systems. However, the use of error correction brings with it the cost of a
greatly increased number of required qubits. The number required to factor
integers using Shor's algorithm is still polynomial, and thought to be between L
and L2, where L is the number of bits in the number to be factored; error
correction algorithms would inflate this figure by an additional factor of L. For
a 1000-bit number, this implies a need for about 104 qubits without error
correction.
A very different approach to the stability-decoherence problem is to
create a topological quantum computer with anyons, quasi-particles used as
threads and relying on braid theory to form stable logic gates.
Benefits of the technology to the business:
This technology will not only affect business, it will cause to solve so
many of the world’s technical problems, it may even cause new discoveries for
scientists. With this new invention, computers will help businesses to work
more efficiently by speeding up the process of analyzing and transforming
data. It would also open new doors for E-businesses by making it more secure
and efficient.
Conclusion:
In conclusion, quantum computing is just a theory and a concept for the
future of the computer world and technology. Quantum computer could be a
replacement to the technology we now use which is silicon ships. This
invention with its ability to solve complicated algorithm real fast and the ability
to store information and exchange it widely will help scientists to discover new
things.
References
1. Quantum Computing with Molecules" article in Scientific American by
Neil Gershenfeld and Isaac L. Chuang - a generally accessible overview
of quantum computing and so on.
2. Neumann, P.; Mizuochi, N.; Rempp, F.; Hemmer, P.; Watanabe, H.;
Yamasaki, S.; Jacques, V.; Gaebel, T.; et al. (June 6, 2008),
"Multipartite Entanglement Among Single Spins in Diamond", Science
320 (5881): 1326–1329, doi:10.1126/science.1157233, PMID
18535240,
http://www.sciencemag.org/cgi/content/abstract/320/5881/1326
3. http://news.cnet.com/Start-up-demos-quantum-computer/2100-1008_36159152.html
4. University of Illinois at Urbana-Champaign. Quantum computer solves
problem, without running, www.physorg.com/news11087.html
5. M. I. Dyakonov, Université Montpellier (2006-10-14). "Is Fault-Tolerant
Quantum Computation Really Possible?". Retrieved on 2007-02-16.