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A Seminar Report on Quantum Computers
ByCH. Anusha
07W01A1205
IV IT
INTRODUCTION
Civilization has advanced as people discovered new
ways of exploiting various physical resources such as
materials, forces and energies. The history of computer
technology has involved a sequence of changes of physical
realization - from gears to relays to valves to transistors to
integrated circuits and so on. Today's advanced lithographic
techniques can squeeze fraction of micron wide logic gates
and wires onto the surface of silicon chips.
what is a 'Quantum Computer'?
A Quantum Computer is a computer that
harnesses the power of atoms and molecules to perform
memory and processing tasks. It has the potential to
perform certain calculations billions of times faster than
any silicon-based computer.
How does a quantum computer work?
In the classical model of a computer, the most
fundamental building block - the bit, can only exist in one of
two distinct states, a '0' or a '1'. In a quantum computer the
rules are changed. Not only can a qubit, exist in the classical
'0' and '1' states, but it can also be in a superposition of both!
In this coherent state, the bit exists as a '0' and a '1' in a
particular manner.
ANALYSIS
Quantum computers are advantageous in the way
they encode a bit, the fundamental unit of information. A
number - 0 or 1, specifies the state of a bit in a classical
digital computer. An n-bit binary word in a typical
computer is accordingly described by a string of n zeros
and ones. A qubit might be represented by an atom in one
of two different states, which can also be denoted as 0 or
1.
CHALLENGES
The current challenge is not to build a full quantum
computer right away but rather to move from the
experiments in which we merely observe quantum
phenomena to experiments in which we can control
these phenomena. This is a first step towards quantum
logic gates and simple quantum networks.
Today's Quantum Computers
Quantum computers could one day replace silicon chips, just like the
transistor once replaced the vacuum tube. But for now, the technology required to
develop such a quantum computer is beyond our reach. Most research in quantum
computing is still very theoretical. The most advanced quantum computers have not
gone beyond manipulating more than 7 qubits, meaning that they are still at the "1 +
1" stage. However, the potential remains that quantum computers one day could
perform, quickly and easily, calculations that are incredibly time-consuming on
conventional computers
BIT Vs QUBITSConsider first a classical computer that operates on a
three-bit register. The state of the computer at any time is a
probability distribution over the 23 = 8 different three-bit strings
000, 001, 010, 011, 100, 101, 110, 111. If it is a deterministic
computer, then it is in exactly one of these states with probability
1.
However, if it is a probabilistic computer, then there is a
possibility of it being in any one of a number of different states.
We can describe this probabilistic state by eight nonnegative
numbers a,b,c,d,e,f,g,h.
The state of a three-qubit quantum computer is similarly
described by an eight-dimensional vector called a ket. However,
instead of adding to one, the sum of the squares of the coefficient
magnitudes, | a | 2 + | b | 2 + ... + | h | 2, must equal one. Moreover,
the coefficients are complex numbers. Since states are represented
by complex wave functions, two states being added together will
undergo interference, which is a key difference between quantum
computing and probabilistic classical computing
OPERATION
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. 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.
POTENTIALInteger factorization is believed to be computationally
infeasible with an ordinary computer for large integers if they are
the product of few prime numbers.By comparison, a quantum
computer could efficiently solve this problem using Shor's algorithm
to find its factors. This ability would allow a quantum computer to
decrypt many of the cryptographic systems in use today, in the sense
that there would be a polynomial time algorithm for solving the
problem. In particular, most of the popular public key ciphers are
based on the difficulty of factoring integers, including forms of
RSA. These are used to protect secure Web pages,
Encrypted email, and many other types of data.
.
DEVELOPMENTS
There are a number of quantum computing candidates,
among those:
Superconductor-based quantum computers
Trapped ion quantum computer
Optical lattices
Topological quantum computer
Quantum dot on surface
Nuclear magnetic resonance on molecules in solution
Solid state NMR Kane quantum computers
queries
RELATION TO COMPUTATIONAL
& COMPLEXITY THEORYThe class of problems that can be efficiently solved by quantum
computers is called BQP, for "bounded error, quantum, polynomial
time".Quantum computers only run probabilistic algorithms, so BQP
on quantum computers is the counterpart of BPP on classical
computers.It is defined solvable with a polynomial-time algorithm,
whose probability of error is bounded away from one half.A
quantum computer is said to "solve" a problem if, for every
instance,its answer will be right with high probability.If that solution
runs in polynomial time,then that problem is in BQP.
ADVANTAGES
Quantum Communication
Quantum Cryptography
Artificial Intelligence
CONCLUSION
Although the future of quantum computing looks promising,
we have only just taken our first steps to actually realizing a
quantum computer.There are many hurdles,which need to be
overcome before we can begin to appreciate the benefits they may
deliver. Researchers around the world are racing to be the first to
achieve a practical system, a task,which some scientists think, is
futile.
BIBLOGRAPHY
http://www.aps.org/units/gqi/newsletters/index.cfm
http://quantum.fis.ucm.es/
http://scienceblogs.com/pontiff/
http://www.scottaaronson.com/blog/