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/