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Quantum Information. Jan Guzowski. From David’s Deutsch weblog: - PowerPoint PPT Presentation
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Quantum InformationJan Guzowski
Universal Quantum Computers are Only
Years AwayFrom David’s Deutsch weblog:
„For a long time my standard answer to the question ‘how long will it be before the first universal quantum computer is built?’ was 'several decades at least’. In fact, I have been saying this for almost exactly two decades … and now I am pleased to report that recent theoretical advances have caused me to conclude that we are within sight of that goal. It may well be achieved within the next decade.
The main discovery that has made the difference is cluster quantum computation, which is a marvellous new way of structuring quantum computations which makes them far easier to implement physically.”
Tuesday, 2005/08/30 - 14:34 BST
Technology of The Future
Nanotechnology: understanding quatnum effects enables further
miniaturization Quantum algorithms:
exponential growth of computational power effective code-breaking complete security of communnication error correction quantum teleportation
Shrinking computer
10-1m ------------------->10-7m Microtechnology reaches quantum limit
Nanocomputer
Transistion from micro to nanotechnology with use of quantum effects
Single-electron transistor (SET)
Nanocomputer
Alternative to transistors: new architecture made up of ‘cells’ (this may be quantum dots)
Nano-scale classical computer
A true quantum computer uses quantum algorithms
A molecule as a physical implementation of qubit
Nanocomputer
Information Theory Information is physical Information is insensitive to exactly
how it is expressed Can have a similar role in physics to
energy and momentum Fundamental question: how the
nature allows or prevents the information to be expressed and manipulated
Maxwell’s Demon (1871)
The demon sets up a pressure difference by only raising the partition when a gas molecule approaches it from the left. This can be done in a completely reversible manner, as long as the demon's memory stores the random results of its observations of the molecules. The demon's memory thus gets hotter. The irreversible step is not the acquisition of information, but the loss of information if the demon later clears its memory.
Turing Machine (1936)
The machine's action on reading a given symbol s depends only on that symbol and the internal state G
The internal construction of the machine specified by a finite fixed list of rules of the form (s,G -> s’, G’,d).
An input `programme' on the tape is transformed by the machine into an output result printed on the tape.
Capable of efficiently simulating all classical computational methods.
Bit ------> qubit 0 or 1------> Quantum algorithm can
incorporate instructions such as „... and now take a superposition of all numbers from the previous operations...”
Quantum Information
10
Computational power 3 qubits describe 8
numbers N qubits describe 2N
numbers We can perform an
operation F simultaneously on 2N N-digit numbers
Computational power grows exponentially
Cryptography Breaking codes becomes possible
with Shor’s quantum algorithm Safety encoding using entanglement
(cloning theorem)
Classical cryptography
The encrypting and decrypting algorithms are publicly announced
The sender and the receiver share a key
Key distribution (classical) allows eavesdropping
Method of public and private key invented (based on difficulty of factorizing large integers)
Shor’s algorithm Shor’s quantum algorithm enables
factorizing large integers in „finite” time (Shor 1994)
Based on quantum Fourier transform (Coppersmith 1994, Deutsch)
Execution time grows as a quadratic function of N
Safety key distribution
Cryptosystem uses quantum entanglement: a pair of correlated particles is generated
An eavesdropper has to detect a particle to read the signal, and retransmit it in order for his presence to remain unknown.
The act of detection destroys quantum correlation ----> no-cloning theorem
Information protected by the laws of physics Complete security of communication
for arbitrary because due tolinearity we have:
No-cloning theorem Assume there exists a machine M such that:
We cannot have
1111
0000
MMR
MMR
10
MMR
MMR 110010
Quantum rerror correction
Based on classical error correction An example: information stored in a qubit
is subjected to random flips (errors) We express by means of a three-qubit
state: After a flip we make two measurments - each one
being a projection onto two state basis:
Result = 00 -----> do nothing Result = 01 -----> flip the rightmost spin etc... State reconstructed
10
10 10
111000
011100110001,101010111000
011100101010,110001111000
111000
Physical Implementation
„Repeat-untill-succes quantum computing using stationary and flying qubits” (Lim, Barret, Beige, Kok, Kwek, 2 Nov 2005)
Based on the idea of one way quantum computer : the entanglement is distributed once for all by preparing an entangled state of all the qubits (cluster state); the logic gates are then applied as sequences of only single-qubit measurements
Stationary qubits: trapped atoms, molecules, ions; quantum dots or defect centers in solids
Flying qubits: photons
Summary New technologies Quantum algorithms Computational power (technical
improvement) Entanglement (effects impossible
without quantum mechanics)