Quantum Computing

David Dvorak

CIS 492

Quantum Computing Overview

• What is it?• How does it work?

– The basics– Clarifying with examples

• Factoring• Quantum Cryptography

• Why should we care?– Societal implications– Bugs to work out– How will it affect the future?

• References

“A quantum computer is to a regular computer, what a laser is to a lightbulb.”

--Seth Lloyd, MIT

One analogy…

What is Quantum Computing?

• Currently, computer chips are filled with gates only fractions of a micron wide

• Gates will move to the atomic level• At an atomic level matter obeys different rules

– Quantum Mechanics– Allows completely new algorithms– Better than cramming more gates on a chip

• Theoretical beginnings in the 80s, experiments in the 90s

The Basics of Quantum Computing

• An atom, not an electron, is the physical bit– An electron is 0 or 1– Quantum mechanics: at atom is 0, 1, or both– “coherent superposition”

• The bit in quantum mechanics is a qubit• What’s the difference?

– n bits can store one of 2n numbers at any time– n qubits can store all 2n numbers at once

The advantage of qubits

• Adding qubits increases storage exponentially

• Can do operations on all superpositions…like parallel computation– One math operation on 2n numbers encoded with

n bits requires 2n steps or 2n parallel processors– The same operation on 2n numbers encoded by n

qubits takes 1 step

• This makes complex problems much easier

Example: Factoring

• Factoring takes longer as digits increase

• Increasing CPU speed only increases calculation linearly, need exponentially

• Factoring 1000 digit number classically would take longer than estimated life of universe

• Quantum computers do this in minutes

• Modeling large complex systems– the brain– the universe

• Can describe an atom with a few bits

• Takes 100 bits to describe atoms interacting

• 2100 or 10100 bits, 1090 particles in whole universe

• Few 100 qubits easily solves this problem

– physics or chemistry

Other uses of Quantum Computing

Cryptography

RSA cryptography relies on the difficulty of factoring large numbers

to be secure…

Quantum Cryptography

• To break RSA a hacker would need a large scale quantum computer (10,000 qubits)

• Quantum computing offers new possibilities for secure communication– “entanglement”– two quantum bits correlated stronger than possible in

regular physics– teleportation– two entangled objects can only be known by their

“owners”…privacy implications

Quantum Cryptography

• Entangled atoms are like keys• Cannot be known to anyone else by laws of

quantum physics– Has transmitted securely over 1km– Bank of England wants to use it locally

• However, transmissions easily interrupted– Denial of service– However, eavesdroppers are easily detected– Can intercept and retransmit, but it will be know

Societal implications

• Has increased thinking, quantum computing opens a world of possibilities

• Common language between the sciences: math, physics, chemistry, computers…

• Thinking of complex problems to solve• Secure communication• Biggest advance yet…changes the way we

think of the universe, ie, Schroedinger’s cat

Kinks to work out

• Must reduce decoherence– Computation spreads beyond local components, effects

other qubits

– Qubits must only interact with themselves, not their environment

• Must control quantum phenomenon• Make quantum computers scalable

– Current quantum computers have 10 or so qubits

– 1000s of qubits would be ideal

The future of quantum computing

• In 100 years quantum computers will be boring– Maybe not in all households, but common– Molecular computers in households?

• Developing better cryptography

• Think up more problems to solve…won’t be able to solve them quite yet

References

• www.qubit.org (Barneco and Ekert)– www.qubit.org/library/intros/comp/comp.html

– www.qubit.org/library/intros/crypt.html

• www.pbs.org (Lloyd, Divincenzo, and Whaley)– www.pbs.org/kcet/closertotruth/transcripts/308_quantu

mcomputers.pdf

– www.pbs.org/kcet/closertotruth/explore/learn_08.html

The End

Questions?