Apr 26
continue discussion of quantum computing
Anything struck you while looking at the
references I posted Tues?
(What follows is again from "Classical & Quantum Information" book, Marinescu Feb 2011.)
quantum computer operations are in parallel
example1: fast fourier transform,
- operate on all samples at once
- classical O(N log(N)) becomes O(log(N))
- do various exp(i pi/n) "phase rotations" on entire subsets of the list of numbers at once
example2: "Grover Search Algorithm" :
- start with initial state where all states are equally likely
- rotate/transform wavefunction in direction of desired final state(s)
- in small increments, sequentially
- final state has all probability in what you're looking for
- using some property of the desired final state(s)
error correction
Classical : (0,1) => (000, 111) redundancy
error flips one bit
correct by finding nearby legal state
Quantum : a|0> + b|1> => a|000> + b|111>
error is small "rotation" away from that state
correct by "partial collapse" back without measuring a,b
building one
Need
- low decoherence
- quantum logic operations
- "adiabatic" (i.e. slow, non-measuring) physical transforms
- scalable to large numbers of qubits
1. cold ion traps
- cold => little thermal modification
- ion => keep in one spot with magnetic fields
- interact with electrons/ions & coupled states via lasers
- scales with more ions & localization wells
- First CNOT quantum logic gate, 1995, used this sort of apparatus.
2. liquid-state NMR
- spin 1/2 nuclei ; Zeeman energy level split in strong B field
- each molecule is one qubit
- radio pulse interactions with lab scale
- 1st generation, late '90s with up to 7 qubits
3. quantum dots
- solid state nanocrystals in lattice; few thousand atoms
- in semiconductor
- various approaches ; active research field
- interact with applied E & M fields
4. photons only
- can do teleportation
- clean; little decoherence
- popular
5. hybrids
- photos for transport
- something else for storage
