1 / 22

From Atoms to Quantum Computers: the classical and quantum faces of nature

From Atoms to Quantum Computers: the classical and quantum faces of nature. Antonio H. Castro Neto Dartmouth College, November 2003. Newton’s equation: m dx = F d t. 2. 2. Isaac Newton. Particles. Waves. Continuous and Deterministic Universe. Quantum mechanics:

cassandra-mckee
Download Presentation

From Atoms to Quantum Computers: the classical and quantum faces of nature

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. From Atoms to Quantum Computers: the classical and quantum faces of nature Antonio H. Castro Neto Dartmouth College, November 2003

  2. Newton’s equation: m dx = F d t 2 2 Isaac Newton

  3. Particles Waves Continuous and Deterministic Universe

  4. Quantum mechanics: A discrete and probabilistic Universe Erwin Schrödinger

  5. i h dY = H Y d t Y = Y + Y 1 2 2 2 2 |Y| = |Y| + |Y| + Y Y + Y Y 1 2 * * 1 2 2 1 Interference

  6. UP DOWN LINEAR SUPERPOSITION

  7. Where do Classical and Quantum Mechanics meet? Schrödinger's cat Y(Life) Y = Y(Life) + Y(Death) Wavefunction Collapse Y(Death)

  8. Schrödinger's cat: molecular magnets

  9. Two-Level System Classical Particle Quantum Particle

  10. <x(t)> Harmonic Oscillator

  11. Ultra small Oscillators: Nanowires -6 Width ~ 10 human hair Courtesy of P.Mohanty BU

  12. Dissipation Coupling to the environment Damped Harmonic Oscillator

  13. Decoherence Universe: system of interest + environment System of interest: y and y Environment: F , < F | F > = 0 n,m=1,2,3... Decoupled at t=0: Y = (y + y ) F |Y | = |y |+|y | + y y + y y After a time t=t : Y = y F + Y F |Y | = |y |+|y | + y y <F |F > + y y <F |F > 1 2 n n m Pure State U 1 2 n -N 2 2 2 * * t = t e D 0 U 1 2 1 2 2 1 Mixture D U 1 n 2 m 2 2 2 * * Classical Result ! U 1 2 1 2 n m 1 2 m n

  14. Jun Kondo Electron moving in a crystal with Magnetic impurities

  15. Kondo effect Spin Flip Multiple Spin flips <S > z

  16. Don Eigler IBM Scanning Tunneling Microscope

  17. Quantum Computation Classical Computer: deterministic and sequential Factorization of: x = x0 20 + x1 21 + …. = (x0 ,x1 ,x2 ,…xN) Solution: Try all primes from 2 to √x → 2N/2 =eN ln(2)/2 Quantum Computer: probabilistic and non-sequential Basis states: y(x0 ,x1 ,x2 ,…xN) Arbitrary state: Y({yi}) = ∑{xi} c{xi}({yi}) y({xi}) Probability: | c{xi}({yi}) |2 Shor’s algorithm: N3 Exponential explosion! Power law growth

  18. Solid State Quantum Computers _Scalable: large number of qubits _States can be initiated with magnetic fields _Quantum gates: qubits must interact _Qubit specific acess Big challenge: How to make the qubits interact and have little decoherence? Use of low dimensional materials – E. Novais, AHCN cond-mat

  19. Quantum Frustration AHCN, E.Novais,L.Borda,G.Zarand and I. Affleck PRL 91, 096401 (2003) Environment with large spin (classical) S=½ The energy is dissipated into two channels coupled to Sx and Sy . However: [Sx ,Sy ] = i ћ Sz

  20. Conclusions _“There is a lot of room at the bottom” R.Feynman _There is a lot of beauty and basic phenomena. _ Experiments are probing the boarders between classical and quantum realities and also the frontiers of technology. _ New theoretical approaches and ideas are required.

More Related