1. |  Introduction to Quantum Computation Bruce Kane
Foundations and Frontiers in Physics Seminar
November 8, 1999 | 

13. Quantum Logic
Any quantum computation can be reduced to a sequence of 1 and 2 qubit operations:
H|in> = H1 H2 H Hn |in>
Conventional operations: NOT, AND Quantum operations: NOT, CNOT

14. 1. Create state which is a superposition of all possible
Grover’s Algorithm
1. Create state which is a superposition of all possible
phone numbers:
 = (1/n)×(|  + |  + …|  + ...| 
1/n
| 
| 
| 

15. 2. Invert the ‘marked’ state:
Average
3. Invert the wave function about its average value:
Average

16. 4. Repeat Steps 2 and 3 n times:1
| 
Wave function is in the ‘marked’ state with >50% probability!

17. Consensus until 1995: thinking about quantum computation
is entirely an academic exercise.

19. Quantum Error Correction
While the amplitudes of states in a wave function are continuous
variables, measurement outcomes are always discrete:
0 or 1
|> = |0> + |1>
Measurement
To do quantum error correction a computation is performed
on the state which determines the answer to the question:
Has bit #4 (for example) been flipped?
A measurement of the answer must either be ‘yes’ or ‘no’
If ‘no’ do nothing to the state; if yes flip bit #4.
The original quantum state has been restored exactly!

20. Quantum error correction means that ‘perfect’
quantum computation can be performed despite
errors and imperfections in the computer.
Accuracy threshold for continuous quantum
computation  1 error every 10,000 steps.
Consensus in 1999: building a quantum computer may still
be a difficult (or impossible) enterprise, but the issue can only
be resolved by doing experiments on real systems that may
be capable of doing quantum computation.

21. Intel P6
Microprocessor

22. Contention:
Spins in silicon are a strong candidate to be the
qubits in a future quantum computer.
But quantum computing using Josephson junctions
is also being pursued at U. of MD. Talk to Chris
Lobb, Fred Wellstood or Bob Anderson to learn
more.

23. Things necessary for a spin quantum computer:
1. Long lived spin states
2. Single spin operations (Q NOT)
controlled spin interactions with an external field
3. Two spin operations (Q CNOT)
controlled interactions between spins
4. Single spin preparation and detection
controlled interactions with external reservoirs
Ideally, each of these operations would be controlled by
externally applied electric fields on gates of a semiconductor device

26. G. Feher c. 1956 (ENDOR) In Si:P at Temperature (T)=1K:
electron relaxation time (T1 ) = 1 hour
nuclear relaxation time = hours

27. “A Silicon-based nuclear spin
quantum computer”
B. E. Kane, Nature, May 14, 1998
~200 Å

28. SINGLE SPIN OPERATIONS (QUANTUM NOT)

29. TWO SPIN OPERATIONS (QUANTUM CNOT)

30. Scanned Tunneling Microscope
“Bottom up” Nanofabrication
Scanned Tunneling Microscope
Images
Single atom Manipulation
using an STM

31. Ion Implantation of Donors
Taken from Vrijen, Yablonovich et al.

32. SINGLE SPIN MEASUREMENT
Assertion: An effective and rapid means of measuring
single electron spins will rely on effective spin interactions
that are a manifestation of the Pauli Principle, rather than
on detecting a magnetic field generated by the electron spin.

34. SINGLE SPIN MEASUREMENT

36. Single Electron Transistor (SET) Coupled to a
Double Donor Two Electron System
Fast SET’s: Schoelkopf et al. Science 280, 1238 (1998).
Scanned-probe SET’s: Yoo et al. Science 276, 579 (1997).
Quantum Measurements with SET’s:
Shnirman et al. Phys. Rev. B 57, (1998).
“Single spin measurement using
single electron transistors to probe
two electron systems”, B. E. Kane
et al. To be published in PRB
(cond-mat/ )

37. Single electron capacitance measurements
R. Ashoori
Demonstrated Sensitivity of
single electron transistor:
10-4 e/ Hz
10-6 e/ Hz may be possible.

38. Band Edge Profile vs. Depth

39. The current state of experimental
quantum computation.
A quantum computer exceeding the
capabilities of conventional computers
using Shor’s or Grover’s algorithms.

40. Quantum Information:
Physics World, March 1998  (