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LPS Quantum computing lunchtime seminar
Friday Oct. 22, 1999
Things necessary for a spin quantum computer:
1. Single spin operations (Q NOT)
2. Two spin operations (Q CNOT)
3. Single spin preparation and detection
:
:
Main Ideas of Vrijen/Yablonovitch:
Do electron spin quantum computing in SiGe
1. Band structure engineering for large g tunability:
fast NOT operations (1 GHz).
2. Use exchange interaction for CNOT operation:
SiGe alloys can have low effective mass so
interaction can occur over large distances
(>1000 Å).
3. Use Standard FET for spin readout
Sixfold
degenerate
Fourfold
degenerate
Single qubit operations
GHz operation
I don’t know
how this curve
was calculated
Two qubit operations
Single spin measurement using substrate FET’s
Donor deposition by ion implantation
Problems with single spin operations
Phase errors in a voltage controlled oscillator

V
 t 
V0
V1
V1
V
V
V0
t
t
For Frequency Independent (white) Noise:
2 = 2 2 t SV
( SV = Volts2 /Hz )
Time it takes to effect a -pulse:
t = /( V)
So:
2 = 3  SV /V
For a given voltage deviation and noise spectral
density, increasing the VCO tuning parameter 
increases the phase error during a  pulse.
SLOW IS BETTER THAN FAST
z
y
x
VCO picture equivalent to rotation of qubit around z-axis
of Bloch sphere. Also need BAC to effect x and y axis
rotations
BAC
Impediments to imposing a large BAC are primarily
technological, but daunting. Maxwell says:
dB/dt = 109 Tesla/sec  V= 1000V/mm2
In order to make z  x,y
for B=2 Tesla and  =50 GHz:
dB/dt = 3×1011 Tesla/sec !
Much more realistic to make BAC  10-3 - 10-4 BDC
Giving a single qubit operation speed of  10 MHz
What is mean square phase error accumulation rate
in region where single qubit rotation are performed?
r = 2/t = 2 2 SV
d
dV
   1013/Volt-sec
SV= 10-18 V2 /Hz
(A 50  transmission line at room
temperature)
r=1 GHz, 100× faster than the  pulse rate!
But many assumptions have been made.
Almost certainly single qubit
rotations should be performed in
a region in which d/dV is as
small as possible.
Problems with two spin operations
Effect of magnetic field on exchange coupling between
donors
Effect of Magnetic field on electron wave function
2
Log (wave function amplitude)
0
-2
Magnetic confinement
only
(B=2 Tesla, lB=180 Å)
-4
-6
-8
-10
-12
Electrostatic confinement only
(aB=64 Å)
-14
-2000
-1000
0
1000
2000
Distance from donor (Å)
Exchange interaction overestimated by factor of 1013!
Won’t be a problem if B is oriented parallel to line joining
donor sites:
B
But will ruin isotropic coupling between neighbors in
any 2D array:
B
It is unlikely that any quantum computer relying on
the exchange interaction and operating in a magnetic
field can be realized at scales greatly exceeding the
magnetic length.
But more calculations are necessary!
Both of these types of problems will be alleviated by
operating the computer at smaller magnetic fields.
So why operate at B=2 Tesla?
Because this will fully spin polarize electrons when
T= 100 mK.
Electron spin quantum computer would operate much
better if an alternative method for polarizing the electron
spins (optical pumping, ferromagnetic contacts, etc.)
could be introduced.
Or, if spin coupling to lattice is extremely weak, on-chip
refrigeration of spins may be possible!
Problems with single spin measurement
What is charge sensitivity of SET’s and FET’s?
FET: qn  10-1 e/Hz
SET: qn < 10-5 e/Hz
How long do you have to signal average to see 0.1 electron?
FET:  1 sec
SET: < 10-8 sec
The signal averaging time can not exceed the spin
relaxation time of the electron being measured (the
spin must not flip during the measurement!).
In pure unstrained Ge T1 1 millisecond
Conclusion: a conventional FET will not be able to resolve
spin in SiGe. It may be that an optimized semiconductor
nanostructure SET will be able to resolve single spin.
What about leakage between adjacent FET channels?
Effect of Alloy disorder on ESR lines in SiGe
Taken from Feher
Inhomogeneous broadening will not be an issue if
individual spins are addressed with calibrated applied
gate biases.
The broader the lines, however, the more the gates
will need to be tuned, increasing the gate noise
coupling to the spins.
Spin-Valley scattering has not been addressed as
a possible decoherence mechanism!
Sixfold
degenerate
Fourfold
degenerate
Electron spin interactions with donor nuclei
will also be important (unless zero spin donors
or acceptors are used).
Rashba effect: Zero magnetic field spin splitting
induced in materials with large spin orbit interactions
that lack inversion symmetry (interface, E field, etc.)
48
Cd
Problems
1. Big spin orbit coupling for Rashba effect
implies strong coupling of spins to phonons:
T1 will be very short.
2. Is having little magnetic contacts immediately
adjacent to spin qubits a good idea???
Moral:
Systems which permit “easy tuning” of spin
(or qubit) energy levels may not always be a
good thing, since what is tunable is also
susceptible to noise.