LPS Quantum computing lunchtime seminarFriday 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 : :

~200 Å

“A Silicon-based nuclear spinquantum computer”

B. E. Kane, Nature, May 14, 1998

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

I don’t knowhow this curvewas calculated

GHz operation

Single qubit operations

Two qubit operations

Single spin measurement using substrate FET’s

Donor deposition by ion implantation

Problems with single spin operations

V

Phase errors in a voltage controlled oscillator

V0 V1

V

t

t t

V

V0

V1

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 spectraldensity, increasing the VCO tuning parameter increases the phase error during a pulse.

SLOW IS BETTER THAN FAST

x

z

y

VCO picture equivalent to rotation of qubit around z-axisof Bloch sphere. Also need BAC to effect x and y axis rotations

BACAC

Impediments to imposing a large BAC AC are primarily are primarily

technological, but daunting. Maxwell says:technological, but daunting. Maxwell says:

dB/dt = 10dB/dt = 109 9 Tesla/sec Tesla/sec V= 1000V/mm V= 1000V/mm22

In order to make z x,y for B=2 Tesla and =50 GHz:

dB/dt = 3×10dB/dt = 3×1011 11 Tesla/sec !Tesla/sec !

Much more realistic to make BAC 10-3 - 10-4 BDC

Giving a single qubit operation speed of 10 MHz

dVd 1013/Volt-sec

What is mean square phase error accumulation ratein region where single qubit rotation are performed?

r = 2/t = 2 2 SV

SV= 10-18 V2 /Hz

(A 50 transmission line at roomtemperature)

r=1 GHz, 100× faster than the pulse rate!

But many assumptions have been made.

Almost certainly single qubitrotations should be performed ina region in which d/dV is assmall as possible.

Problems with two spin operations

Effect of magnetic field on exchange coupling betweendonors

-2000 -1000 0 1000 2000

-14

-12

-10

-8

-6

-4

-2

0

2

Magnetic confinement only (B=2 Tesla, lB=180 Å)

Electrostatic confinement only (aB=64 Å)Lo

g (w

ave

func

tion

am

plitu

de)

Distance from donor (Å)

Effect of Magnetic field on electron wave function

Exchange interaction overestimated by factor of 1013!

Won’t be a problem if B is oriented parallel to line joiningdonor sites:

B

But will ruin isotropic coupling between neighbors inany 2D array:

B

It is unlikely that any quantum computer relying onthe exchange interaction and operating in a magneticfield can be realized at scales greatly exceeding themagnetic length.

But more calculations are necessary!

Both of these types of problems will be alleviated byoperating the computer at smaller magnetic fields.

So why operate at B=2 Tesla?

Because this will fully spin polarize electrons whenT= 100 mK.

Electron spin quantum computer would operate muchbetter if an alternative method for polarizing the electronspins (optical pumping, ferromagnetic contacts, etc.)could be introduced.

Or, if spin coupling to lattice is extremely weak, on-chiprefrigeration 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 spinrelaxation time of the electron being measured (thespin must not flip during the measurement!).

In pure unstrained Ge T1 1 millisecond

Conclusion: a conventional FET will not be able to resolvespin in SiGe. It may be that an optimized semiconductornanostructure 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 ifindividual spins are addressed with calibrated appliedgate biases.

The broader the lines, however, the more the gateswill need to be tuned, increasing the gate noisecoupling to the spins.

Sixfold degenerate

Fourfold degenerate

Spin-Valley scattering has not been addressed asa possible decoherence mechanism!

Electron spin interactions with donor nucleiwill also be important (unless zero spin donorsor acceptors are used).

Rashba effect: Zero magnetic field spin splittinginduced in materials with large spin orbit interactionsthat lack inversion symmetry (interface, E field, etc.)

Cd48

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 agood thing, since what is tunable is alsosusceptible to noise.