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

I don’t know how this curve was 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 V0V0 V1V1  V  t  tt V V0V0 V1V1

For Frequency Independent (white) Noise:  2 =  2  2 t S V ( S V = Volts 2 /Hz ) Time it takes to effect a  -pulse: t =  /(   V) So:  2 =  3  S V /  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

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

AC B AC AC are primarily Impediments to imposing a large B AC are primarily technological, but daunting. Maxwell says: dB/dt = 10 9 Tesla/sec  V= 1000V/mm 2 dB/dt = 10 9 Tesla/sec  V= 1000V/mm 2 In order to make  z   x,y for B=2 Tesla and =50 GHz: dB/dt = 3×10 11 Tesla/sec ! Much more realistic to make B AC  B DC Giving a single qubit operation speed of  10 MHz

10 13 /Volt-sec What is mean square phase error accumulation rate in region where single qubit rotation are performed? r =  2 /t =  2  2 S V S V = V 2 /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 Exchange interaction overestimated by factor of  !

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: q n  e/  Hz SET: q n < e/  Hz How long do you have to signal average to see 0.1 electron? FET:  1 sec SET: < 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 T 1  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.

Sixfold degenerate Fourfold degenerate Spin-Valley scattering has not been addressed as a possible decoherence mechanism!

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.)

Cd 48

Problems 1. Big spin orbit coupling for Rashba effect implies strong coupling of spins to phonons: T 1 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.