Gordon Godfrey Workshop on Spins, Topology and Strong Electron Correlations

School of Physics, The University of New South Wales, Sydney, Australia

Program: https://newt.phys.unsw.edu.au/Godfrey/2022/program_oral/

Mark Friesen | Wiggle Well: engineering valley and spin-orbit properties of silicon

wiggle well solves two problems related to scale up
- reliably large valley splitting
- large intrinsic spin-orbit coupling without micromagnets
Valley splitting variations are very large
Valley vs spin qubits
- quantum dot qubits are formed at the very bottom of the conduction band in silicon,
- Note conduction band minimum doesn’t fall within the center of the brillouin zone
- two valleys form - the valley states compete with the spin as a possible qubit. 2x2-fold energy level degeneracy in a quantum well -if the valley splitting is very small, relative to the zeeman splitting then the valley will be the qubit rather than the spin
- Want sharp interfaces and narrow quantum wells to increase the valley splitting but there is still large variability. 0.33nm sharp interface
Shape of the dot changes but not the location
Valley splitting behaviour is fully explained by alloy disorder of random Si-Ge alloying
Variability occurs because the dot samples fluctuations differently at different locations
Concentration fluctuations have a small component of short-period wiggle well

deterministic scheme: find a way to grow the short-period wiggle well
randomly dominated scheme: add uniform Ge to the quantum well and find a way to reposition the dot

Electrically Driven spin resonance with a micromagnet
- fab a micromagnet on top of the dot, drive it electrically
EDSR via spin-orbit coupling (Rashba 1960s)
Experimental suggestion of spin orbit coupling in wiggle well because g-factor is not equal to 2. -sp3d5s theory predicts large enhancements of dresselhaus spin-orbit coupling

wiggle wells exist
enhancing valley splitting
- deterministic strategy short-period WWW
- Randomly dominated strategy: Ge in the quantum well; reposition dot
Enhancing spin-orbit coupling
- deterministic strategy: long-period wiggle well

novel integration
Si MOS
- best for valley splitting , worst for charge noise due to oxide interface and defects
Si/SiGe
- worst for valley splitting, best for charge noise
Interface characterisation via Hall
- can be done at relatively higher T
- fast measurements
- process optimization

Climate forecasting
- sea surface index and a function of years - el nino and la nina
- increase in data - better predictions
quantum information forecasting
- nuclear and electron spin paris with hyperfine coupling
- we know there is fluctuation per hour
- humans can forecast a stable point in the data
- useful to have a theoretical framework to forecast
Increase in data
- 1+ GB data/hour with engineering efforts (low latency FPGA)
- temporally and spatially correlated signals
  - spatially as we are looking at the differences between qubit one and qubit two
- better predictions Environemntal modelling and software
  - lots of literature out there on wavelets so taking inspiration from climate science
Wavelet is a wavepacket localised in time and frequency
A wider wavelet means that the amplitude of the wavelet will be smaller Why wavelets - edge detection
- edge detection for sharp features e.g. readout events or two-level fluctuators robust against 1/f noise
quantum computing
- Variance transformation - correlations in the larmor frequency we see long scale drift which is removed after the variance transformation
Use in quantum computing
- why wavelets - useful for edge detection - we really want to understand the noise in our devices so if we can break down the noise into its frequency components then we can understand the sources of noise.
  - this can also lead to better controled pulses
  - less feedback
  - efficient quantum error correction

as you cool down the devices you see these Coulomb peaks where are beleived to be coming from the vacancy centres

qubit noise is often limiting quantum gate fidleieties and qubit coherence. Charge noise is the issue across the board, even for superconducting qubits
dephasing/longitudinal noise often most dangerous
characterize noise - many methods and results
efficient characterisation needed also in qubit arrays
characterising noise qubit noise - quantum dot ransport flank method, do it by sitting on the flank of a Coulomb noise,
- This doesn’t actually measure the qubit noise though
dynamical decoupling (need high-fidelity issues)
here: cavity QED with general qubit
how to do circuit QED
- Really just need some qubit with energy splitting coupled to a cavity mode
- magnetic field gradient, put a single electron in a double dot

Majorana recipe
- one=dimensional quantum wire
- spin-orbit interaction superconductivity, tune chemical potential and apply magentic field
- induce p wave superconductor with majorana zero modes
How do we measure Majoranas?
Burden of proof:
- why is the gap so soft
- why is the zero bias peak so small?
Soft gap linekd to discorder - majorana signatures mimicked by disorder
- became a materials science problem
Got better materials but didn’t have a better way of measuring
- Non-local conductance measurements - measure the full conductance matrix of the device
- Would give information about the induced gap
Topological gap protocol
- stage 1
  - tune to N=1 subband
  - local conductance shows regions of parameter space with stable ZBPs at each end, do this across many gate voltages
- stage 2
  - non local conductance shows bulk phase transition - gap closing and reopening
Prospects for realiszing majorana machines:
- topological gap 20-30ueV
- need to keep all experiemntal parameters below this
  - temperature
  - readout frequency
- disorder dominates
- Going to be hard to build these devices and scenarios
What can we do?
- Better dielectrics:
- Dit ~0.5e12 (InAs) Dit ~0.1e11 Si/SiGe
- new superconductors Pb, Sn
  - challenging to process due to phase changes
- New semiconductors: Ge/SiGe? PbTe
- More robust measurements

The Innsbruck quantum processor - characteristics