1. Optimal Interesting Quantum Gates with Quantum Dot Qubits David DiVincenzo Spinqubits summer school, Konstanz
Hall Effect Gyrators and Circulators I will begin by explaining the very important role that microwave circulators play in current microwave quantum optics work.  The Faraday-effect circulator was invented in the 1950's, at which time circulators using the Hall effect were also considered.  It was "proved" then that a Hall bar cannot make a good gyrator (a close cousin to the circulator).  This proof is flawed, and we have shown that good gyrators are possible for Hall angle -> 90 degrees (aka "quantum Hall state") if the device is contacted capacitively.  We predict that the resulting Hall circulator can be much more miniaturized than the Faraday kind.  We will discuss the relation of this device functionality to the physics of chiral edge magnetoplasmons in the Hall conductor.
I will give an overview of my work in a team of researchers at IBM on achieving highly coherent two level systems (qubits) in superconducting Josephson-junction devices. I will review the basic phenomenology that makes coherence possible, and discuss the startling progress in reducing decoherence in these systems. I will end with concepts for coupling arrays of qubits coherently to make a fault-tolerant quantum computer.
Should have more of basic circuit theory
Title: Scalable Scheme for Multiqubit Parity Measurement Abstract: Error correction for quantum computation is envisioned to involve local interactions in a two-dimensional structure, with frequent measurement of ancillas to acquire syndrome information.  Since cavities are involved both in mediating the necessary quantum gates and in enabling the measurement, we have investigated how both functions can be accomplished in one step, and how ancilla qubits can be dispensed with.  This single step is non-demolition measurement of a multi-qubit parity.  The measurement is accomplished by using a microwave tone to interrogate the scattering phase shift of a resonant structure with multiple, closely spaced resonant modes, each coupled dispersively to the set of qubits whose parity is to be determined. I will show an explicit concept for an implementation with 3D cavities; almost cubical cavities would give the necessary near-degeneracy of modes. 

2. Sebastian Mehl, PhD 2014, FZ Juelich

3. Virtual fluctuations with real implications:
Not for today…
Poster A38: Michael Hell
Virtual fluctuations with real implications:
Renormalization-induced torques in
spin-qubit control and readout
virtual fluctuations
of quantum
dot electrons
induce torques affecting
the qubit Bloch vector
induce spin torque
→ coherent backaction
→ anomalous spin resonance
source
ferro-
magnet
sensor
quantum dot
quantum
dot
charge / spin
qubit
ferro-
magnet
drain

4. QD Arrays – how can we use them to make effective gates?
Petta, Science (2005)
Shulman, Science (2012)
Medford, Nature (2013)
Higginbotham, PRL (2014)
| DiVincenzo
Title

5. Outline double quantum dots high bias phase gates
how more electrons can be useful
double quantum dots of different sizes
new sweet spot
manipulation with spin-orbit interactions
two-qubit gates for double quantum dots
triple quantum dots
| DiVincenzo

6. DQD: High bias phase gate
singlet-triplet qubit
Levy, PRL (2002)
PRB 88, (2013)
| DiVincenzo

7. DQD: High bias phase gate
singlet-triplet qubit
Levy, PRL (2002)
exchange interaction, low bias
magnetic field gradient
PRB 88, (2013)
| DiVincenzo

8. DQD: High bias phase gate
Pauli spin blockade
sweet spot
PRB 88, (2013)
| DiVincenzo

9. DQD: High bias phase gate
go deep into (2,0) – triplet using excited state orbital comes into play
sweet spot
| DiVincenzo
PRB 88, (2013)

10. DQD: High bias phase gate
charge noise in leading order:
orbital picture for doubly occupied states:
Can we find ?
PRB 88, (2013)
| DiVincenzo

11. DQD: High bias phase gate
Fock-Darwin states: “atomic” orbitals for quantum dots
For Fock-Darwin conditions (circular, harmonic dot) L orbitals are complex conjugates of one another.
Story is more complicated for any other shell.
PRB 88, (2013)
| DiVincenzo

12. DQD: High bias phase gate
Fock-Darwin states: “atomic” orbitals for quantum dots
4 electron configuration has unique charge density, independent of spin
use
(3,3) <-> (4,2)
instead of
(1,1) <-> (2,1)
PRB 88, (2013)
| DiVincenzo

13. 2. Playing with confinement and spin-orbit interaction: finding a different kind of sweet spot

14. DQDs of different sizes
Different kind of sweet spot?
Can we get rid of ?
arXiv
| DiVincenzo

15. DQDs of different sizes
(l0=20nm vs. 100nm)
Different kind of sweet spot?
singlet-triplet inversion:
strongly confined QD favors singlet
weakly confined QD favors triplet
degeneracy of singlet and triplet
in (1,1)
sweet spot?
arXiv
| DiVincenzo

16. DQDs of different sizes
is sufficient to operate a STQ at the sweet spot
Also spin-orbit interactions do it!
Estimate:
ΔSO=25 MHz (GaAs), 250MHz (InAs)
arXiv
| DiVincenzo

17. 3. Achieving longer-ranged coupling for two-qubit gates “Conventional” ST qubit, but with new type of coupler

18. Entangling operation of STQs
single quantum state couples QD2 and QD3
empty/doubly occupied: (super) exchange
singly occupied: exchange
PRB 90, (2014)
| DiVincenzo

19. Entangling operation of STQs
empty/doubly occupied: (super) exchange
note: works also for direct exchange between QD2 and QD3
PRB 90, (2014)
| DiVincenzo

20. Entangling operation of STQs
singly occupied: exchange
PRB 90, (2014)
| DiVincenzo

21. Entangling operation of STQs
excellent control:
exchange interaction can be controlled
with independent gate at QS
magnetic fields at QD1 and QD4 do not matter
noise discussion, cf. paper
PRB 90, (2014)
| DiVincenzo

22. Entangling operation of STQs
more complicated gates for
e.g. for (1,1,0,1,1) and (1,1,2,1,1):
PRB 90, (2014)
| DiVincenzo

23. Outline double quantum dots high bias phase gates
how more electrons can be useful
double quantum dots of different sizes
new sweet spot
manipulation with spin-orbit interactions
two-qubit gates for double quantum dots
triple quantum dots
| DiVincenzo

24. Triple Quantum Dot Qubit
exchange-only qubit
theory: DiVincenzo, Nature (2000)
experiment: Medford, Nature (2013)
Noise discussion:
PRB 87, (2013)
| DiVincenzo
Title

25. Triple Quantum Dot Qubit
exchange-only qubit
PRB 87, (2013)
| DiVincenzo
Title

26. Triple Quantum Dot Qubit
exchange-only qubit
PRB 87, (2013)
| DiVincenzo
Title

27. Triple Quantum Dot Qubit
exchange-only qubit
PRB 87, (2013)
| DiVincenzo
Title

28. Triple Quantum Dot Qubit
Fidelity:
Qubit encoding in
all other states have different quantum numbers
decoherence free subspace
But:
dominant noise channels are local
e.g. hyperfine interactions
PRB 87, (2013)
| DiVincenzo
Title