Optimal Interesting Quantum Gates with Quantum Dot Qubits David DiVincenzo 19.8.2014 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. 

Sebastian Mehl, PhD 2014, FZ Juelich

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

QD Arrays – how can we use them to make effective gates? Petta, Science (2005) Shulman, Science (2012) Medford, Nature (2013) Higginbotham, PRL (2014) 18.-21.08.2014 | DiVincenzo Title

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 18.-21.08.2014 | DiVincenzo

DQD: High bias phase gate singlet-triplet qubit Levy, PRL (2002) PRB 88, 161408 (2013) 18.-21.08.2014 | DiVincenzo

DQD: High bias phase gate singlet-triplet qubit Levy, PRL (2002) exchange interaction, low bias magnetic field gradient PRB 88, 161408 (2013) 18.-21.08.2014 | DiVincenzo

DQD: High bias phase gate Pauli spin blockade sweet spot PRB 88, 161408 (2013) 18.-21.08.2014 | DiVincenzo

DQD: High bias phase gate go deep into (2,0) – triplet using excited state orbital comes into play sweet spot 18.-21.08.2014 | DiVincenzo PRB 88, 161408 (2013)

DQD: High bias phase gate charge noise in leading order: orbital picture for doubly occupied states: Can we find ? PRB 88, 161408 (2013) 18.-21.08.2014 | DiVincenzo

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, 161408 (2013) 18.-21.08.2014 | DiVincenzo

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, 161408 (2013) 18.-21.08.2014 | DiVincenzo

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

DQDs of different sizes Different kind of sweet spot? Can we get rid of ? arXiv 1408.1010 18.-21.08.2014 | DiVincenzo

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 1408.1010 18.-21.08.2014 | DiVincenzo

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 1408.1010 18.-21.08.2014 | DiVincenzo

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

Entangling operation of STQs single quantum state couples QD2 and QD3 empty/doubly occupied: (super) exchange singly occupied: exchange PRB 90, 045404 (2014) 18.-21.08.2014 | DiVincenzo

Entangling operation of STQs empty/doubly occupied: (super) exchange note: works also for direct exchange between QD2 and QD3 PRB 90, 045404 (2014) 18.-21.08.2014 | DiVincenzo

Entangling operation of STQs singly occupied: exchange PRB 90, 045404 (2014) 18.-21.08.2014 | DiVincenzo

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, 045404 (2014) 18.-21.08.2014 | DiVincenzo

Entangling operation of STQs more complicated gates for e.g. for (1,1,0,1,1) and (1,1,2,1,1): PRB 90, 045404 (2014) 18.-21.08.2014 | DiVincenzo

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 18.-21.08.2014 | DiVincenzo

Triple Quantum Dot Qubit exchange-only qubit theory: DiVincenzo, Nature (2000) experiment: Medford, Nature (2013) Noise discussion: PRB 87, 195309 (2013) 18.-21.08.2014 | DiVincenzo Title

Triple Quantum Dot Qubit exchange-only qubit PRB 87, 195309 (2013) 18.-21.08.2014 | DiVincenzo Title

Triple Quantum Dot Qubit exchange-only qubit PRB 87, 195309 (2013) 18.-21.08.2014 | DiVincenzo Title

Triple Quantum Dot Qubit exchange-only qubit PRB 87, 195309 (2013) 18.-21.08.2014 | DiVincenzo Title

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, 195309 (2013) 18.-21.08.2014 | DiVincenzo Title