**Rainer Blatt**, University of Innsbruck, Austria

Quantum Information Science: Experimental Implementation with Trapped Ions

- Implementation concepts and basic techniques
- Generics of quantum information processing
- Realization concepts
- Ion trap quantum computer - the basics
- Physics of ion traps
- Ion strings for quantum computation
- Spectroscopy in ion traps
- Laser cooling in ion traps
- Addressing individual ions
- Basic gate operations, composite pulses
- Quantum gate operations and entanglement with ions
- Cirac-Zoller CNOT gate operation with two ions
- Entanglement and Bell state generation
- State tomography
- Process tomography of the CNOT gate
- Tripartite entanglement (W-states, GHZ-states)
- Multipartite entanglement
- Teleportation
- Entanglement Swapping
- Toffoli gate operation
- Advanced procedures, scaling the ion-trap quantum computer
- Mølmer-Sørensen gate operation with ions
- Multi-qubit operations and entanglement decay
- Quantum information toolbox, optimizing operations
- Quantum error correction
- Quantum simulations with trapped ions
- Simulation of the Dirac equation
- Simulation of Klein tunneling
- Scaling the ion trap quantum computer
- Coupling quantum information across distances

**Immanuel Bloch**, MPI Garching, and LMU Munich, Germany

Ultra-cold atom lattices

- Fundamentals of Optical Lattices
- Basics of Ultracold Atoms
- Optical Dipole Potentials
- Optical Lattices Types
- Lattice types
- Spin dependent lattices
- Superlattices
- Engineered tunnel coupling
- Realizing Strongly Correlated Quantum Phases
- Bose Hubbard Model
- Fermi Hubbard Model
- Low Dimensional systems
- Detection Schemes
- Time of Flight Imaging
- Quantum Noise Correlations
- HBT bunching
- HBT antibunching
- Pair correlations
- Quantum Magnetism
- Superexchange Interactions
- Entropy Considerations
- Novel Cooling Schemes
- High Resolution Imaging
- Single Site Imaging
- Temperature & Entropy Determination
- Hidden Non-Local Order
- Coherent Light Scattering
- Engineering Entanglement with Ultracold Atoms
- Controlled Collisions
- Interaction Blockade
- Spin Changing Collisions
- Generation of Minimal Version of Topologically Ordered States
- Single Spin Manipulation
- Single Spin Removal
- Coherent Single Spin Addressing
- Continuous Time Quantum Walks
- Outlook
- Rydberg Atoms
- Polar Molecules

**Isaac Chuang**, MIT, USA

Quantum error correction

- Unraveling models of quantum noise
- Single quantum systems
- Quantum monte-carlo wavefunction: atom + vacuum
- Spontaneous emission and dephasing
- Reversing quantum noise
- The operator sum representation
- Relationship of OSR to master equations
- Simple quantum error correction codes
- Quantum error correction
- Quantum vs. classical coding
- Operator measurement and error syndromes
- Shor's 9 qubit code
- QEC criteria
- Modern quantum codes
- Efficient code families
- Fault tolerant QC
- Quantum Information
- Quantum vs. classical information
- Noiseless coding theorm
- Noisy coding theorem
- Quantum Cryptography
- Quantum key distribution
- Entanglement distillation by QEC
- Quantum privacy amplification

**John Clarke**, UC Berkeley, USA

SQUID Amplifiers

- Introduction and overview
- The resistively shunted junction
- Equations of motion
- Classical noise: the classical Langevin equation
- Quantum noise: the quantum Langevin equation
- Observation of quantum fluctuations
- The dc SQUID
- Equations of motion
- Current-voltage characteristic, flux to voltage transfer function
- Voltage noise, current noise and their cross-correlation
- Low frequency SQUID amplifiers
- Noise temperature
- Optimization & performance
- High frequency SQUID amplifiers: The microstrip SQUID amplifier
- Optimization & performance: The quantum limit
- Parametric solutions for the SQUID amplifier: A new approach
- Applications
- Readout of flux qubits
- The axion detector: A quantum limited amplifier to search for cold dark matter

**Aashish Clerk**, McGill University, Canada

Quantum noise and quantum measurement

- Basics of quantum noise
- Asymmetric quantum-noise spectral densities
- Effective temperature of a non-equilibrium system
- Relation to classical Langevin descriptions
- Fundamental Heisenberg inequality on quantum noise
- Quantum limit on QND qubit detection
- Principle of "no wasted information"
- Relation to conditional measurement theory
- Examples: quantum point contact, Mach-Zender interferometer
- Quantum limit on linear amplification and position detection: "op-amp" mode
- Quantum limit on the noise temperature
- Role of noise correlations
- Concept of "power gain"
- Quantum limit on linear amplification: "scattering" mode
- Caves formulation
- Inequivalence of the two linear-amplifier quantum limits
- Backaction evasion
- Single-quadrature amplification in both op-amp and scattering modes
- Relation to conditional squeezing

**Daniel Esteve**, CEA Saclay, France

Readout of superconducting quantum bits

- Qubit readout: an example of quantum measurement
- Weak versus strong measurement, measurement basis, single shot readout.
- Wish list for qubit readout, readout fidelity and projection fidelity, back action, link between readout signal and back action, minimal back action, non-demolition readout versus destructive readout.
- Qubit readout as a quantum process: qubit state after readout, evolution of the density matrix, measurement operators.
- Partial measurements.
- Readout methods for different sc qubits
- Which physical property for measuring a qubit?
- Overview of readout methods for the different sc qubits.
- Linear dispersive readout of the Cooper Pair Box: principle, performance, back action, perspectives.
- Non-linear dispersive readout of transmon qubits
- Non-linear dispersive readout with the Josephson Bifurcation Amplifier.
- Back action of the non-linear dispersive readout: is readout at the quantum limit?
- Readout of multi qubit circuits: cross talk issue, operation of a two qubit processor fitted with single shot readout.
- Production and characterization of entangled states, violation of Bell inequality, CHSH criterion.
- Readout of multiqubit circuits: implementation of Grover's algorithm in a two qubit processor with single shot readout.
- Perspectives for readout in scalable architectures: multiplexing.

**Steven Girvin**, Yale University, USA

Quantum information processing with superconducting circuits

- Introduction to Quantum Machines
- Why are there so few degrees of freedom in SC circuits?
- Superconducting excitation gap
- Strong Coulomb force

- Brief Introduction to the Quantum to Classical Crossover -- why is it hard to make large objects that are quantum and not classical, and that have simple spectra like atoms?
- Elements of a quantum electrical circuit: L,C,JJ
- Quantization of a lumped-element LC oscillator
- What is a photon? First quantization and second quantization
- Role of circuit admittance Y(ω)
- Distributed element resonators: Box modes and quantizing them using admittance
- Josephson junctions
- Just what is superconductivity anyway?
- How does a Josephson junction JJ work?
- Superconducting Qubits
- Brief survey of different SC qubit topologies and geometries: charge, phase, flux, fluxonium
- Dephasing and decay mechanisms, T
_{1}, T_{2}, sweet spots - Strengths and weaknesses of different qubit designs
- The transmon: World's simplest SC qubit: a JJ and an antenna
- Introduction to Cavity and Circuit QED
- Jaynes-Cummings model for a two-level atom
- Dressed atom/polariton picture
- Vacuum Rabi coupling and degenerate regime
- dispersive regime
- Strong dispersive regime, number splitting
- Weakly anharmonic transmon in a cavity: perturbation expansion in the anharmonicity; α ∼ g
- Input-Output Theory
- Qubit driving via driving cavity
- Quantum noise, dissipation, decay and the Purcell effect
- Linear readout, back action, quantum Zeno
- Non-linear readout methods
- Josephson bifurcation amplifier
- Chirped JBA
- Using the self-non-linearity induced by qubit
- Quantum Control and Algorithms
- Single qubit rotations, Rabi, Ramsey
- Two-qubit entangling operations using conditional phase-shifts
- Qubit-cavity entangling operations in the strong-dispersive regime
- QND measurement of photon number
- Bell/CSHS inequalities
- Grover Search and Deutsch-Josza algorithms on a two-qubit processor
- GHZ/Mermin inequalities
- Towards Quantum Error Correction
- Measurement based QEC
- Non-measurement based QEC
- Towards Scaling up to Many Qubits
- Importance of large on-off coupling ratios
- Houck double transmon
- Multiple-cavity architectures and communication protocols
- Cavities as quantum memories
- Cavities as qubits
- Qubits as switches
- Many-body physics with lattice models for strongly interacting polaritons

**Konrad Lehnert**, University of Colorado, USA

Quantum electromechanics

- Introduction to quantum electro-mechanical and opto-mechanical systems
- The role of mechanical oscillators in measurement science
- Parametric coupling between mechanical oscillators and optical or electrical cavities
- Interferometric measurement of motion
- Inferred noise and quantum back-action of interferometric measurements
- Back-action evading measurements
- Dynamical back-action of parametric coupling: cooling, amplification and feedback
- Mechanical and electrical oscillators in the strong coupling regime

**Hideo Mabuchi**, Stanford University, USA

Quantum feedback

- Overview of concepts and methods
- Goals and domain of real-time estimation and control; major branches
- Quantum input-output models; optical cavity, cQED as canonical examples
- Measurement-based versus coherent feedback control
- Observers/filters and the separation principle
- The Kalman filter and LQG control
- The SSE/SME as quantum filters
- Recursive filtering: continuous observation of open quantum systems
- Retroactive quantum jumps
- Posterior decoding; quantum smoothing?
- The Wonham filter; error-state observer for stabilizer codes
- Risk-sensitive filtering and contingency of the Born rule
- Measurement-feedback quantum control
- Mollow doublet
- Change-point detection
- Continuous quantum error correction as hybrid control
- Linear and nonlinear filter/model reduction
- Concatenated quantum error correcting codes
- Stochastic switching in single-atom cavity QED
- Quantum stochastic differential equations and coherent feedback
- Two cavities example; preview of QEC example
- Quantum Itô calculus
- QSDE model for single-atom cavity QED
- Concatenation and series products
- Bouten-Silberfarb-vanHandel Limit theorem
- Coherent-feedback quantum control
- Photonic switch
- Parity probe
- Autonomous circuit for coherent QEC

**Florian Marquardt**, University of Erlangen-Nuremberg, Germany

Quantum optomechanics

- Introduction: Radiation forces and optomechanical systems
- Basic aspects of the linearized dynamics (readout, optical spring, cooling, amplification)
- Nonlinear classical and quantum dynamics
- Creating and reading out simple nonclassical quantum states of light or mechanical motion
- Optomechanical entanglement
- Fundamental tests of quantum physics using optomechanical systems
- Hybrid systems
- The ultrastrong coupling limit of optomechanics
- Optomechanical multimode setups and arrays

**John Martinis**, University of Santa Barbara, USA

Arbitrary photon state preparation and measurement

- Quantum computation with pictures
- Description of Bloch sphere
- Gates on the Bloch sphere
- Gates with the chevron curve
- Coupled operations, iSWAP and sqrt(iSWAP)
- c-phase gates
- Tofolli gates
- Errors: single qubit and DRAG
- Errors: MOVE operations
- Errors: adiabatic and non-adiabatic requirements
- Quantum Von Neumann experiment
- Generation of arbitrary photon and NOON states
- Fock states
- Arbitrary states
- Wigner Tomography
- Bell states
- Noon states and tomography
- RezQu Archictecture
- Why it's needed for fixed coupling systems
- Basic operations

**Jean-Michel Raimond**, Ecole Normale Superieure de Paris, France

Exploring the quantum world with Rydberg atoms and photons trapped in
cavities

- Ideal photon counting
- A short history of CQED
- Microwave CQED techniques
- Dispersive and resonant interactions, relaxation.
- Absorption-free photon counting and quantum jumps of light.
- Quantum Zeno effect.
- Decoherence
- Photon number states
- Schrödinger cat states
- Resonant cat preparation
- Dispersive cat preparation
- Reconstruction of a cat's life.
- Quantum feedback and perspectives
- On-demand preparation and protection of Fock states
- A quantum feedback experiment.
- Optimal QND measurement.
- Quantum reservoir engineering
- Quantum Zeno dynamics

**Amir Yacoby**, University of Harvard, USA

Two electron spin qubits in GaAs

- Introduction to spin qubits
- Logical spin qubits
- Single electron devices
- Spin to charge conversion
- Single shot readout
- Controlling two electron spin qubits
- Hyperfine interaction and dynamic nuclear polarization
- Nuclear programming
- Single qubit tomography
- Controlling the nuclear environment - Feedback
- Decoupling from the environment
- Nuclear recurrences
- Nuclei as a non Markovian noise
- Extending coherence
- Charge noise
- Two qubit operations
- Two qubit gates
- Dynamically decoupled gates
- Entanglement

© Design, Graphics and Programming adapted from David Jörg by Benjamin Huard.