Courses (click on course titles to access their outlines)
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, T1, T2, 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
Seminars
Olivier Buisson (Néel Institute, Grenoble, France)
Jack Harris (Yale University, USA)
Alexander Korotkov (UC Riverside, USA)
Yasunobu Nakamura (NEC, Japan)
Irfan Siddiqi (UC Berkeley, USA)
Andreas Wallraff (ETH Zurich, Switzerland)
© Design, Graphics and Programming adapted from David Jörg by Benjamin Huard.