Quantum information and optics with superconducting systems
Course information
 Title: 16:750:681 Advanced Topics in Solid State I
 Prerequisites: Phys 501/502: Graduate quantum mechanics or Phys 417: Intermediate Quantum Mechanics or an equivalent course. Contact the instructor if you are worried about your QM background.
 Instructor: Srivatsan Chakram (Vatsan), schakram@physics.rutgers.edu
 Textbooks/Reading Material:
 Quantum Optics/Superconducting circuits
 Exploring the Quantum: Atoms, Cavities, and Photons (Serge Haroche, JeanMichel Raimond)
 Quantum information and optics with Superconducting Circuits (Juan Jose Garcia Ripoll)
 Lecture notes, Theses and Review papers on Superconducting circuits
 Textbooks on superconductivity
 Degennes, Schrieffer, Tinkham
 Simulations
 Quantum Optics/Superconducting circuits
 Class Location: Serin 385E
 Class times: Tuesdays and Fridays, 12:10 PM – 1:30 PM
 Assignments and Grading: Biweekly assignments and a final report/presentation on a contemporary topic in Superconducting Quantum Information.

01:750:681 Advanced Solid State I is a special topics course that will introduce superconducting quantum systems/optics. The first part of the course will provide introduce Quantum optics, Superconductivity, and Superconducting circuits. The latter half of the course will explore quantum information and optics through contemporary experiments in the field, ending with recent developments in quantum error correction.

Module Topic # of lectures 1 Engineered quantum systems 2 2 Primer on Quantum mechanics 2 3 Introduction to Quantum Optics 3.5 4 Primer on Superconductivity 2 5 Quantum electrical circuits 2 6 Superconducting qubits 3 7 Decoherence in Superconducting Qubits, Open Quantum systems 2 8 Circuit Quantum Electrodynamics 2 9 Superconducting Quantum Optics 2 10 Quantum Computing with superconducting qubits 2 11 Quantum error correction 3 Engineered quantum systems
 Introduction
 DiVincenzo Criteria
 Overview of different platforms
 Atoms
 Ions
 Photons controlled by atoms
 Solid state defects
 Superconducting circuits
Primer on Quantum mechanics
 Review of postulates of Quantum Mechanics
 Qubits, Spin 1/2 system, Bloch sphere, Density matrices
 Entanglement, Reduced density matrices, Entanglement entropy
 Quantum measurement
Introduction to Quantum Optics
 Oscillators
 Quantization of fields in the cavity and free space
 Properties of photons, field commutation relations
 Number states, coherent states, squeezed states
 Semiclassical lightmatter interactions
 Coupling a qubit to an oscillator: JaynesCummings model
 Cavity Quantum electrodynamics
 Stimulated and spontaneous emission processes
Primer on superconductivity
 Phenomenology
 BCS theory
 Josephson effect
 Single particle quantum mechanics of the superconducting phase
Quantum electrical circuits
 Quantum LC oscillator
 Charge and phase as conjugate variables
 Circuit quantization
 Transmission lines
Superconducting qubits
 Charge qubits
 Transmon
 Flux qubits/Fluxonium
 Decoherence and Noise in Superconducting Circuits
 Protected qubits, zero pi, current mirror, Bifluxon
Open quantum systems
 Density matrix description
 The Lindblad operator and master equations
 Decay and dephasing in the driven Rabi model
 Ramsey experiments
 T1, Spin echo measurements and Dynamical decoupling
Circuit Quantum Electrodynamics
 Interaction between a superconducting qubit and a microwave resonator
 Protecting a qubit from the continuum, The Purcell effect
 Vacuum Rabi oscillations
 The dispersive limit, dispersive shift, SchriefferWolf transformation
 Concept of coopoperativity
 Quantum Measurements
Quantum optics with superconducting cavities and circuits
 Photon number splitting
 Universal Quantum control of cavity states
 Selective number dependent arbitrary phase (SNAP) gates
 4wave mixing using the nonlinearity of the Josephson Junction.
 Photon Blockade
 Coherent homodyne and heterodyne detection, coherence functions, Wigner tomography
 Generating nonclassical states, Cat States, Fock states
 Cavity gates, CNOT, Beamsplitters
Quantum computing with superconducting qubits
 Fixed frequency versus tunable architectures
 Cavities as a bus between qubits
 Parametric gates
 Cross resonance gate
Quantum error correction
 Errorcorrection with distributed qubits
 Bit flip code
 Laflamme criterion
 Shor/Steane codes
 Surface code
 Quantum error correction of cavity states
 Amplitude damping codes
 Cat codes
 Binomial codes
 GKP codes
 Autonomous error correction

Lecture Dates Topic Notes Module 1 Sep. 6 Course Overview, Introduction to Engineered Quantum Systems Lec 1 notes Module 1 2 Sep. 9 Overview of different physical platforms – Atoms, Ions, Photons, Defect Center, Superconducting qubits, DiVincenzo Criteria Lec2 notes Module 1 3 Sep. 13 Primer on Quantum Mechanics, Quantum states and observables, Qubits, Bloch Spheres, Quantum Measurement, Unitary evolution, Canonical Quantization, Density Matrices Lec3 notes Module 2 4 Sep. 16 Composite Systems, Entanglement, Oscillators, Quantization of fields, Commutation relations, Number States Lec4 Notes Module 2 5 Sep. 20 Coherent States, Phase space representations of an oscillator, Husimi Q function, Wigner functions, Cat states, Squeezed States Lec5 Notes Module 3 6 Sep. 23 Phase space distributions continued, Quantizing electromagnetic fields, Semiclassical lightmatter interactions, Rabi oscillations, Ramsey experiments Lec 6 Notes Module 3 7 Sep. 27 Cavity QED, Jaynes Cummings model, Vacuum Rabi oscillations, Universal control, Dispersive limit of JC model Lec 7 Notes Module 3 8 Sep. 30 QND measurements using the dispersive interaction, Start of Primer on Superconductivity, Superconductivity Phenomenology Lec 8 Notes Module 4 9 Oct. 4 London’s equations, Explaining the Meissner effect, Penetration depth, The isotope effect and role of electronphonon coupling, Cooper instability, Cooper pairs Lec 9 Notes Module 4 10 Oct. 7 BCS theory, Wavefunction, Number and phase as canonical conjugates, Mean field approximation, Bogoliubov Quasiparticles, Gap equation Lec10 Notes Module 4 11 Oct. 10 Ginzburg Landau theory for superfluids and superconductors, Gauge symmetry, Coherence length and penetration depth, Meissner effect, Fluxoid quantization, Josephson effect Lec 11 notes Module 4 12 Oct. 14 Canonical conjugateness of Number/Charge and Phase revisited, More on the Josephson effect, Current Phase relation, AC Josephson effect, Ambegaonkar Baratoff Relation, Introduction to superconducting electrical circuits, LC Oscillator Lec 12 notes Module 4 13 Oct. 21 Lumped circuit elements, Quantum LC Oscillator, Relation between flux and phase, Zero point flux, phase, and voltage fluctuations, Coupled LC oscillators Lec 13 notes Module 5 14 Oct. 28 Circuit networks, Node and Branch variables, SQUIDs and flux periodicity, Generalization of Kirchoff’s laws Module 5 15 Nov. 1 Circuit quantization, Spanning trees and closure branches, Flux in a loop, Method of nodes, Transmission lines Lec 14 and 15 notes Module 5 16 Nov 4 Overview of superconducting qubits, Charge qubits, Inductively shunted qubits, Cooper pair box, Hamiltonian and spectrum, Sensitivity to charge noise, Eliminating charge noise – the transmon Lec 16 notes Module 6 17 Nov. 8 The analogy between a CPB and a quantum Rotor, The Cooper pair box in the phase basis, The transmon, Charge & Phase fluctuations, Connections with Bloch theory, the dependence of wavefunctions on ng, exponential suppression of charge noise dephasing Lec 17 notes Module 6 18 Nov. 11 More on the transmon, insensitivity to charge noise dephasing, Anharmonicity and gate speed, Charge matrix elements, and sensitivity to decay, Tunable transmon Lec 18 notes Module 6 19 Nov. 15 JC model revisited, Vacuum Rabi oscillations, Dispersive limit, Readout, Quantum NonDemolition Measurement using cQED Lec 19 Notes Module 6 20 Nov. 17 The Fluxonium Circuit, Junction array as a superinductor, Fluxonium Hamiltonian, Insensitivity to offset charges, Potential as a function of flux, Fluxons and Plasmons, Spectra, wavefunctions, and transitions, Matrix elements Lec 20 Notes Module 6 21 Nov. 18 Fluxonium contd. Qubit relaxation/decay, Fermi’s golden rule, Qubit connected to an environmental impedance, Quantum limit of Johnson noise, Effect of a finite temperature bath, Detailed balance. Module 7 22 Nov. 22 Sources of qubit decay (capacitive loss, quasiparticles) and dephasing (flux and charge noise), Coherence time versus flux for fluxonium, The Purcell effect Module 7 23 Nov. 29 Open quantum systems, Markovian baths, CPTP maps, The Lindblad Master equation, master equation for qubit decay, measuring decoherence: T1 & Ramsey expts, qubit spectroscopy Lec 23 Notes Module 7 24 Dec. 1 Quantum computing with superconducting qubits, Fixed frequency versus tunable architectures, Cavities as a bus between qubits, Parametric gates, Cross resonance gates, Randomized Benchmarking, Process Tomography 25 Dec 2 Quantum optics with High Q cavities, Control of cavity states with a superconducting qubit, Photon number splitting, SNAP gates, 4wave mixing, Parity measurements, Wigner tomography, Cavity gates – CNOT, Beamsplitter operations, 26 Dec. 6 Errorcorrection with superconducting qubits, Bit flip code, Laflamme criterion, Shor/Steane codes, Surface code, Quantum error correction of cavity states 27 Dec. 9 Course Presentations 28 Dec. 13 Course Presentations