# QIC 890/891 - Selected Advanced Topics in Quantum Information

Quantum Information and Computing (QIC) 890/891 - Selected Advanced Topics in Quantum Information is not a cross-listed course.

Code QIC 890/891 Spring 2014 Ashwin Nayak Mike & Ophelia Lazaridis Quantum-Nano Centre (QNC) 1201, unless otherwise noted May 5-July 30: Monday, Wednesday 10:00-11:20 July 8-17: Tuesday, Thursday 10:30-11:50

## Prerequisites

The course should be accessible to students who have completed QIC 710 or equivalent, and have sufficient mathematical maturity.

Each module will have an assignment. There will also be a short final assignment on any topic in quantum information (e.g. write a proposal for a future topics course in quantum information). These assignments will form the basis of the final grade.

(90% on module assignments, 10% on final assignment)

QIC 891: Complete 3 modules
QIC 890: Complete 6 modules

## Module 1 - Weak measurements, the two vector formalism and post-selection paradoxes

Instructor: Aharon Brodutch

10:00-11:20 on May 5, 7, 12, 14

Abstract:

We usually think of quantum states evolving from the past to the future. Accordingly we set our boundary conditions in the past and calculate probabilities for future events. Since quantum theory is time symmetric it is possible to include future boundary conditions in our description. In this time symmetric approach the present is described by a two state vector, a past (pre-selected) state evolving forward and a future (post-selected) state evolving backwards. Now questions about the system in the present can lead to seemingly paradoxical results such as a spin without an electron or a single system being in two boxes simultaneously.

Weak measurementsare a natural tool for probing quantum systems in the two state vector formalism since they do not change the relation between future and past events as do  projective measurements. The result of a weak measurement is a weak value - an unbounded complex number that depends on the two state vector.

In these lectures I will derive the formalism and show a number of interesting `paradoxes' that lead to strange weak values. These include the 'three box paradox', 'Hardy's paradox' and the 'Quantum Cheshire cat'. I will also outline the experiments used to verify these paradoxes. Finally I will discuss some of the open problems as well as some of the unexpected applications of weak measurements in optical experiments.

### Lecture Notes:

Module 1 Lecture 1 notes (pdf)

Module 1 Lecture 2 notes (pdf)

Module 1 Lecture 3 notes (pdf)

## Module 2 - Entanglement detection

Instructor: Nathaniel Johnston

10:00-11:20 on May 21, 26 (QNC 1102), 28 (QNC 1102), June 2 (QNC 1102). Note the change in rooms.

Abstract:

Quantum entanglement is one of the most important properties of quantum systems, and is both a necessary and sufficient resource for many quantum information processing tasks. However, determining whether or not a given quantum state is entangled seems to be a very difficult problem. We will investigate the mathematical tools that can be used to prove that a state is entangled (or not entangled) and discuss the effectiveness of these tests. We also focus on techniques for improving these entanglement tests and discuss how to construct states with "weak" entanglement that these criteria can not detect.

### Lecture Notes

Module 2 Lecture notes (pdf)

### Assignment

Module 2 Assignment (pdf)

## Module 3- Tensor networks in Quantum Information (QI)

Instructor: Oliver Buerschaper

10:00-11:20 on June 4 (QNC 1102), 9, 11, 16. Note the change in rooms.

Abstract:

While the Hilbert space associated with a quantum many-body system is vast, most phenomena occurring at low energies can be described extremely accurately by quantum states occupying only a small portion of that space. Tensor networks have proven an invaluable tool for studying such states, both from a conceptual and practical point of view. We will cover matrix product states (MPS) and their relatives in dimensions higher than one in order to get a glimpse of how entanglement, symmetry and topology shape quantum many-body systems at low energies.

### Assignment

Module 3 Assignment (pdf)

## Module 4 - Molecular spins for implementing Quantum Information Processing (QIP)

10:00-11:20 on June 18, 23, 25, July 2

Abstract:

Molecular electron-nuclear spin coupled systems have intrinsic properties important for implementing Quantum Information Processing (QIP). Nuclear spins with long coherence time play the role of quantum memories. Electron spins bring enhancement of spin polarization. Fast nuclear spin manipulation is possible because of the coupling between electron and nuclear spins. The above advantages are combined with the flexibility offered by synthetic chemistry for designing molecular spin systems for QIP. In these lectures, we learn concepts of experimental skills and tools, in addition to fundamental physics of spin systems. We will cover some interesting examples of implementing algorithmic cooling, non-classical correlation witness and multi-run quantum error correction.

### Assignment

Module 4 Assignment (pdf)

## Module 5 - Quantum Games

Instructor: Zhengfeng Ji

10:00-11:20 on July 7, 9, 14, 16

Abstract:

In this module, we will discuss the theory of quantum nonlocal games, a bridge that connects Bell inequalities and quantum nonlocality on the one hand and quantum multi-prover interactive proofs on the other. We will cover the analysis of several special games, including for example the CHSH game and the magic square game, the Tsirelson's bound for XOR games, and reductions of certain quantum CSPs defined by pseudo-telepathy games. Time permitted, we will briefly introduce the NEXP lower bound for MIP* and some key ingredients of its proof.

### Lecture Notes

Module 5 Lecture 1 notes (pdf)

Module 5 Lecture 2 notes (pdf)

Module 5 Lecture 3 notes (pdf)

Module 5 Lecture 4 notes (pdf)

### Assignment

Module 5 Assignment (pdf)

## Module 6 - Nitrogen Vacancy (NV) centers

Instructor: Osama Moussa

10:30-11:50 on July 8, 10, 15, 17

Abstract:

Negatively charged Nitrogen Vacancy (NV) centers in diamond are model quantum systems with long coherence times, and the ability to initialize and read-out individual centres. This makes them attractive for applications in QIP, magnetometry and magnetic imaging, as well as other sensing technologies. In this four-lecture module, I will elaborate on the previous two sentences in the first and last lectures, respectively, while the two middle lectures will be dedicated to discussing the rich (yet not complicated) spin-physics of the electronic ground manifold of states and the interaction with nuclear spins in the diamond lattice.

### Assignment

Module 6 Assignment (pdf)

## Module 7 - Nanowires in QIP

Instructor: Daryoush Shiri

10:00-11:20 on July 21 (QNC 1102), 23, 28, 30. Note the change in rooms.

Abstract:

Using spin of electron and holes in semiconducting nanowires is another agenda to implement quantum information processing devices. This is actively pursued by investigating group III-V semiconductors, e.g. InSb and InAs which provide strong spin-orbit interaction (SOI)1. Large hole spin relaxation time (T1) of 0.6msec was observed in Si/Ge nanowire systems2 which promises spin qubits free from relaxations due to hyperfine interaction with nuclear spins.

In this module we learn about:

• Writing up the Spin Orbit Interaction (SOI) Hamiltonians in nanowires (for both Rashba and Dresselhaus terms).
• Calculating atomistic and effective mass band structures of nanowires.
• Calculating spin relaxation rates due to (1) D’yakonov-Perel, (2) Elliot-Yafet, (3) Bir-Aronov-Pikus and (4) Hyperfine interaction with nuclear spins.
• Calculating phonon spectrum (dispersion) in nanowires and electron (hole)-phonon scattering rates.

The above mentioned topics help the graduate researcher to computationally investigate his/her observations in the laboratory and follow the state of the art literature in the area of spin qubit implementation in semiconducting nanowires.

### Lecture Notes

Module 7 Lecture notes part 1 (ppt)

Module 7 Lecture notes part 2 (ppt)

Module 7 Lecture notes part 3 (ppt)

Module 7 Lecture notes part 4 (ppt)

Module 7 Lecture notes part 5 (ppt)

Module 7 Lecture notes part 6 (pdf)

### Assignment

Module 7 Assignment (pdf)

1 See Leo Kouwenhoven’s Lab in the Quantum Transport Group at http://kouwenhovenlab.tudelft.nl/
2 See Charles M. Lieber’s group at http://cml.harvard.edu/