# (Spring 2017) CS 410/510 - Intro to Quantum Computing

## Course Project

## Instructions

2-3 people group projects. You may choose to do a *literature review*
project or (more exciting) *original research*. For literature review,
you’d read a few papers around a topic, understand the connection of
this topic to the general field of quantum computing as well as the of
various works under this topic. The final outcome would be a *survey*
paper including interesting open problems. For research project,
identify clearly a problem (e.g., designing/improving an algorithm for
a specific task) and let your *creativity* guide you while maintaining
reasonable *precision*! You are not requried to completely solve a
problem (big congrats if you do!).

### Specs

**Proposal**: 1-2 pages consisting of 1) the topic, background, context, motivation; 2) brief summary of the relevant works and core papers to be studied; and 3) a goal you intend to achieve and a plan.**Mid-term report**: ~5 pages. After more reading and group discussion, your mid-term report should have a polished and expanded version of your proposal. You also need to demonstrate the progress you’ve made since the proposal.**Oral presentation**: Each group will have about 20mins to present your project, demonstrating both*breath*and*depth*: you should aim for a clear introdution of your topic with sufficient background and motivation that would**interest**the audience; and then you may choose to explain 1-2 techincal ideas in a little detail. Every group member needs to participate, and your group will be graded by other fellow students. You may give your the presentaion on board or with slides.**Final report**: ~10 pages. This should resemble a real research paper: a short abstract; 2) an introduction that motivates the topic/problem and gives an overview of the entire paper; 3) details including proper preliminary materials (e.g., notations & defintions), explaning some main technical results; and finally 4) further discussion and open questions.**Report format**: single-column, single-space (between lines) format on letter-size paper. LaTeX and BibTeX are highly recommended. Here is a simple [TeX PDF] template. You may follow a suitable 2017 ACM Article Template (e.g.,*ACM Small*format). Many LaTeX and MS word templates are availabe there.

### Timeline

**Week 1 & 2**: forming groups.**Week 3 & 4**: meeting and discussing project ideas.**April 27**: proposal due.**May 18**: mid-term report due.**Week 10**: in-class presentations.**June 15**: final report due.

## Suggested Topics

Also available in (PDF). Feel free to pursue a project not on this list. Good venues to look for inspirations: QIP, Qcrypt and more general TCS conferences (e.g., STOC, FOCS, Crypto).

### Quantum Algorithms

**General survey**[CvD10]*Quantum algorithms for algebraic problems*by Andrew M. Childs, Wim van Dam.**Non-abelian Hidden subgroup probelm**A tough case for HSP, but connected with many interesting problems, e.g., graph isomorphism, and (unique) shortest vector problem critical in lattice-based crypto.**(Generalized) hidden shift problem****High dimensional continuous abelian HSP**. nice generalization and new formalization of HSP on continuous groups with applications in sovling basic number theoretic problems and breaking some lattice crypto.- [EHKS14]
*A Quantum Algorithm for Computing the Unit Group of an Arbitrary Degree Number Field*by Kirsten Eisenträger, Sean Hallgren, Alexei Kitaev and Fang Song. - [BS16]
*Efficient quantum algorithms for computing class groups and solving the principal ideal problem in arbitrary degree number fields*by J. Biasse and F. Song.

- [EHKS14]
**Quantum random walk**. An extension of classical random walk to the quantum setting. It has become a framework for quantum algorithm design that usually achieves polynomial speedup.

### Quantum simulation related algorithms

Original motivation of quantum computers. They are already meaningful and possible on a “small” quantum computer with say 50 clean qubits. Thesre algorithms have wide applications such as machine learning.

- [HHL09]
*Quantum algorithm for solving linear systems of equations*by Aram W. Harrow, Avinatan Hassidim, Seth Lloyd. - [CKS16]
*Quantum linear systems algorithm with exponentially improved dependence on precision*by Andrew M. Childs, Robin Kothari, and Rolando D. Somma. - [BCK15]
*Hamiltonian simulation with nearly optimal dependence on all parameters*by Dominic W. Berry, Andrew M. Childs, and Robin Kothari. - Application in quantum
**machine learning**. ML, of course… but be critical about what you see. **Quantum supremacy**. Recent advances in physical implementation has brought up the hot topic on demonstrating: on a*small*(special-purpose) quantum device, is there a clear quantum speedup for some task, motivated by the goal of overturning the Extended Church-Turing Thesis as confidently as possible.- [AC16]
*Complexity-Theoretic Foundations of Quantum Supremacy Experiments*by S. Aaronson and L. Chen.

- [AC16]

### Quantum Information Theory

- Broad survey on
**Quantum entanglement**[HHHH08]*Quantum entanglement*by R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki. **Quantum error correcting**. We only scratch the surface of QECC in class.**Project idea**: a summary of the genearl error correcting theory and the stablizer formalism, and discussing a particular code (e.g. surface code).**Thoery of quantum fault-tolerant computing**. Fault-tolerance is critical for physical implementation of a quantum computer.**Project idea**: a gerenal overview and explaining some of the key compenents in detail would be suitable for a course project.**Quantum Shannon theory**. It deals with communicating information via noisy channel. Many surprsing and distinct features in the quantum generaliztion.- Quantum information and
**black holes**.

### Quantum Computational Complexity

There is a large body of research that explores abstractly the power and the limits of quantum computing.

**General survey**[W09]*Quantum Computational Complexity*by J. Watrous.- Quantum
**interactive proofs** **Non-local**games. Introduced for the purpose of testing quantum theory, it turns out to be far more influential and connets to many areas such as interactive proofs, operator theory, cryptography, etc.**Hamiltonian Complexity**How difficult is it to determin the ground energy of a physical system?

### Quantum Query & Communication Complexity

- [MW13]
*A Survey of Quantum Property Testing*by Ashley Montanaro, Ronald de Wolf. - [G01]
*Quantum Communication Complexity (A Survey)*by Gilles Brassard. - Separations of classical/quantum complexity
- [ATYY16]
*Exponential Separation of Quantum Communication and Classical Information*by Anurag Anshu, Dave Touchette, Penghui Yao, Nengkun Yu. **Query lower bound**- Polynomial
method. [BBCMW98]
*Quantum Lower Bounds by Polynomials*by R. Beals et al. - Adversarial
method. [A00]
*Quantum lower bounds by quantum arguments*by Andris Ambainis. - [HLS07]
*Negative weights make adversaries stronger*P. Hoyer T. Lee, R. Spalek. - [R09]
*Span programs and quantum query complexity: The general adversary bound is nearly tight for every boolean function*by Ben W. Reichardt.

- Polynomial
method. [BBCMW98]

### Quantum and crypto

**Post-quantum crypto**cope with quantum*codebreakers*- [R04]
*Quantum Computation and Lattice Problems*by Oded Regev. - [Z12]
*How to Construct Quantum Random Functions*by Mark Zhandry. - [Z13]
*Quantum-Secure Message Authentication Codes*by Dan Boneh and Mark Zhandry. - [S14]
*A Note on Quantum Security for Post-Quantum Cryptography*by F. Song. - [HHS11]
*Classical Cryptographic Protocols in a Quantum World*by Sean Hallgren, Adam Smith, Fang Song. - [BDF+11]
*Random Oracles in a Quantum World*, by Dan Boneh et al. - [KLLNP16]
*Breaking Symmetric Cryptosystems using Quantum Period Finding*by Marc Kaplan, Gaëtan Leurent, Anthony Leverrier, María Naya-Plasencia.

- [R04]
**Quantum cryptograpy**equip*codemakers*with quantum information processing**Survey**. [BS15]*Quantum Cryptography Beyond Quantum Key Distribution*by Anne Broadbent, Christian Schaffner.**QKD**[R05]*Security of Quantum Key Distribution*by Renato Renner.- Quantum key exchange a la
**Merkle**[BHK+11]*Merkle Puzzles in a Quantum World*by G. Brassard, P. Hoyer, K. Kalach, M. Kaplan, S. Laplante, L. Salvail. - [BCG+02]
*Authentication of Quantum Messages*by Howard Barnum et al. - Quantum
**Secure Computation**: a nice (a litte dated) talk by Adam Smith. **Quantum Money**[AC12]*Quantum Money from Hidden Subspaces*by Scott Aaronson, Paul Christiano.**Quantum homomorphic encryption**[DSS16]*Quantum homomorphic encryption for polynomial-sized circuits*by Yfke Dulek, Christian Schaffner, Florian Speelman.- [U13]
*Revocable quantum timed-release encryption*by Dominique Unruh.

**Device-independence, randomness amplification**What if your devices for cryptography cannot be trusted (recall what NSA did)? Quantum non-locality enables certified security and a lot many fanscinating tasks.

### Other models of quantum computation

**Adiabetic quantum computation**[AvDK+04]*Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation*by D. Aharonov et al.**Topological quantum computation**[K97]*Fault-tolerant quantum computation by anyons*by A. Yu. Kitaev.**Measurement-based**[RB01]*A One-Way Quantum Computer*by Robert Raussendorf and Hans J. Briegel.- A non-univeral model concerning
**bonson sampling**. [AA11]*The Computational Complexity of Linear Optics*by S. Aaronson and A. Arkhipov. - Qubit is precious, be
conservative. [KL98]
*On the Power of One Bit of Quantum Information*by E. Knill, R. Laflamme.

### Quantum software and logic

- Universal quantum gates. Quantum computer is digital!
- [SHT16]
*ProjectQ: An Open Source Software Framework for Quantum Computing*by Damian S. Steiger, Thomas Häner, Matthias Troyer. More info. on their project website. - [WS14]
*LIQUi|>: A Software Design Architecture and Domain-Specific Language for Quantum Computing*by QuArC @ Microsoft Research. Github. - [GLRSV13]
*Quipper: A Scalable Quantum Programming Language*by A. S. Green et al. Project website. - [PRZ17]
*QWIRE: A Core Language for Quantum Circuits*by Jennifer Paykin Robert Rand Steve Zdancewic. - [YYW17]
*Invariants of Quantum Programs: Characterisations and Generation*by M. Ying, S. Ying and X. Wu.

### Quantum-inspired proofs for classical theorems

The techniques and formalism in quantum information processing have inspired proofs for mathematical theorems that seem to have nothing to do with Quantum.

- [DW11]
*Quantum Proofs for Classical Theorems*by Andrew Drucker, Ronald de Wolf. - [FMP+11]
*Linear vs. “Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds*by S. Fiorini, S. Massar, S. Pokutta, H. R. Tiwary, R. de Wolf. - [A11]
*A Linear-Optical Proof that the Permanent is #P-Hard*by Scott Aaronson.