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Home , Aram Harrow, Elham Kashefi, Quantum sort

Report on the ICTS Programme on Processing 5 December 2007 to 4 January 2008

Name of the programme: Quantum Information Processing

Organisers: Jaikumar Radhakrishnan, School of Technology and Computer Science, TIFR, [email protected] Pranab Sen, School of Technology and Computer Science, TIFR, [email protected].

Duration: 5 December 2007 to 4 January 2008.

Preamble: Quantum information processing is a thriving area of research that at- tempts to recast information processing in the quantum mechanical framework. Several remarkable recent works in this area have challenged our understand- ing of computation and shaken the foundations of well-established areas such as algorithms, complexity theory, and cryptography. Over the last decade, fol- lowing ’s efficient quantum factoring algorithm (1994) and Grover’s quantum search algorithm (1996), several works have consolidated and gener- alised the insights obtained in these early works. In parallel, fundamental issues have been addressed in the area of quantum information theory, entanglement, quantum communication complexity, etc. In 2002, TIFR organised a very successful successful event on a similar subject under the title Quantum Physics and Information Processing. Several developments have taken place in the area Quantum Information Pro- cessing in recent years. The purpose of the present program was to get the re- searchers in India, and TIFR in particular, acquainted with these developments.

Structure of the program: The program was split between two locations: TIFR, Mum- bai, and India International Centre, New Delhi. We invited (to TIFR) experts who had made significant recent contributions, especially in areas where there is strong interest in TIFR, e.g. Quantum Information Theory, Quantum Algo- rithms, Quantum Communication Complexity, Quantum Interactive Proof Sys- tem, Quantum Lower Bounds. In addition, we organised a workshop in New Delhi. This workshop called QIP 2008, was the eleventh in the series of QIP workshops. This event will feature ten invited talks showcasing the most significant work in the area in the last year. The detailed program of the workshop is attached.

Pedagogical lecture courses: To set the stage and acquaint students with the area, two tutorials were included in the beginning of the QIP 2008 Workshop in New Delhi.

• Ronald de Wolf, CWI Amsterdam, Quantum computation and Shor’s fac- toring algorithm (tutorial). • Scott Aaronson, An invitation to quantum complexity theory (tutorial). Seminar speakers (at TIFR): The following experts visited TIFR in this period, in- teracted with members of the STCS faculty and gave talks.

1. Ronald de Wolf, CWI Amsterdam (5 Dec to 11 Dec 2007). Seminar: Fault-tolerant data structures (10 Dec 2007) 2. Avi Ben-Aroya, Tel-Aviv University (23 Dec to 25 Dec 2007) Seminar: Quantum expanders (24 Dec 2007) 3. Frederic Magniez, LRI Orsay (22 Dec to 28 Dec 2007) 4. Rahul Jain, University of Waterloo (23 Dec 2007 to 4 Jan 2008) Seminar: Direct-product theorems in quantum communication complexity 5. Hartmut Klauck, University of Frankfurt (23 Dec 2007 to 4 Jan 2008)

Highlighted works The steering committee of the workshop selected ten works speak- ers whose works most influenced the field in the last year. The list of invited talks appears as part of the attached program. We have noted here some of the most striking presentations.

1. Andris Ambainis, University of Latvia and University of Waterloo. Prof Ambainis is the originator of several striking ideas in quantum algorithms and lower bounds. In his prolific career, he has made several signifi- cant breakthroughs in these areas. He is a co-author of the paper Every NAND formula of size N can be evaluated in time N 1/2+o(1) on a quantum computer Authors: Andris Ambainis (Waterloo), Andrew M. Childs (Cal- tech), Ben W. Reichardt (Caltech), Robert Spalek (UC Berkeley), Shengyu Zhang (Caltech), arXiv:quant-ph/0703015 This is perhaps the most signif- icant work on quantum algorithms in view of the novel techniques used, and it solves a problem that remained open for several years despite a lot of attention. Ambainis spoke about this work at the workshop. In fact, this work was considered so important that the Steering Committee decided to devote two talks to the subject, the other one by Ben Reichardt. 2. Ben Reichardt, Caltech. He is a co-author of the paper on quantum algo- rithms for NAND-formulas. He presented recent extensions of the above mentioned work using a different perspective. 3. Dorit Aharonov, Hebrew University. She is the author of some highly ac- claimed recent results, including the very recent result Polynomial Quan- tum Algorithms for Additive approximations of the Potts model and other Points of the Tutte Plane with Itai Arad, Elad Eban, Zeph Landau. quant- ph/0702008 (February 2007). In this work, she used novel methods based on knot theory in order to give quantum algorithms for highly important problems in discrete mathematics and physics. 4. Patrick Hayden. He recently disproved an important conjecture about quantum channels: The maximal p-norm multiplicativity conjecture is false, arXiv:0707.3291. This is considered to be a breakthrough in quantum in- formation theory. 5. Oded Regev, Tel-Aviv University. He is a leading expert on computational problems on lattices, and quantum and classical interactive proofs. He has

2 several algorithms and lower bounds in both quantum and classical models of computation. He spoke on his fundamental work on “A hypercontractive inequality for matrix-valued functions. 6. Falk Unger, CWI Amsterdam. He is one of the authors of the recent lower bound on fault-tolerance threshold of quantum computation. He is an up- coming young researcher who has also worked on non-locality in quantum information. He spoke at QIP 2008 on his work on fault-tolerance. 7. Renator Renner, Geneva, spoke on Generalized Entropies, and its applica- tions to extracting quantum randomness. Non-speaking participants Please see below for the complete list. Conclusion of the program The ICTS program on Quantum Information Processing was successful in bringing together an outstanding set of researchers and ex- posing the audience to the latest work. The visits to TIFR by these researchers helped in obtaining a deeper understanding of these results and the techniques used in obtaining them. Everybody who attended the events thought highly of the program. We have put together the complete archives of the talks, and hope to make them available through the ICTS: at http://icts.tifr.res.in/sites/QIP-2008 (this site is under preparation but the talks are accessible). We believe the timing of the event did not allow some other scientists to spend longer periods in India, and in future such programs should preferably be organ- ised differently, with greater focus on people spending more time in Mumbai. Regrettably, the participation from Indian researchers in the area was rather low. We had hoped for large student participation (as was the case in QPIP 2003), but that did not happen. More effort must be made in terms of publicity to attract this section to such meets where cutting edge work is being discussed. We are grateful to ICTS for supporting this event.

List of contributed papers accepted for 30 minute talks at QIP 2008

1. Oded Regev and Ben Toner. Simulating Quantum Correlations with Finite Com- munication. 2. Graeme Smith. The private with a symmetric side channel 3. Julia Kempe, Hirotada Kobayashi, Keiji Matsumoto and Thomas Vidick. Using Entanglement in Quantum Multi-Prover Interactive Proofs 4. Gabor Ivanyos, Luc Sanselme and Miklos Santha. An efficient quantum algo- rithm for the hidden subgroup problem in nil-2 groups 5. Andrew Cross, Graeme Smith, John Smolin and Bei Zeng. Codeword Stabilized Quantum Codes 6. Toby Cubitt, Aram Harrow, Debbie Leung, Ashley Montanaro and Andreas Winter. Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0

3 7. Nikhil Bansal, Sergey Bravyi and Barbara Terhal. Classical approximation schemes for the ground-state energy of quantum and classical Ising glasses on planar graphs

8. Simon-Pierre Desrosiers and Frederic Dupuis. Quantum entropic security and approximate quantum encryption

9. Julia Kempe, Oded Regev and Ben Toner. The Unique Games Conjecture with Entangled Provers is False

10. Gilles Brassard, Anne Broadbent, Joseph Fitzsimons, Sebastien Gambs and Alain Tapp Anonymous quantum communication

List of contributed papers accepted for 20 minute talks at QIP 2008

1. Ivan Damgaard, Serge Fehr, Louis Salvail and Christian Schaffner. Secure Iden- tification and QKD in the Bounded-Quantum-Storage Model

2. Jean Christian Boileau, Lana Sheridan, Martin Laforest and Stephen Bartlett. Quantum Reference Frames and the Classification of Rotationally-Invariant Maps

3. Ivan Damgaard, Serge Fehr, Renato Renner, Louis Salvail and Christian Schaffner. A Tight High-Order Entropic Quantum Uncertainty Relation With Applications

4. Stefano Pironio, Antonio Acin, Nicolas Brunner, Nicolas Gisin, Serge Massar and Valerio Scarani. Device-independent security of

5. Stephanie Wehner and Andreas Winter. Higher entropic uncertainty relations for anti-commuting observables

6. Stefano Pironio, Miguel Navascues and Antonio Acin. Quantum probabilities, semidefinite programming, and optimization over Hilbert spaces

7. Zhengfeng Ji, Jianxin Chen, Zhaohui Wei and Mingsheng Ying. The LU-LC conjecture is false

8. Scott Aaronson. Quantum Copy-Protection

9. Julia Kempe, Hirotada Kobayashi, Keiji Matsumoto, Ben Toner and Thomas Vidick. On the Power of Entangled Provers: Immunizing games against entan- glement

10. Daniel E. Browne, Elham Kashefi, Mehdi Mhalla and Simon Perdrix. Deter- minism in Measurement based quantum computation

11. Dan Browne, Matthew Elliot, Steven Flammia, Seth Merkel, Akimasa Miyake and Anthony Short. Phase transition of computational power in the resource states for one-way quantum computation

12. Aram Harrow. Quantum expanders from any classical Cayley graph expander

4 13. Tsuyoshi Ito, Hirotada Kobayashi, Daniel Preda, Xiaoming Sun and Andrew C.- C. Yao. Generalized Tsirelson Inequalities, Commuting-Operator Provers, and Multi-Prover Interactive Proof Systems

14. Keiji Matsumoto. Self-teleportation and its application on LOCC estimation and other tasks

15. Kazuo Iwama, Harumichi Nishimura, Rudy Raymond and Shigeru Yamashita. Unbounded-Error Classical and Quantum Communication Complexity

16. Robert Koenig and Renato Renner. Sampling of min-entropy relative to quan- tum knowledge

17. Matthias Christandl and Ben Toner. De Finetti theorems for finitely exchange- able conditional probability=20 distributions

18. Yi Zhao, Fred Fung, Bing Qi, Christine Chen and Hoi-Kwong Lo. Quantum hacking: experimental demonstration of time-shift attack

19. Julien Degorre, Marc Kaplan, Sophie Laplante and Jeremie Roland. The com- plexity of simulating non-signaling distributions

20. Jonathan Walgate and Andrew Scott. Completely Entangled Random Subspaces

Poster presentations at QIP 2008

1. Jingbo Wang and Brendan Douglas. Graph identification by quantum walks

2. Yasuhiro Takahashi and Noboru Kunihiro. A Fast for Addition with Few

3. Christian Schaffner, Barbara Terhal and Stephanie Wehner. Cryptography from Noisy Quantum Storage

4. Go Kato and Yasuhito Kawano. Quantum Protocols using Quantum Orthog- onal States: “Collapsing Quantum Digital Signatures” and “Quantum Identity Authentication”

5. Amit Bhar, Indrani Chattopadhyay and Debasis Sarkar. A comparative study on measures of pure state entanglement through Incomparability

6. Debasis Sarkar and Indrani Chattopadhyay Incomparability of Pure bipartite states as non-locality beyond Entropy of Entanglement.

7. Ashley Montanaro. Quantum search of partially ordered sets

8. Andre Chailloux and Iordanis Kerenidis. The role of help in Classical and Quan- tum Zero-Knowledge

9. Andre Chailloux and Iordanis Kerenidis. Honest-Verifier Quantum Statistical Zero Knowledge for all Interactive Protocols

5 10. Dan Browne. Efficient classical simulation of the Quantum Fourier Transform

11. Yumi Nakajima, Yasuhito Kawano, Hiroshi Sekigawa, Masaki Nakanishi, Shigeru Yamashita and Yasuhiko Nakashima. Synthesis of quantum circuits for d-level systems using KAK decomposition

12. Charles Hill and Jason Ralph. Control of Two Systems with Hamiltonian Feedback

13. Tathagat Tulsi. Quantum computers can search rapidly by using almost any oracle transformation

14. Joseph Fitzsimons and Jason Twamley. Globally controlled fault-tolerant quan- tum computation

15. Jop Briet and Peter Hoyer. Purification of Non-Stabilizer States

16. Sougato Bose, Abolfazl Bayat, Stefano Mancini and Daniel Burgarth. Spin Chains as with Memory and Antiferromagnets as Channels

17. Somshubhro Bandyopadhyay. Lower bounds and exact entanglement cost in distinguishing orthogonal quantum states by LOCC

18. Donny Cheung, Dmitri Maslov and Simone Severini. Translation Techniques Between Quantum Circuit Architectures

19. Apoorva Patel. Improving Quantum Random Walk Search on a Hypercubic Lattice

20. Shuang Wang, Zheng-fu Han and Guangcan Guo. A novel secure quantum di- rect communication protocol without quantum memory

21. Andrew Scott. Optimizing quantum process tomography with unitary 2-designs

22. Chirag Dhara and ND Hari Dass. Reconstruction of unknown qubit states after measurements

23. Shohini Ghose and Neil Sinclair. Tripartite entanglement and nonlocality in 3- qubit states

24. Phaneendra HD and Shivakumar MS. Quantum Sort: An efficient approach to sort the elements than classical

25. Phaneendra HD and Shivakumar MS. Quantum Traveling: An efficient approach for solving Traveling salesman problem

26. Vidya Raj Chitradurga and Shivakumar MS. Quantum framework for graph iso- morphism problem

27. Toshiki Ide. Accidental cloning of a single photon qubit in two-channel continuous- variable

28. Francois Le Gall and Yoshifumi Inui. Quantum Property Testing of Group Solv- ability

6 29. Brendan Douglas and Jingbo Wang. Efficient implementation of quantum walks

30. Aram Harrow and Richard Low. Random Circuits are Approximate 2-designs

31. Anindita Banerjee and Anirban Pathak. Probabilistic model of fault detection in quantum circuits

32. Dong Pyo Chi, Jeong Woon Choi, Taewan Kim, Jeong San Kim and Soojoon Lee. Three-party d-level quantum secret sharing protocol

33. Vidya Raj Chitradurga and Shivakumar MS. Analysis of fast for hamiltonian circuits

34. Arijit Ghosh, Sudebkumar Pal, Anupam Prakash and Virendra Singh Shekhawat. Generation of higher order n-CAT states.

35. Akira SaiToh and Robabeh Rahimi. Yet another framework of a quantum non- cooperative game

36. Sebastien Gambs. Quantum learning tasks

Complete list of particpants at the QIP 2008 workshop

Scott Aaronson (MIT), Majid Abedi (Institute for Advanced Studies in Basic Sciences (IASBS)), Siddharth Agarwal (Indian Institute of Technology Delhi), Dorit Aharonov (Hebrew University, Israel), Andris Ambainis (University of Waterloo and University of Latvia), Shreyas B.G. (IIITB, Bangalore), Subramanian Balakrishnan (National In- stitute if Techonology), Anindita Banerjee (Jaypee Institute of Information Technology University, Noida), Kishor Barman (Tata Institute of Fundamental Research, Mumbai), Avraham Ben-Aroya (Tel-Aviv University), Suparna Bhattacharya (Indian Institute of Science), Jean Christian Boileau (University of Toronto), Fernando Brandao (), Dirk Brendel (Frankfurt University), Anne Broadbent (Universit de Montral), Arti Chamoli (Indian Institute of Information Technology Allahabad), In- drani Chattopadhyay (Netaji Subhas Open University), Jianxin Chen (Tsinghua Uni- versity), DongPyo Chi (Seoul National University), Byung-Soo Choi (Ewha Wom- ans University), Jeong Woon Choi (Seoul National University), Matthias Christandl (University of Cambridge), Durga Bhaktavatsala Rao Dasari (Indian Institute of Tech- nology, Kanpur), Neha Dave (UC Berkeley), Ronald de Wolf (CWI), Julien Degorre (Laboratoire d’Informatique de Grenoble), Chirag Dhara (Tata Institute of Fundamen- tal Research), Brendan Douglas (University of Western Australia), Frdric Dupuis (Uni- versit de Montral / McGill University), Chinmoy Dutta (TIFR), Sagarmoy Dutta (IIT Kanpur), Elad Eban (Hebrew University), ghazaleh Erfanianfar (sharif university of technology), Sbastien Gambs (Universit de Montral), Sevag Gharibian (University of Waterloo), Shohini Ghose (Wilfrid Laurier University), Arpita Ghosh (Indian Statisti- cal Institute), Arijit Ghosh (Indian Institute Of Technology,Kharagpur), Jozef Gruska (Faculty of informatics, Masaryk University), Aram Harrow (University of Bristol), Patrick Hayden (Mcgill University), Phaneendra HD (The National Institute of Engi- neering), Charles Hill (University of Liverpool), Jaroslav Hruby (Institute of Physics AV CR), Toshiki Ide (Okayama Institute for Quantum Physics), Tsuyoshi Ito (National

7 Institute of Informatics), Kazuo Iwama (Kyoto University), Rahul Jain (University of Waterloo), Ashok Jallepalli (DA-IICT), Kab Gyun Jeong (Seoul National University), Zhengfeng Ji (LCS, ISCAS), Elham Kashefi (Laboratoire d’Informatique de Greno- ble), Go Kato (NTT Communication Science Laboratories, NTT Corporation), Li Ke (Key Laboratory of Quantum Information, USTC, China), Azadeh Keivani (Sharif University of Technology), Viv Kendon (University of Leeds), Sreyash Kenkre (IIT Bombay), Iordanis Kerenidis (CNRS - Univ. Paris-Sud), Faraz Khan (Indian Insti- tute of Technology Delhi), Taewan Kim (Seoul National University, Korea), Hartmut Klauck (Institut Informatik), Robert Koenig (Caltech), Atul Kumar (Indian Institute of Technology Madras, Chennai), Anand L (IIT Delhi), Sophie Laplante (LRI, Univer- sit Paris-Sud XI), Francois Le Gall (ERATO-SORST, Japan Science and Technology Agency), Hoi-Kwong Lo (University of Toronto), Richard Low (University of Bris- tol), Chandrashekar Madaiah (Institute for ), Frederic Magniez (Univ Paris-Sud, CNRS), Kaplan Marc (LRI, Universit Paris-Sud 11), Shubham Mit- tal (Indian Institute of Technology, Delhi), Ashley Montanaro (University of Bristol), Sourav Mukherjee (IIT Kharagpur), Yumi Nakajima (NTT Communication Science Laboratories), Geetu Narang (Guru Nanak Dev University, Amritsar, Punjab), Haru- michi Nishimura (Osaka Prefecture University), Arindam Pal (IIT Delhi), Alok Kumar Pan (Bose Institute), MV Panduranga Rao (Tata Research Design and Developement Centre), Apoorva Patel (Indian Institute of Science), Simon Perdrix (Oxford University Computing Laboratory), Stefano Pironio (ICFO), Anupam Prakash (IIT Kharagpur), Dr.Ramachandra Pujeri (PSG Colege of Technology), Srikanth Radhakrishna (Poor- naprajna Institute of Scientific Research), Jaikumar Radhakrishnan (Tata Institute of Fundamental Research), KS Raghunathan (-), Vidya Raj (The National Institute of Engineering), Oded Regev (Tel-Aviv University), Benjamin Reichardt (California In- stitute of Technology), Renato Renner (ETH, Zurich), Jrmie Roland (UC Berkeley), Pranaw Rungta (Poornaprajna Institute of Scientific Research), Akira SaiToh (Osaka University), Sina Salek (University of ), Luc Sanselme (LRI), Miklos Santha (CNRS, Univ. Paris-Sud), Debasis Sarkar (University of Calcutta), Jayalal Sarma (In- stitute of Mathematical Sciences), Or Sattath (Hebrew University, Jerusalem, Israel), Christian Schaffner (CWI Amsterdam), Andrew Scott (Griffith University), Pranab Sen (Tata Institute of Fundamental Research, Mumbai), Ritabrata Sengupta (Indian Institute of Technology Madras), Sitansh Sharma (International Institute of informa- tion technology), Ankit Sharma (Indian Institute of Technology Kanpur, India), Naresh Sharma (TIFR), Daniel Shepherd (Bristol University), Mayank Singhal (TCS), Agnis Skuskovniks (University of Latvia), Mahesh T S (Indian Institute of Science Educa- tion and Research), Yasuhiro Takahashi (NTT Communication Science Laboratories), Alain Tapp (Universite de Montreal), Barbara Terhal (IBM), Ben Toner (CWI), Mozh- gan Torabifard (Sharif University of Technology), Pushkar Tripathi (Indian Institute of Technology, Delhi), Tathagat Tulsi (Indian Institute of Science), Falk Unger (CWI), Sarvagya Upadhyay (University of Waterloo), Pranav Kumar Vasishta (International Institute of Information Technology, Hyderabad), Umesh Vazirani (UC Berkeley), Thomas Vidick (UC Berkeley), MURALIDHARA VN (IIT Delhi), Jonathan Walgate (Perimeter Institute), Jingbo Wang (The University of Western Australia), Stephanie Wehner (CWI), Andreas Winter (University of Bristol), Michael Marc Wolf (MPQ germany), Agnese Zalcmane (University of Latvia), Yi Zhao (University of Toronto)

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