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Below are the abstracts for some of the seminars listed on the "Seminars & Workshops" page. | ||||||||||
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2009 |
| January 20: IST Lunch Bunch Alexei Kitaev 12:00 pm, 74 Jorgensen Title: Topological quantum computation Abstract: To achieve scalability, a quantum computer must tolerate some amount of de-coherence and inaccuracy in the gate implementation. This issue may be addressed by using quantum error-correcting codes, but that only works if the physical gates are sufficiently good. In may talk, I will discuss an alternative approach in which the errors are eliminated at the physical level. The role of the error-correcting code is played by a degenerate ground state of a suitable quantum system cooled to a low temperature. In this scheme, the protection against errors is due to topology. |
| January
20: IQI Seminar Guifre Vidal, University of Queensland 3:00 p.m., 74 Jorgensen Title: Entanglement renormalization: Foundations, status and prospects Abstract: Entanglement Renormalization (ER) is a real space renormalization group transformation for quantum lattice systems [Phys. Rev. Lett. 99, 220405 (2007)]. Its main novelty is the use of disentanglers, namely unitary transformations that act across a spin block boundary, to remove short range entanglement from the system. The related Multi-scale Entanglement Renormalization Ansatz (MERA) is the basis of simulation algorithms for lattice systems. In this talk I will review the basic concepts underlaying ER and MERA and present a summary of the most recent results: characterization of quantum critical phenomena and simulation of 2D frustrated antiferromagnets that cannot be addressed with Monte Carlo sampling techniques. |
| January
21: IQI Group Meeting Stephen Bartlett, University of Sydney 5:30 p.m., 156 Jorgensen Title: Identifying phases that are universal for measurement-based quantum computation Abstract: The cluster state can be viewed as the ground state of a quantum many-body system, and this perspective may lead to some potential physical realizations. It would be unfortunate, however, if the usefulness of a ground or low-temperature thermal state for quantum computation was critically dependent on the details of the system's Hamiltonian. A much more powerful result would be the existence of a robust ordered phase which is characterized by the ability to perform measurement-based quantum computation. Using some simple toy models, we investigate the existence of such a computational phase of matter. |
| January
22: Condensed Matter Seminar Kang-Kuen Ni, JILA 2:00 p.m., 156 Jorgensen Title: Ultracold polar molecules Abstract: Ultracold atomic gases have enjoyed tremendous success as model quantum systems in which one can precisely control the particles' internal and external states. Many new theoretical proposals have now turned attentions to more complex systems such as ultracold polar molecules. These systems promise study of quantum phase transition, quantum simulations of condensed matter spin systems, and schemes for novel quantum information. These new proposals require a high phase-space-density gas of polar molecules where the electric dipole-dipole interaction is significant. We have recently met this goal by creating a gas of absolute ground-state polar molecules from a near quantum degenerate gas of KRb Feshbach molecules using a single step of STImulated Raman Adiabatic Passage (STIRAP) state transfer. We achieved transfer efficiency of 92% with no measurable heating in the transfer process resulting 4x10^4 ultracold polar molecules trapped in an optical dipole trap. The polar molecular gas has a peak density of 10^12 per cubic centimeter at a temperature of 350 nanoKelvin. The KRb molecules in the absolute ground state possess a permanent electric dipole moment that we measure to be 0.566(17) Debye. Currently, we are investigating the collisional stability of these molecules and seeing preliminary evidence of ultracold chemical reaction. This ability to create a quantum gas of ground-state molecules paves the way for future studies of dipolar Fermi gases and dipolar Bose-Einstein condensates. |
| January
27: IQI Seminar Christian Schaffner, CWI 3:00 p.m., 74 Jorgensen Title: The operational meaning of min- and max-entropy Abstract: We show that the conditional min-entropy H_min(A|B) of a bipartite state rho_AB is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the B-part of rho_AB are allowed. In the special case where A is classical, this overlap corresponds to the probability of guessing A given B. In a similar vein, we connect the conditional max-entropy H_max(A|B) to the maximum fidelity of rho_AB with a product state that is completely mixed on A. In the case where A is classical, this corresponds to the security of A when used as a secret key in the presence of an adversary holding B. Because min- and max-entropies are known to characterize information-processing tasks such as randomness extraction and state merging, our results establish a direct connection between these tasks and basic operational problems. For example, they imply that the (logarithm of the) probability of guessing A given B is a lower bound on the number of uniform secret bits that can be extracted from A relative to an adversary holding B. http://arxiv.org/abs/0807.1338, joint work with Renato Renner and Robert Koenig |
| January 28: Group Meeting Salman Beigi, MIT 5:30 p.m., 156 Jorgensen Title: Quantum multiple-Merlin-Arthur games and separability problem Abstract: A k-Merlin-Arthur protocol, QMA(k), is a proof system in which k un-entangled Merlins send a k-partite witness to Arthur, and Arthur in quantum polynomial time decides whether to accept or to reject. QMA(k), for k greater than 1, is much more complicated to characterize than QMA=QMA(1). Even the gap amplification problem is not a trivial one for this complexity class. In this talk, I will present a gap amplification protocol for QMA(k) based on the "Weak Additivity Conjecture". Also, I will describe the power of QMA(k); I will show that NP has a QMA(2)-protocol with short witnesses. Based on the idea of this protocol, I will discuss that finding an upper bound for QMA(k) is somehow equivalent to the characterization of separable states. I will show that non of the known criteria for detecting entanglement, are useful in this direction. First part of the talk is a joint work with Aaronson, Drucker, Fefferman and Shor. |
| January 30: IQI Special Seminar Netanel Lindner, Technion, Israel Institute of Technology 3:00 pm, 74 Jorgensen Title: A photonic cluster state machine gun Abstract: We present a method which can be used to convert certain single photon sources, such as quantum dots, into devices capable of emitting large strings of photonic cluster states in a controlled and pulsed “on demand” manner. Such sources greatly alleviate the resources required to achieve linear optical quantum computation. Standard spin errors, such as dephasing, are shown to affect only 1 or 2 of the emitted photons at a time. This allows for the use of standard fault tolerance techniques, and shows that the machine gun can be fired for arbitrarily long times. Using realistic parameters for current semiconductor quantum dot sources, we conclude high entangled-photon emission rates are achievable, with Pauli-error rates less than 0.2%. |
| February 11: Group Meeting Liang Kong 5:30 pm, 156 Jorgensen Title: Boundaries, defects and Categorification Abstract: I will briefly introduce 2-d conformal field theory with boundaries and defects. It can be described by a Frobenius algebra and its modules in some nice tensor categories. Then I will discuss the categorification of such theory and its relation to 3-d topological field theory. In the end, I will discuss its relevence to topological order in condensed matter physics by proposing a lattice model, which is an extension of that of Levin-Wen, to support this picture. Some mathematical conjectures will be given. |
| February 17: IQI Seminar Hector Bombín, Universidad Complutense, Madrid 3:00 pm, 74 Jorgensen Title: Interacting anyonic fermions in a two-body color code model Abstract: We introduce a two-body quantum Hamiltonian model of spin-1/2 on a 2D spatial lattice with exact topological degeneracy in all coupling regimes. There exists a gapped phase in which the low-energy sector reproduces an effective color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. The model exhibits a Z_2xZ_2 gauge symmetry and string-net integrals of motion, which are related to the existence of topological charges that are invisible to moving high-energy fermions. |
| February 24: IQI Seminar Daniel Gottesman, Perimeter Institute 3:00 pm, 74 Jorgensen Title: Continuous vs. discrete oracles Abstract: In the field of quantum computation, we frequently think of time as occuring in discrete steps, and quantum circuits as a series of distinct gates. However, in reality, time is continuous, or at any rate can occur in very tiny intervals. In the quantum circuit model, this corresponds to the existence of very small rotations, but in the standard model, a small rotation and a large rotation cost us the same amount of effort. We consider the oracle model, which counts the cost of an algorithm by the number of questions it asks of a black box encoding the problem. Specifically, we compare a discrete oracle, which causes a big phase shift dependent on the outcome of a query, to a continuous oracle, which can be run for varying amounts of time to produce a large or small phase shift. We show that the discrete oracle model can simulate a continuous-time oracle model with roughly the "correct" cost: In particular, given a continuous-time algorithm applying the oracle for a total time T, we find a discrete-time oracle algorithm that makes O(T log T) queries to the discrete oracle. This implies that lower bounds proven in the discrete-time oracle model still apply to continuous-time algorithms, with at most a log T loosening of the bound. This is joint work with Cleve, Mosca, Somma, and Yonge-Mallo. |
| March 10: IQI Seminar Thomas Vidick, UC Berkeley 3:00 pm, 74 Jorgensen Title: Entanglement in quantum games Abstract: The violation of Bell inequalities by quantum mechanics raises important theoretical and practical - leaving alone the philosophical - questions. In particular, with a cryptographic or complexity-theoretic context in mind, it is important to study the extent to which those inequalities can be violated by quantum mechanics. Maybe even more importantly, one would like to understand how such violations could be prevented, if at all possible. In joint work with Julia Kempe, Hirotada Kobayashi, Keiji Matsumoto, and Ben Toner, we develop methods for restraining the extent to which malicious parties can benefit from the use of shared entangled states to violate a given Bell inequality. More precisely, in terms of games we show how any 2-prover game can be modified in order to be (moderately) robust against cheating entangled provers. In this talk I will present our technique, describe a mathematical conjecture to which its efficiency is tied, and discuss some of its shortcomings. |
| March 25: Group Meeting Juerg Wullschleger, University of Bristol 5:30 pm, 156 Jorgensen Title: Oblivious transfer from weak noisy channels Abstract: Various results show that oblivious transfer can be implemented using the assumption of noisy channels. Unfortunately, this assumption is not as weak as one might think, because in a cryptographic setting, these noisy channels must satisfy very strong security requirements. Unfair noisy channels, introduced by Damgaard, Kilian and Salvail [Eurocrypt '99], reduce these limitations: They give the adversary an unfair advantage over the honest player, and therefore weaken the security requirements on the noisy channel. However, this model still has many shortcomings: For example, the adversary's advantage is only allowed to have a very special form, and no error is allowed in the implementation. In this paper we generalize the idea of unfair noisy channels. We introduce two new models of cryptographic noisy channels that we call the weak erasure channel and the weak binary symmetric channel, and show how they can be used to implement oblivious transfer. Our models are more general and use much weaker assumptions than unfair noisy channels, which makes implementation a more realistic prospect. |
| April 7: IQI Seminar Sergey Bravyi, IBM, Research 3:00 pm, 74 Jorgensen Title: Quantum algorithms for testing properties of probability distributions Abstract: Suppose we have an access to black boxes generating samples from two unknown probability distributions P and Q on some N-element set. How many samples do we need to test whether the two distributions are close or far from each other in the L_1 norm? This problem known as Statistical Difference has been extensively studied during the last years in the field of property testing. I will describe quantum algorithms for several special cases of Statistical Difference problem that provide a polynomial speed up in terms of query complexity compared to the best possible classical algorithms. These special cases include testing closeness, testing orthogonality, and testing uniformity. Closeness tester must decide whether the distributions P and Q are the same, or the L_1 distance between P and Q is above some constant threshold value. Orthogonality tester must decide whether the distributions P and Q have disjoint supports, or the overlap between P and Q is above some constant threshold value. Testing uniformity is a special case of testing closeness in which one of the distributions is uniform. It will be shown that quantum query complexity is O(N^{1/2}) for testing closeness and O(N^{1/3}) for testing orthogonality and uniformity. In constrast, classical query complexity is approximately N^{1/2} for testing orthogonality and uniformity, and approximately N^{2/3} for testing closeness. This is a joint work with Aram Harrow (University of Bristol) and Avinatan Hassidim (The Hebrew University). |
| April 21: IQI Seminar Norbert Schuch, Max Planck Institute for Quantum Optics 3:00 pm, 74 Jorgensen Title: Simulating quantum systems using Tensor Networks and Monte Carlo Abstract: In this talk, we discuss methods for the simulation of quantum systems which combine the advantages of quantum-information based variational methods such as PEPS with Monte Carlo sampling. They allow for the simulation of frustrated quantum systems in both 2D and 3D and with periodic boundaries, something which can be done neither using PEPS nor Quantum Monte Carlo. To this end, we introduce string-bond states, a class of states derived from PEPS which allows for the efficient computation of physical quantitites using Monte Carlo sampling, and which performs very well in simulating frustrated quantum systems in both two and three dimensions with open and periodic boundaries. We then show that the concept of string-bond states can be extended to so-called plaquette states which turn out to work extremely well in the description of two-dimensional frustrated problems, and which allow for generalizations to e.g. molecules. |
| April 28: IQI Seminar Steve Flammia, Perimeter Institute 3:00 pm, 74 Jorgensen Title: Heralded polynomial-time quantum state tomography Abstract: Everybody hates tomography. And with good reason! Experimentalists hate it because it is inefficient and difficult. Theorists hate it because it isn't very "quantum", and hence boring. But in part because of our current lack of meso-scale quantum computers capable of convincingly performing non-classical calculations, and the need to certify quantum state preparation, tomography seems like a necessary evil. In this talk, I will attempt to banish quantum state tomography to the Hell of Lost Paradigms where it belongs. I hope to achieve this by introducing several heuristics for learning quantum states more efficiently, in some cases exponentially so. One such heuristic runs in polynomial time and outputs a polynomial-sized classical approximation of the state (in matrix product state form.) Another takes advantage of the fact that most interesting states are close to pure states to get an (essentially) quadratic speedup using ideas from compressed sensing. Both algorithms come with rigorous error bounds. |
| May 4: CMP/IQI Seminar Simon Foelling, Harvard 4:00 pm, 107 Downs Title: An optical Gas Microscope for quantum simulation Abstract: Ultracold quantum gases are used as models to studying fundamental questions of modern condensed matter physics with atomic physics experiments. They allow for creating very clean implementations of complex many-body systems, and can enable the realization of tools for manipulating and probing the gas which are not available for classical condensed matter systems. I will present our experiment that enables the preparation of a cold quantum gas in a single, strongly two-dimensional trapping potential. This potential is located a few micrometers from a glass surface, allowing for optical access with an extremely high numerical aperture. This enables us to image and manipulate the quantum gas with a resolution on the scale of 500\,nm. We can generate optical lattices by direct projection through the lens and detect the atoms with flourescence imaging inside the trap. In this way, we can detect individual atoms in each lattice site, allowing for full site-resolved readout and preparation of the quantum state. |
May 5: IQI Seminar Joint work with Michael Ben-Or and Haran Pilpel |
May 19: IQI Seminar |
| May 21: IQI Special Seminar **Thursday** Yi Zhao, University of Toronto 2:45 pm, 74 Jorgensen Title: Quantum Cryptography in Real-life Applications Abstract: Are current QKD systems really secure? In this talk, I will present my experimental and theoretical studies in seek of answering the above question. Experimentally, several assumptions that are widely made in security proofs will be tested and enhanced. Theoretically, some imperfections in practical devices and their security consequence will be analyzed. I will discuss our achievements include: 1) the first experimental demonstration of decoy state QKD; 2) the first experimental demonstration of active phase randomization in QKD; 3) the first quantum hacking demonstration; and 4) the first security proof for QKD with an unknown and untrusted source. Our achievements significantly improved the security of real-life QKD systems, although the ultimate solution to guarantee the unconditional security of QKD in real-life applications is yet to be discovered. |
| May 26: IQI Special Seminar Volkher Scholz, University of Waterloo 3:00 pm, 74 Jorgensen Title:Tsirelson's Problem and approximability questions Abstract: |
| June 23: IQI Seminar Tony Short, University of Cambridge 3:00 pm, 74 Jorgensen Title:A quantum approach to thermal equilibrium Abstract: |
| June 30: IQI Seminar Miguel Aguado, Max Planck Institute for Quantum Optics 3:00 pm, 74 Jorgensen Title: Some topological applications of tensor networks Abstract: References: F. Verstraete, M. M. Wolf, D. Perez-Garcia and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006), arXiv:quant-ph/0601075. M. Aguado and G. Vidal, Phys. Rev. Lett. 100, 070404 (2008), R. Koenig, B. W. Reichardt and G. Vidal, arXiv:0806.4583 [cond-mat]. O. Buerschaper, M. Aguado and G. Vidal, Phys. Rev. B79, 085119 (2009), Zh.-Ch. Gu, M. Levin, B. Swingle and X.-G. Wen, Phys. Rev. B79, 085118 (2009), arXiv:0809.2821 [cond-mat]. |
September 29: IQI Seminar |
October 19: CMP Seminar |
October 20: IQI Seminar This is joint work with Stephen Bartlett, Gavin Brennen, and Akimasa Miyake. [1] Brennen and Miyake, Phys. Rev. Lett. 101, 010502 (2008). |
| October 28: IQI Special Seminar **WEDNESDAY** Frank Vallentin, Delft University of Technology 3:00 pm, 121 Annenberg, Building 16 Title: The positive semidefinite Grothendieck problem with rank constraint Abstract: Given a positive integer k and an n x n positive semidefinite matrix A the positive semidefinite Grothendieck problem with rank-k-constraint can be expressed as a semidefinite program: SDP-k. In this paper we design a polynomial time approximation algorithm achieving an approximation ratio of 1 − Θ(1/k). We show that under the assumption of the unique games conjecture the achieved approximation ratio is optimal: There is no polynomial time algorithm which approximates SDP-k with a ratio greater than 1 − Θ(1/k) . We improve the approximation ratio of the best known polynomial time algorithm for SDP-1 slightly from 2/π to 2/(πγ (n)) = 2/π + Θ(1/n), and we determine the optimal constant of the positive semidefinite case of a generalized Grothendieck inequality. Grothendieck's constant has applications for approximation algorithms, as well as interactive proof systems with two entangled provers. Joint work with J. Briet and F. M. Filho. |
| November 2: IQI/CMP Seminar Chris Laumann, Princeton 4:15 pm, 107 Downs Title: Random quantum satisfiability: statistical mechanics of quantum optimization Abstract: Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. Inspired by the success of the statistical study of classical constraint optimization problems, we study random ensembles of the QMA$_1$- complete quantum satisfiability (QSAT) problem introduced by Bravyi. QSAT appropriately generalizes the NP-complete classical satisfiability (SAT) problem. We show that, as the density of clauses/ projectors is varied, the ensembles exhibit quantum phase transitions between phases that are product satisfiable, entangled satisfiable and unsatisfiable. Remarkably, almost all instances of QSAT for a fixed interaction graph exhibit the same dimension of the satisfying manifold. This establishes the generic QSAT decision problem as equivalent to a purely graph theoretic property and that the hardest typical instances are likely to be localized in a bounded range of clause density. Based on papers: C.R. Laumann, A.M. Lauchli, R. Moessner, A. Scardicchio, and S.L. |
| November 3: IQI Seminar Chris Heunen, University of Oxford 3:00 pm, 105 Annenberg Title: Categorically isolating quantum properties Abstract: One benefit of using categories as semantics for quantum physics is the ability to isolate qualitative properties that are responsible for quantum behaviour. As an example, we axiomatically define Hilbert categories. The name is justified by proving an embedding theorem: any Hilbert category whose monoidal unit is a simple generator embeds into the category of Hilbert spaces and continuous linear functions, preserving tensor products, adjoint morphisms and all finite (co)limits. In particular, complex numbers emerge without having been prescribed explicitly. |
November 10: IQI Seminar |
| November 17: IQI Seminar Ben Reichardt, University of Waterloo 3:00 pm, 105 Annenberg Title: Faster quantum algorithm for evaluating game trees Abstract: We give a time sqrt(n)*polylog(n) quantum algorithm for evaluating size-n AND-OR formulas, also known as two-player game trees. The algorithm is based on a new method of quantum recursion or composition, and has a recursive structure that mirrors the formula's structure. In contrast, the previous sqrt(n)*2^O(sqrt log n)-time quantum algorithm required rebalancing the formula first. The optimal classical algorithm cannot work recursively following the formula's structure, must make at least n^0.51 queries, and is conjectured to require at least n^0.75 queries. |
| November 17: IQI Seminar Kaveh Khodjasteh, Dartmouth College 3:00 pm, 105 Annenberg Title: Dynamically corrected gates Abstract: Dynamically corrected gates (DCG) are specially pre-set sequences of simple gates that not only perform a unitary operator but also correct the error due to the environment that occurs during the operation of each component. The efficiency of DCGs is asymptotic in the sense that one needs to start with small gate errors to have DCGs with much smaller errors. My talk will contain an introduction to simple examples of DCGs along with their limitations, followed by more recent constructions that allow reaching arbitrary orders of error correction in the asymptotic limit through a recursive design. |
| December 2: IQI Seminar Matthew Neeley, University of California, Santa Barbara 3:00 pm, 107 Annenberg Title: Emulation of a quantum spin using a superconducting phase qudit Abstract: Quantum computers are typically thought of as being composed of qubits, or two-level quantum systems. However, one can also use qutrits (three-level systems) or general qudits (d-level systems) in quantum information processing, which can simplify certain computational tasks. Like many physical realizations of qubits, the superconducting phase qubit is a quantum system with multiple energy levels that is usually operated as a qubit by restricting it to the lowest two energy states. Here, we relax this restriction and instead use the higher levels to operate this device as a qudit up to d=5. We show how to manipulate and measure the qudit state, and then use it to emulate the dynamics of single spins with principal quantum number s=1/2, 1 and 3/2. In particular, we use this emulation to show the even (odd) parity of integer (half-integer) spins under 2\pi rotation. |
| December 8: IQI Seminar Mohammad Hafezi, University of Maryland, JQI 3:00 pm, 105 Annenberg Title: Photonic non-equilibrium quantum transport in a nonlinear medium Abstract: Recent experiments using ultra-cold atoms and optical photons have opened the door for studies of a novel form of quantum transport involving strongly correlated photons. While many similarities exist between these photonic systems and strongly correlated systems in condensed matter physics, the photonic systems also present a unique set of challenges. In particular, they do not thermalize, and are inherently open, driven systems, which highlights the need to develop novel techniques for analysis. In this talk, I present a theoretical study of the transmission of few-photon quantum fields through a strongly nonlinear optical medium. |
| December 15: IQI Seminar Spiros Michalakis, Los Alamos National Laboratory 3:00 pm, 107 Annenberg ***NOT 105*** Title: Topological quantum order: Stability under local perturbations Abstract: We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. We focus on 2D models of TQO for which the unperturbed Hamiltonian H_0 can be written as a sum of local pairwise commuting projectors. A perturbed Hamiltonian H=H_0+ epsilon V involves a generic perturbation V that can be written as a sum of short-range bounded-norm interactions. Let lambda_1, ldots, lambda_g be the set of g lowest eigenvalues of H, where g is the ground state degeneracy of H_0. We prove that if |epsilon| is below a constant threshold value then all eigenvalues lambda_1, ldots, lambda_g coincide up to exponentially small corrections and separated from the rest of the spectrum of H by a constant gap. This result implies that H and H_0 can be connected by an adiabatic path without closing the gap. Our proof goes by setting up Hamiltonian flow equations transforming a generic perturbation to a special "block-diagonal" perturbation that preserves the ground subspace of H_0. These flow equations are analyzed using Lieb-Robinson bounds and the theory of relatively bounded operators. Our technical tools might be useful for analyzing other stability problems for quantum spin systems. |
