Seminar Schedule

In spring 2010, the seminar takes place Friday 11am in Hennings room 309B (unless marked otherwise); any question, please email Tzu-Chieh Wei at twei-at-phas-dot-ubc-dot-ca

       Future visitors: Zhengfeng Ji (Oct. 16 -23), Valentin Murg (early November), Dave Bacon, etc.

       --- July 17-30, 2010: Tenth Canadian Summer School on Quantum Information (QI10) and The Workshop on Quantum Algorithms, Computational Models, and Foundations of Quantum Mechanics (QAMF, July 23-25)

--- July 16, 2010: Open discussions and preparation for the QI summer school

--- July 9, 2010: Pradeep Sarvepalli, Bounds on the Information Rate of Quantum Secret Sharing Schemes

Abstract: An important metric of the performance of a quantum secret sharing scheme is its information rate. Beyond the fact that the information rate is upper bounded by one, very little is known in terms of bounds on the  information rate of quantum secret sharing schemes. Further, not every scheme can be realized with rate one. In this talk I derive new upper bounds for the information rates of quantum secret sharing schemes. I show  that there exist quantum access structures on n players for which the information rate cannot be better than  O((\log_2 n)/n). These results are the quantum
analogues of  the bounds for classical secret sharing schemes proved by Csirmaz.

--- July 2, 2010: Vicky Choi (Virgina Tech), Adiabatic Quantum Algorithms for the NP-Complete Maximum-Weight Independent Set, Exact Cover and 3SAT Problems

Abstract: The problem Hamiltonian of the adiabatic quantum algorithm for the maximum-weight independent set problem (MIS) that is based on the reduction to the Ising problem (as described in [Choi08]) has flexible parameters. We show that by choosing the parameters appropriately in the problem Hamiltonian (without changing the problem to be solved) for MIS on CK graphs, we can prevent the first order quantum phase transition and significantly change the minimum spectral gap. We raise the basic question about what the appropriate formulation of adiabatic running time should be. We also describe adiabatic quantum algorithms for Exact Cover and 3SAT in which the problem Hamiltonians are based on the reduction to MIS. We point out that the argument in Altshuler et al.(arXiv:0908.2782[quant-ph]) that their adiabatic quantum algorithm failed with high probability for randomly generated instances of Exact Cover does not carry over to this new algorithm.
 
http://arxiv.org/abs/1004.2226

--- June 25, 2010: Maritza Hernandez, Coherence and entanglement in a two-qubit system

Abstract: Quantum entanglement is a physical resource, associated with the peculiar non classical correlations that are possible between  separated quantum systems. Entanglement can be measured, transformed, and purified. A pair of quantum systems in an  entangled state can be used as a quantum information channel to perform computational and cryptographic tasks that are impossible for classical systems.  The aim of this work is to study various aspects of quantum entanglement and coherence, illustrated by several examples. We relate the concepts of decoherence and disentanglement, via a model of two two-level atoms in different types of reservoir, including both cases of independent and common bath. Finally, we relate decoherence and disentanglement, by focusing on the sudden death of the entanglement and the dependence of the death time with the "distance" of our initial condition, from the decoherence free subspace. In particular, we study the sudden death of the entanglement, in a two-atom system with a common reservoir.
 
References:  Advances in Optics and Photonics, Vol.2, Issue 2, pp.229-286 (2010), PRA.78, 042114 (2008).

--- June 18, 2010: Tzu-Chieh Wei, Quantum 2-SAT and frustration-free Hamiltonians

Abstract: Classical satisfiability problems can be either difficult or hard depending on the maximum number of "literals" (or variables) in all clauses. If this number is three (i.e. 3-SAT) or larger, the problem is known to be NP-complete. On the contrary, classical 2-SAT has polynomial-time algorithm. The quantum analogue of SAT is only known to be QMA_1 complete if the number of qubits involved in specifying a "clause" is four (i.e. Quantum 4-SAT) or larger. Similar to classical case, Quantum 2-SAT has a polynomial-time algorithm, constructed by Bravyi. I will describe his construction and discuss some recent results by Chen et al. on the ground-state wavefunction of two-body frustration free qubit Hamiltonians.

Refs: quant-ph/0602108, arXiv:1004.3787

--- June 11, 2010: Robert Raussendorf, Measurement based quantum computing
and temporal order

--- June 4, 2010: Len Goff, Simulation of fermionic systems using Gaussian states

Abstract: I'll introduce the notions of a Gaussian state, a Gaussian operator, and a Gaussian linear map for fermions.  These mathematical objects can all be parametrized by matrices which are much smaller in dimension than their counterparts in the fermion Hilbert space, which provides an efficient classical simulation procedure for certain fermionic systems.  I'll also discuss an application of this formalism to the classical 2D Ising model.

References: Sergey Brayvi: "Lagrangian representation for fermionic linear optics", http://arxiv.org/abs/quant-ph/0404180

--- May 28, 2010: Poya Haghnegahdar, Transitivity of local complementation and switching on graphs

Abstract: Abstract: The operations complementation C, local complementation λ_x, and switching σ_x for the vertices x of a finite undirected graph are considered. The operation λ_x complements the subgraph induced by the neighbourhood of x in the given graph, and the switching σ_x changes the neighbourhood of x to its complement vertex set. It is proved that the compositions δ_x=λ_xC (for vertices xD) generate a transitive group on the graphs with vertex set D, that is, for any two graphs g and h on D, there exists a composition α of operations δ_x such that h=α(g). It is also shown that the compositions τ_x=λ_xσ_x (for xD) generate a transitive group on the graphs.

You can find the complete abstract and paper at the following link. http://dx.doi.org/10.1016/j.disc.2003.04.001

--- May 21, 2010: Michael Uhlmann, "Time-resolved density correlations as probe of  squeezing in toroidal Bose-Einstein condensates"

Abstract: I'm going to discuss some ideas related  to my recent paper, 1005.2645, and use the paper only as starting point for  an (open) discussion about what I'm going to do  next (it might involve adiabatic quantum computing).

--- May 14, 2010: Matthew Scholte, Topological Color Codes on Union Jack Lattices: A Stable Implementation of the Whole Clifford Group

Abstract: I will present a summary of the above paper (arxiv:0910.0573)  and related papers. I will give a summary of the hexagonal and  square-octagonal lattice colour codes and their duals, the triangle and  Union Jack lattices, how the Clifford group can be implemented, and (time  permitting) discuss the error thresholds and their comparison to the toric  code.

--- May 7, 2010: Tzu-Chieh Wei

--- April 30, 2010: Pradeep Sarvepalli, Decoding Topological Quantum Codes

Abstract:  In this talk I will give a brief overview of decoding algorithms for topological
quantum codes namely, the surface codes and color codes. I will first
present two decoding algorithms for surface codes; one of which is based on
Edmonds' algorithm for minimum weight matching in a graph and another
proposed by Cianci and Poulin (PRL 104, 050504) which uses a combination of
iterative decoding and renormalization methods that significantly lower
the complexity and improve the performance. I will then consider a
generalization of the matching algorithm for color codes due to Wang et al
(arXiv:0907.1708) and a potential extension of the iterative algorithm for
color codes.

--- April 23, 2010: open discussion

--- April 16, 2010: paper discussion session

1. "Gravity from Quantum Information", J-W Lee, H-C Kim, and J. Lee, arXiv:1001.5445
2. "On the Origin of Gravity and the Laws of Newton", E. Verlinde, arXiv:1001.0785

--- April 9, 2010: Robert Raussendorf, Measurement-based QC with planer codes states - the   problem of partial overlaps

Astract:  Measurement-based quantum computation (MQC) on planar code states has been shown to be efficiently classically simulatable, if we assume an additional technical condition [Bravyi+RR, 2006]. Namely, the sets of measured and unmeasured qubits must remain connected (wrt to the underlying planar graph) at all times. Likely, this condition cannot be relaxed very much. However, it is conceivable that this connectedness requirement follows from a more natural assumption, namely that the MQC be deterministic. Here,``deterministic'' means that the randomness introduced by the local measurements can be accounted for by adaption of measurement bases, and thus does not creep into the logical processing. In this talk, I present partial results towards establishing that classical simulation of deterministic MQC on planar code states is efficient.

--- April 2, 2010: Good Friday, no talk scheduled

--- March 26, 2010: Len Goff, State Overlaps of the 2D Color Code States (Part II)

--- March 19, 2010 (joint with Gravity group): Don Page, The Born Rule Fails in Cosmology

*** Notice place changed to Hennings 318 and time changed to 12:00pm ****

Astract:  The Born rule may be stated mathematically as the rule that probabilities in  quantum theory are expectation values of a complete orthogonal set of  projection operators. This rule works for single laboratory settings in  which the observer can distinguish all the different possible outcomes  corresponding to the projection operators. However, theories of inflation  suggest that the universe may be so large that any laboratory, no matter how  precisely it is defined by its internal state, may exist in a large number  of very distantly separated copies throughout the vast universe. In this  case, no observer within the universe can distinguish all possible outcomes  for all copies of the laboratory. Then normalized probabilities for the  local outcomes that can be locally distinguished cannot be given by the  expectation values of any projection operators. Thus the Born rule dies and  must be replaced by another rule for observational probabilities in  cosmology. The freedom of what this new rule is to be is the measure problem  in cosmology. A particular volume-averaged form is proposed.

--- March 12, 2010: Len Goff, State Overlaps of the 2D Color Code States (Part I)

Astract: 
 
Topological color codes (TCCs) are a class of quantum stabilizer codes that are defined in terms of a graph with certain colorability properties, and can be used for fault-tolerant computations or memory.  But one might also explore the possibility of performing measurement based quanum computation (MBQC) using TCC states as initial resource states. Simulating such a computation on a classical computer would involve evaluating the overlaps between a TCC state and suitable qubit product states.  In this talk I will introduce a class of TCC states defined on 2D graphs and present a result by Bombin and Martin-Delgado that relates their state overlaps to the partition function of a classical Ising model in two-dimensions.  This Ising model contains three-body interactions, in contrast to MBQC on planar code states which yields a classical Ising model with two-body interactions.  I will roughly sketch special cases where exact solutions to the three-body Ising model are known, while leaving the general case as an open problem.
 
H. Bombin & M.A. Martin-Delgado, "Statistical mechanical models and topological color codes":  http://pra.aps.org/abstract/PRA/v77/i4/e042322

--- March 5, 2010: Philip Ketterer, Introduction to Clifford quantum cellular automata

*** Notice place changed to Hennings 318 and time changed to 9:30am ****

Astract:  I will present a basic introduction to Clifford quantum cellular automata (CQCA). CQCA are a special kind of quantum cellular automata (QCAs) that incorporate Clifford group operations for the time evolution. Despite being classically simulable, they can be used as basic building blocks for universal quantum computation. After a basic definition and some examples I will show that CQCAs are equal to a classical system. This formalism allows an easy classification of CQCA and an analysis of various properties of CQCA such as entanglement generation.
  
The talk is based on the papers: arXiv:0804.4447, arXiv:0906.3195, and arXiv:1001.1062.

--- Feb 12, 2010: Tzu-Chieh Wei, Introduction to Local Hamiltonian Problems and complexity class QMA (part II)

--- Feb 5, 2010: Tzu-Chieh Wei, Introduction to Local Hamiltonian Problems and complexity class QMA (part I)

Abstract: I will give an introduction of a quantum computational complexity class: Quantum Merlin-Arthur (QMA), introduced by Kitaev. QMA is an analogue of the classical computational complexity class NP. I will also describe the Local Hamiltonian problems, which belong to QMA and are actually complete in QMA.

References:
"Quantum NP - A Survey", D. Aharonov and T. Naveh, quantu-ph/0210077
"Classical and Quantum Computation", a book by A. Yu Kitaev, A. Shen and M. N. Vyalyi

--- Feb 1, 2010 (Theory Seminar): David Feder (U Calgary), Measurement-based quantum computing in a fermionic ground state

Time and Location: Monday, Feb 1, 12 noon, Hennings 318/ coffee and sandwiches

Abstract: Quantum computers have the potential to solve various problems more efficiently than any conceivable classical computer, but building such a device is a major challenge. The main problem is that one needs to have precise control of the components, while otherwise keeping them as isolated as possible from the rest of the environment. Ideally then, a quantum computer would be closely related to the gapped ground state of some natural quantum system, with manipulations on it (such as local rotations and measurements) preserving this central characteristic. Finding candidate Hamiltonians has been difficult, however. It turns out that the vast majority of quantum mechanical states are not useful for quantum information processing in such a model. Even worse, no one even knows what are the important properties that make a state useful or not!

I will discuss the fundamental properties of fermions, and show that under very specific circumstances the gapped ground state of these indistinguishable particles can in fact constitute a universal resource for quantum computation. In this model the quantum information itself becomes fundamentally non-local. Entanglement is associated with fermionic antisymmetry, but alone cannot be used to perform tasks such as quantum teleportation; for this one also needs local particle interactions.

--- Jan 29, 2010: Poya Haghnegahdar, Review of the paper "Graphical Quantum Error-Correcting Codes" by Sixia Yu, Qing Chen, C.H. Oh

Astract of the paper:  We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes, which are potentially more efficient, is not as well understood as that of stabilizer codes. Our graphical approach provides a unified and classical way to construct both stabilizer and nonadditive codes. In particular we have explicitly constructed the optimal ((10,24,3)) code and a family of 1-error detecting nonadditive codes with the highest encoding rate so far. In the case of stabilizer codes a thorough search becomes tangible and we have classified all the extremal stabilizer codes up to 8 qubits.

--- Jan 22, 2010: Len Goff (UBC), Generalized entanglement

Abstract: In this talk I will discuss the idea of "generalized entanglement", which is a research program aimed at extending the notion of entanglement beyond a subsystem based decomposition of Hilbert space.  Mainly, I will provide an introduction to the idea based on the two references listed below.  I will also discuss the motivation for this approach, and we will check that generalized entanglement contains the Schmidt rank measure of conventional entanglement as a special case.  Time permitting, I will discuss the prospect of applying generalized entanglement to systems of non-interacting fermions.

L. Viola, H. Barnum, E. Knill, G. Ortiz, R. Somma: “Entanglement Beyond Subsystems” arxiv: quant-ph\0403044v1
L. Viola, H. Barnum: “Entanglement and Subsystems, Entanglement beyond Subsystems, and All That” arxiv: quant-ph/070112v1

--- Jan 12, 2010: Discussion

Time and Location: Tuesday, Jan 12, 4pm, Hennings 311

In fall 2009, if not explicitely stated otherwise, the seminar takes place Wednesdays 3pm in the Theory Centre (Hennings, room 311).

• November 4, 2009: Tzu-Chieh Wei (UBC), Review of "Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation" by Aharonov, van Dam, Kempe, Landau, Lloyd and Regev, quant-ph/0405098.

  Time and Location: Wednesday, November 4, 3pm, Hennings 309B

• October 28, 2009: Michael Uhlmann (UBC), Review of "Decoherence in dynamical quantum phase transitions of the transverse Ising chain", Phys. Rev. A 76, 030304(R) and arXiv:0910.1750 by Sarah Mostame, Gernot Schaller, and Ralf Schuetzhold.

  Time and Location: Wednesday, October 28, 3pm, Hennings 301

  Abstract: For the prototypical example of the Ising chain in a transverse field, we study the impact of decoherence on the sweep through a second-order quantum phase transition. Apart from the advance in the general understanding of the dynamics of quantum phase transitions, these findings are relevant for adiabatic quantum algorithms due to the similarities between them. It turns out that (in contrast to first-order transitions studied previously) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins or qubits), which might limit the scalability of the system.

• October 21, 2009: Matthew Scholte (UBC), Path Integrals for Multiply Connected Spaces

  Time and Location: Wednesday, October 21, 3pm, Hennings 309B

  Abstract: We derive the propagator for a particle constrained to a torus and to a Klein Bottle. This is accomplished by considering relative symmetries between the desired system and a system for which the propagator is known. This result is checked against the propagator derived via the method of stationary state construction, for which the entire spectrum of the Hamiltonian is required. We also briefly consider the application of further constraints to the systems, and the implications of different symmetries on the same constraint.

• October 14, 2009: Pradeep Kiran Sarvepalli (UBC), Review of the LU-LC conjecture and its refutation

  Time and Location: Wednesday, October 14, 3pm, Hennings 318

  Abstract: An interesting problem in quantum information theory is the LU-LC conjecture. This conjecture asserted that the local unitary and local Clifford equivalence classes of stabilizer states were the same. Although much of the previous work seemed to suggest that this conjecture was true, it was refuted recently by Ji et al. In this talk I will give an overview of this result by first giving an introduction to this conjecture, its reformulation as a problem involving quadratic forms over GF(2) and its subsequent refutation by Ji et al by means of an explicit counterexample. The talk is based on the papers arXiv:0707.4000 and arXiv:0709.1266.

• October 7, 2009: Jonathan Oppenheim (University of Cambridge), Quantum Privacy and Distributed Compression

  Time and Location: Wednesday, October 7, 3pm, Hennings 309B

  Abstract: We introduce the concept of mutual independence-correlations shared between distant parties which are independent of the environment. This notion is more general than the standard idea of a secret key - it is a fully quantum and more general form of privacy. The states which possess mutual independence also generalize the so called private states - those that possess private key. We then show that the problem of distributed compression of quantum information can be solved in terms of mutual independence. We suspect that mutual independence is a highly singular quantity, i.e. that it is positive only on a set of measure zero; furthermore, we believe that its presence is seen on the single copy level. This appears to be born out in the classical case.

• September 9, 2009: Robert Raussendorf (UBC), Quantum computation, discreteness, and contextuality

  Time and Location: Wednesday, September 9, 2pm, Hennings 318

  Abstract: We establish a link between contextuality of quantum mechanics and quantum-mechanical computation. Specifically, we show that no deterministic measurement-based quantum computation evaluating a non-linear function can be described by a non-contextual hidden-variable model. We give examples for such computations derived from quantum codes with suitable transversality properties, and from a counterexample to the LU-LC conjecture.

  References: R. Raussendorf, arXiv:0907.5449.

• July 29, 2009: Pradeep Kiran Sarvepalli (UBC), Matroids in Quantum Computing and Quantum Cryptography

  Time and Location: Wednesday, July 29, 2pm, Hennings 318

  Abstract: In this talk I will briefly survey the use of matroids in quantum computation and quantum cryptography. I review a recent work by Shepherd and Bremner which claims that even restricted models of quantum computation, such as those consisting of abelian gates, give rise to probability distributions that cannot be sampled effciently by a classical computer. I will sketch their arguments that use the theory of binary matroids to substantiate their claim.

  I next consider an open problem related to the classiffication of a class of quantum states called the stabilizer states. A restricted version is to classify the equivalence classes of a sublcass of stabilizer states (namely, the CSS states) under the action of the local unitary group and a subgroup of the local unitary group, called the local Clifford group. Speciffically, we seek necessary and sufficient conditions as to when a CSS stabilizer state has distinct equivalence classes. I show that CSS stabilizer states whose equivalence classes are distinct must arise from binary matroids which are neither graphic nor cographic. In the process we also arrive at a class of minor closed matroids (whose excluded minors appear to be uncharacterized).

  Finally, I consider applications of matroids to an important cryptographic primitive namely, quantum secret sharing, which deals with the problem of distribution of a quantum state among n players so that only authorized players can reconstruct the secret. I present the first steps toward a matroidal characterization of quantum secret sharing schemes. This characterization allows us to construct efficient schemes from self-dual matroids that are coordinatizable over a finite field. In the process we also provide a connection between a class of quantum stabilizer codes and secret sharing schemes.

• July 7, 2009: Miguel Aguado (MPQ Garching/ Germany), Topological uses of tensor networks

  Time and Location: Tuesday, July 7, 2pm, Hennings 309B

  Abstract:Many-body tensor product ansaetze (e.g., of the PEPS and MERA type) have found application in the description of topologically ordered ground states of lattice systems (such as Kitaev's quantum double models, and Levin and Wen's string-net models.) I will describe the basic constructions and discuss work in progress (among others, with O. Buerschaper, M. Christandl, and G. Vidal) on the relations among several topological systems, and extensions to more general models.

  References:

  1. F. Verstraete, M. M. Wolf, D. Perez-Garcia and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006), arXiv:quant-ph/0601075.
  2. M. Aguado and G. Vidal, Phys. Rev. Lett. 100, 070404 (2008), arXiv:0712.0348 [cond-mat].
  3. R. Koenig, B. W. Reichardt and G. Vidal, arXiv:0806.4583 [cond-mat].
  4. O. Buerschaper, M. Aguado and G. Vidal, Phys. Rev. B79, 085119 (2009), arXiv:0809.2393 [cond-mat].
  5. Zh.-Ch. Gu, M. Levin, B. Swingle and X.-G. Wen, Phys. Rev. B79, 085118 (2009), arXiv:0809.2821 [cond-mat].

• Jun 10, 2009: Michael Uhlmann (UBC), O(N) symmetry breaking quantum quench -- defect creation and scaling

  Time and Location: Wednesday, June 10, 2pm, Hennings 318

  Abstract: The rapid sweep through a symmetry-breaking second-order quantum phase transition entails fascinating non-equilibrium phenomena. Quantum fluctuations become unstable and their exponential growth seeds the formation of causally disconnected spatial domains. If the final phase permits topological defects, e.g., vortices in two dimensions, they will generally be created by a quantum version of the Kibble-Zurek mechanism. In this talk, I will discuss the O(N) breaking quantum quench in N spatial dimensions, with special emphasis on the case N = 2 as this was realized in a recent experiment using spin-1 Bose-Einstein condensate [L.E. Sadler et al., Nature (London) 443, 312]. An ab initio derivation of the winding number statistics will be presented, where no approximations apart from the large N limit are employed. The final result is non-perturbative in N, i.e., cannot be obtained by an expansion in 1/N.

• May 27, 2009: Mohammad Amin (D-wave), First Order Quantum Phase Transition in Adiabatic Quantum Computation

  Time and Location: Wednesday, May 27, 2pm, Hennings 318

  Abstract:A key question regarding the adiabatic quantum computation (AQC) approach to solving NP-hard problems is how the computation time scales with the problem size. Thus far attempts to answer this question have been limited to analytical solutions for very special examples and numerical solutions for small scale problems. However, significant insight can be obtained using concepts of quantum phase transitions. I will use these concepts to demonstrate that the computation time in AQC may show exponential or polynomial behavior depending on whether the quantum phase transition can be classified as first or second order, respectively. I will discuss both cases in some detail and relate the existence of first order quantum phase transitions to the properties of local minima in the problem Hamiltonian. I will then provide a simple example of the weighted maximum independent set problem, showing agreement between a perturbative theory and numerical diagonalization. Finally, I will show how these concept can help understanding more general examples of random spin glasses, studied using quantum Monte Carlo technique.

• May 20, 2009: Robert Raussendorf (UBC), Review of Quantum Error Correction in Spatially Correlated Quantum Noise, by R. Klesse and S. Frank.

  Time and Location: Wednesday, May 20, 2pm, Hennings 318

  Abstract: [J-Ref: Phys. Rev. Lett. 95, 230503 (2005)] We consider quantum error correction of quantum-noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kind of noise correlations have a strong negative impact on quantum error correction.

• Apr 29, 2009: Pradeep Kiran Sarvepalli (UBC), Quantum Secret Sharing with CSS Codes

  Time and Location: Wednesday, April 29, 2pm, Hennings 318

  Abstract: Quantum secret sharing deals with the distribution of secure information, (which can be either classical or quantum), among n players. Each player receives a quantum state related to the secret, but only authorized subsets of players can reconstruct the secret. The authorized subsets constitute the access structure of the secret sharing scheme. Every quantum secret sharing scheme can be viewed as a quantum error correcting code, but the converse is not true. Motivated by this we sought to find quantum codes which can be converted to secret sharing schemes. First, I will show that if we restrict ourselves to sharing classical secrets using quantum information, then we can convert every pure [[n; 1; d]]_q CSS code to a perfect quantum secret sharing scheme. These secret sharing schemes are perfect in the sense the unauthorized parties do not learn anything about the secret. Then I will show that the access structure of the secret sharing scheme can be characterized in terms of the minimal codewords of the classical code underlying the CSS code. Then I will consider how these results can extended to the sharing of quantum secrets i.e. quantum states. I will conclude with a brief discussion on how these schemes can be related to matroids.

• Apr 22, 2009: Charles Foell (UBC), Towards quantum information processing with NV centers in silicon photonic crystal cavities

  Time and Location: Wednesday, April 22, 2pm, Hennings 318

  Abstract: [Charles A. Foell, A. M. Zagoskin, Jeff F. Young] We pursue a two-qubit gate scheme proposed by Zagoskin et al. [PRB 76, 014122 (2007)]. In this scheme two nitrogen-vacancy (NV) defect centres in diamond couple via an off-resonant, high-Q cavity mode. Feasibility of realizing this scheme by using NV centres in diamond nanoparticles, placed in a silicon-based photonic crystal cavity, is evaluated with a combination of 1) detailed analytical work including derivation of a consistent Hamiltonian of the NV centre interacting with cavity and laser fields, 2) FDTD simulations, and 3) quantitative estimation of model parameters. Experimental gains towards this end are presented.

• Apr 7, 2009: Len Goff (UBC), Review of Efficient simulation of one-dimensional quantum many-body systems, by Guifre Vidal, quant-ph/0310089.

  Abstract: I will discuss a proposal by Dr. Guifre Vidal presented in the paper "Entanglement Renormalization" (http://arxiv.org/abs/cond-mat/0512165) for implementing a renormalization group transformation for systems on a lattice. The idea builds upon the more traditional Density Matrix Renormalization Group method by applying at each iteration unitary transformations that reduce short-range entanglement around a block. The resulting reduced density matrices for each block are then used to define the Renormalization Group transformation for the next iteration. I will discuss the method and its motivation, and some resuts for the 1D Ising model. Notably, Vidal finds that these "disentagling" transformations can be used to keep the entanglement entropy between a block and the rest of the lattice at criticality constant throughout the RG transformation, reflecting the scale invariance of the system.

  Time and Location: Tuesday, April 7, 2pm, Hennings 311

• Mar 18, 2009: Bill Unruh (UBC), False loss of coherence

  Time and Location: Wednesday, Mar 18, 2pm, Hennings 318

  Abstract: The loss of coherence of a quantum system coupled to a heat bath as expressed by the reduced density matrix is shown to lead to the miss-characterization of some systems as being incoherent when they are not. The spin boson problem and the harmonic oscillator with massive scalar field heat baths are given as examples of reduced incoherent density matrices which nevertheless still represent perfectly coherent systems.

• Mar 11, 2009: Philip Stamp (UBC), Can error correction work under realistic conditions?

  Time and Location: Wednesday, Mar 11, 2pm, Hennings 311

  Abstract: TBA.

• Mar 10, 2009: Eduardo Mucciolo (University of Central Florida), Long-Time Dynamics and Quantum Error Correction in the Presence of Correlated Environments

  Time and Location: Tuesday, Mar 10, 2pm, Hennings 309B or 311

  Abstract: In this talk I will discuss the long time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is indeed possible, I will show how one can derive formal expressions for the probability of a faulty path and the residual decoherence encoded in the reduced density matrix. The key assumption in this formulation is that the propagation of signals through the environment is slower than the QEC period (hypercube assumption), such that a local error probability for a qubit is well defined. This allows an explicit calculation in the case of a generalized spin-boson model and a quantum frustration model. The key result is a dimensional criterion: If the correlations decay sufficiently fast, the system evolves toward a stochastic error model for which the threshold theorem of fault-tolerant quantum computation has already been proven. On the other hand, if the correlations decay slowly, the traditional proof of this threshold theorem does not hold. This dimensional criterion bears many similarities to criteria that occur in the theory of quantum phase transitions.

• Feb 18, 2009: Markus Grassl (CQT Singapore), Mutually unbiased bases & SIC-POVMs -- An Overview

  Time and Location: Wednesday, Feb 18, 2pm, Hennings 311

  Abstract: The talk gives an introduction to the problems of finding maximal sets of mutually unbiased bases (MUBs) and the related problem of so called SIC-POVMs. After presenting some known constructions, recent results for small dimensions will be discussed.

• Wednesday, Feb 11: Group meeting. Discussion

  Time and Location: Wednesday, Feb 11, 2pm, Hennings 311

• Feb 2, 2009: Tzu-Chieh Wei (IQC, University of Waterloo), Geometric entanglement in spin chains with quantum phase transitions

  Time and Location: Monday, Feb 2, 3pm, Hennings 309B

  Abstract: We consider ground-state entanglement of one-dimensional spin chains with quantum phase transitions. We characterize entanglement by the geometric measure, which compares the state in question to the set of suitably defined product states. If the product states consist of direct product of arbitrary L-spin states, a notion of entanglement under the RG transformation on quantum states emerges. We find that near critical points, the ground-state entanglement under the RG transformation exhibits singular behavior. The singular behavior under finite steps of the RG reveals the correlation length exponent. However, under the infinite steps of the RG transformation, the singular behavior is rendered different, and it is not universal unless the critical point can be described by a conformal field theory.

• Wednesday, Jan 28: Group meeting. Discussion

  Time and Location: Wednesday, Jan 28, 2pm, Hennings 311

• Jan 27, 2009: Charlotte Gils (ETH Zurich), Topology in systems of interacting non-abelian anyons

  Time and Location: Tuesday, Jan 27, 2pm, Hennings 309B

  Abstract: Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics, which is more general than that of bosons or fermions. Such anyons emerge as quasiparticles in fractional quantum Hall states and certain frustrated quantum magnets. Non-abelian anyons have recently attracted interest in the context of topological quantum computation. In the first part of the talk, I discuss the collective states in systems of interacting non-abelian quasiparticles. I consider so-called su(2) level k anyons which form a bridge between ordinary SU(2) spin degrees of freedom and non-abelian anyons.

  In the second part, I discuss a novel type of continuous quantum phase transition that is driven by quantum fluctuations of topology. This phase transition arises in a microscopic model of interacting non-abelian anyons, which has an exact solution at the critical point. A global (topological) symmetry plays an important role in the models I present.

Seminars in 2008