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 diff erent 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:
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.