# Perimeter Institute Quantum Discussions

This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.

## Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

## Physical Implementation of Quantum Random Walks

Wednesday May 06, 2009
Speaker(s):

Quantum random walks have received much interest due to their non-
intuitive dynamics, which may hold a key to radically new quantum
algorithms. What remains a major challenge is a physical realization
that is experimentally viable, readily scalable, and not limited to
specific connectivity criteria. In this seminar, I will present an
implementation scheme for quantum walking on arbitrarily complex
graphs. This scheme is particularly elegant since the walker is not

Scientific Areas:

## Decoherence and Entanglement Dynamics of Coupled Qubits

Monday Mar 23, 2009
Speaker(s):

We study the entanglement dynamics and relaxation properties of a system of two interacting qubits in the two cases (I) two independent bosonic baths and (II) one common bath, at temperature $T$. The entanglement dynamics is studied in terms of the concurrence C(t) between the two spins and of the von Neumann entropy S(t) with respect to the bath, as a function of time. We prove that the system does thermalize. In the case (II) of a single bath, the existence of a decoherence-free (DFS) subspace makes entanglement dynamics very rich.

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## Permutational quantum computation and spin networks

Wednesday Mar 04, 2009
Speaker(s):

In topological quantum computation the geometric details of a particle trajectory become irrelevant; only the topology matters. This is one reason for the inherent fault tolerance of topological quantum computation. I will speak about a model in which this idea is taken one step further. Even the topology is irrelevant. The computation is determined solely by the permutation of the particles.

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## Quantum algorithm for Statistical Difference problem

Wednesday Feb 18, 2009
Speaker(s):

Suppose we are given two probability distributions 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 Statistical Difference problem that provide a polynomial speed up in terms of the query complexity compared to the known classical lower bounds.

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## Quantum computation with Topological Lattice Field Theories

Wednesday Feb 04, 2009
Speaker(s):

Recent results have shown that quantum computers can approximate the value of a tensor network efficiently. These results have initiated a search for tensor networks which contract to computationally interesting quantities. Topological Lattice Field Theories (TLFTs) are one source of such networks; when defined appropriately, networks arising from TLFTs contract to give topological invariants. In this elementary talk, we will define and classify TLFTs which lead to invariants of surfaces, and sketch out the corresponding quantum algorithm.

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## Interacting Anyonic Fermions in a Two-Body Color Code Model

Wednesday Jan 21, 2009
Speaker(s):

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 group symmetry and string-net integrals of motion, which are related to the existence of topological charges that are invisible to moving high-energy fermions.

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## Quantum boolean functions

Wednesday Dec 03, 2008
Speaker(s):

In recent years, the analysis of boolean functions has arisen as an important theme in theoretical computer science. In this talk I will discuss an extension of the concept of a boolean function to quantum computation. It turns out that many important classical results in the theory of boolean functions have natural quantum analogues. These include property testing of boolean functions; the Goldreich-Levin algorithm for approximately learning boolean functions; and a theorem of Friedgut, Kalai and Naor on the Fourier spectra of boolean functions.

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## Hybrid quantum information processing and communication

Wednesday Nov 26, 2008
Speaker(s):

With the aim of proposing feasible, quantum optical realizations of quantum information protocols and minimizing the resource costs in such implementations, we will discuss various, so-called hybrid approaches. These include, for instance, schemes based upon both discrete and continuous quantum variables.

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## Measurement Pattern Interpolation: Theory, and potential applications

Wednesday Nov 19, 2008
Speaker(s):

Quantum computation by single-qubit measurements was proposed by Raussendorf and Briegel [PRL 86, 5188] as a potential scheme for implementing quantum computers. It also offers an unusual means of describing unitary transformations. To better understand which measurement-based procedures perform unitary operations, we may consider the following problem: under what circumstances can a measurement-based procedure for a unitary U be found, provided a similar procedure for U which relies on post-selection?

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## The Toric Code, Perturbed

Wednesday Nov 12, 2008
Speaker(s):

By storing quantum information in the degenerate ground state of a Hamiltonian, it is hoped that it can be made quite robust against noise processes. We will examine this situation, with particular emphasis on the Toric code in 2D, and show how adversarial effects, either perturbations to the Hamiltonian or interactions with an environment, destroy the stored information extremely quickly.

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