Vortex Arrays in a Rotating Superfluid Fermi Gas University of Calgary | Publication | 2004-11-01 | D. Feder |

Superfluid-to-Solid Crossover in a Rotating Bose-Einstein Condensate University of Calgary | Publication | 2001-10-01 | D. Feder, C. W. Clark |

Dark-soliton states of Bose-Einstein condensates in anisotropic traps University of Calgary | Publication | 2000-10-01 | D. Feder, M. S. Pindzola, L. A. Collins, B. I. Schneider, C. W. Clark |

Nucleation of vortex arrays in rotating anisotropic Bose-Einstein condensates University of Calgary | Publication | 1999-12-01 | D. Feder, C. W. Clark, B. I. Schneider |

Twin boundaries in d -wave superconductors University of Calgary | Publication | 1997-09-01 | D. Feder, A. Beardsall, A. J. Berlinsky, C. Kallin |

Statistics and superfluidity University of Calgary | Publication | 1995-10-01 | D. Feder, C. Kallin |

Perfect Quantum State Transfer with Spinor Bosons on Weighted Graphs University of Calgary | Publication | 2006-11-01 | D. Feder |

Cooling ultracold bosons in optical lattices by spectral transform University of Calgary | Publication | 2009-01-01 | D. Feder |

Maximally entangled gapped ground state of lattice fermions University of Calgary | Publication | 2012-01-01 | D. Feder |

One-way quantum computing with ultracod atoms in optical latticesIn the 'one-way' model of quantum computation, one only needs to make a
series of measurements on qubits in highly entangled states, known as
cluster or graph states. These states can be efficiently generated with
ultracold atoms confined in optical lattices, which are periodic potentials
formed by laser interference. Two significant experimental hurdles impeding
one-way computation in these systems are the inability to produce perfect
cluster states and to perform single-qubit measurements. I will show that
both of these can in fact be easily overcome using standard experimental
techniques. I will also sketch out ideas about how to implement fault-
tolerance within the one-way model.
University of Calgary | Presentation | 2007-11-22 | D. Feder |

Quantum mechanics can help analyze complex networks University of Calgary | Presentation | 2008-01-23 | D. Feder |

Cooling ultracold bosons in optical lattices with quantum walks University of Calgary | Presentation | 2009-03-04 | D. Feder |

Fermions in lattices as a universal resources for quantum information processing University of Calgary | Presentation | 2009-05-05 | D. Feder |

Ground states of quantum many-body systems via graph theory University of Calgary | Presentation | 2012-07-24 | D. Feder |

Les Graphes dans la Mecenique QuantiqueAll fundamental particles in the universe come in two types:
fermions and bosons. The former category contains electrons, protons,
and neutrons, and forbids two particles from occupying the same quantum
state (the Pauli exclusion principle); the latter category, which
contains photons and other force-carrying particles, has no such
restriction. When bosons and fermions are confined in lattices, such as
in solid-state systems, the equations of motion can be phrased in terms
of the adjacency matrix of an undirected and generally weighted graph.
The properties of these quantum many-particle systems can therefore be
analyzed in terms of graph theory. I will discuss these relationships,
and show that by using graph theory, it is possible to obtain a more
efficient determination of the eigenstates (and therefore the properties
and dynamics) of interesting physical systems. University of Calgary | Presentation | 2012-07-19 | D. Feder |

Measurement-based quantum computing in a fermionic ground state University of Calgary | Presentation | 2010-02-01 | D. Feder |

Are fermions useful for quantum computation? University of Calgary | Presentation | 2009-10-09 | D. Feder |

Cooling ultracold bosons in optical lattices by quantum walks University of Calgary | Presentation | 2009-04-24 | D. Feder |

Cooling ultracold bosons in optical lattices by quantum walks University of Calgary | Presentation | 2009-04-22 | D. Feder |

Cooling ultracold bosons in optical lattices by quantum walks University of Calgary | Presentation | 2009-04-17 | D. Feder |

Cooling ultracold bosons in optical lattices by quantum walks University of Calgary | Presentation | 2009-04-15 | D. Feder |

Can the ground states of low-dimensional many-body systems be useful for quantum computation? University of Calgary | Presentation | 2009-04-07 | D. Feder |

Measurement-based quantum computing in a fermionic ground state University of Calgary | Presentation | 2010-07-22 | D. Feder |

Mott-Insulator transition in coupled cavity arrays University of Calgary | Presentation | 2012-02-18 | D. Feder |

Fermionized photons in one-dimensional coupled cavitiesWe consider the properties of a one-dimensional array of evanescently coupled high-finesse cavities each containing a single neutral atom, in the limit of low photon densities. The ground state of the corresponding Jaynes-Cummings-Hubbard (JCH) model is obtained numerically using the Density Matrix Renormalization Group algorithm. We find strong evidence for the existence of a Tonks-Girardeau phase, in which the photons are strongly fermionized, between the Mott-insulating and superfluid phases as a function of the inter-cavity coupling. Results for photon and spin excitation densities, one- and two-body correlation functions, and superfluid and condensate fractions are all found to be consistent with this conclusion. University of Calgary | Presentation | 2014-03-05 | D. Feder, A. D'Souza, B. C. Sanders |

Measurement-based quantum computation using imperfect cluster states University of Calgary | Presentation | 2005-09-01 | D. Feder, M. Garrett, J. Briët |

Graphs in quantum information theoryI will discuss some of the relationships between quantum information and graph theory that have been developed over the past few years. There are two main points of contact between these seemingly disparate fields. One of these is to consider a graph as a collection of vertices in either real or configuration space, connected by edges. A major effort in this case is to construct quantum algorithms that can efficiently determine properties of the graph, and I will describe in detail one such approach which is based on quantum walks. The other point of contact is to consider each vertex as a qudit, with edges representing an entangling operation. In this picture, each graph is uniquely associated with a highly entangled quantum state known as a graph state or stabilizer state. I will discuss the relationship between stabilizers and the theory of quantum error correction. I will also show that certain graph states, known as cluster states, are a resource for universal quantum computation based only on measurements.
University of Calgary | Presentation | 2006-08-11 | D. Feder |

Quantum search algorithm with many bosons in optical latticesOne approach to implementing quantum algorithms is the quantum walk (QW). In the continuous-time formulation, the QW is equivalent to the time-evolution of a quantum state under the influence of a discrete-space Hamiltonian. Building on a duality between many boson systems and weighted graphs, I will discuss how one can implement a QW search algorithm with ultracold bosons confined in optical lattices. By applying a specified external potential (using an external laser), the atoms in a shallow lattice will evolve from the uniformly populated ground state to all occupying one particular site. The results indicate that quantum algorithms exhibiting polynomial speed-up should be feasible with current experimental technology.
University of Calgary | Presentation | 2007-03-07 | D. Feder |

Quantum algorithms with quantum walks University of Calgary | Presentation | 2007-06-13 | D. Feder |

Implementing a spectral transform with ultrabold atoms in optical lattices University of Calgary | Presentation | 2008-04-18 | D. Feder |

Quantum computation in the ground state of interacting fermionsIn measurement-based quantum computation (MBQC), an algorithm proceeds entirely by making projective measurements on successive qubits comprising some highly entangled `resource state.' While two-dimensional cluster states are known to be universal resources for MBQC, it has been proven that they cannot be the unique ground states of any two-body spin Hamiltonian. We show that a particular ground state of non-interacting fermions (equivalent to a many-body spin system) is formally equivalent to a cluster state, though only capable of simulating a limited set of quantum operations. In the presence of two-particle interactions, however, the ground state becomes a universal resource for MBQC. This result suggests that arbitrary quantum algorithms could be simulated fault-tolerantly simply by measuring a cold gas of interacting fermions, such as ultracold atoms in optical lattices. University of Calgary | Presentation | 2010-03-18 | D. Feder, G. Shlyapnkov |

Measurement-based quantum computing in a fermionic ground state University of Calgary | Presentation | 2011-02-20 | D. Feder |

Quantum computation: the big picture of the very small University of Calgary | Presentation | 2012-06-12 | D. Feder |

Graphs in quantum many-body theoryThe Hamiltonian for bosonic and fermionic particles hopping on lattices can be interpreted as the adjacency matrix of an undirected and generally weighted graph. The properties of these quantum many-body systems can therefore be analyzed in terms of graph theory. For example, the simple graph for non-interacting distinguishable particles is the Cartesian product of each particle’s adjacency matrix; if these particles become indistinguishable, the graph collapses via a graph equitable partition. In the presence of strong interactions between the particles, the graphs are generally decomposable as weak products (i.e. they are the Kronecker products of adjacency matrices). Under various circumstances, these techniques can allow for the efficient calculation of the eigenstates (and therefore the properties) of physically interesting quantum many-body systems. University of Calgary | Presentation | 2012-06-04 | D. Feder |

Solitons in a Bose-Einstein condensate University of Calgary | Publication | 2000-01-01 | D. Feder |

Microscopic derivation of the Ginzburg-Landau equations for a d-wave superconductor University of Calgary | Publication | 1997-01-01 | D. Feder |

Twin boundaries in d-wave superconductors University of Calgary | Publication | 1997-01-01 | D. Feder |

Error-correcting one-way quantum computation with global entangling gates University of Calgary | Publication | 2009-09-01 | J. Joo, D. Feder |

Bose condensates in a harmonic trap near the critical temperature University of Calgary | Publication | 2000-05-01 | T. Bergeman, D. Feder, N. L. Balazs, B. I. Schneider |

Numerical approach to the ground and excited states of a Bose-Einstein condensed gas confined in a completely anisotropic trap University of Calgary | Publication | 1999-03-01 | B. I. Schneider, D. Feder |

Beyond the Thomas-Fermi approximation for a trapped condensed Bose-Einstein gas University of Calgary | Publication | 1998-10-01 | A. L. Fetter, D. Feder |

Validity of the lowest-Landau-level approximation for rotating Bose gases University of Calgary | Publication | 2006-09-01 | A. G. Morris, D. Feder |

Gaussian Potentials Facilitate Access to Quantum Hall States in Rotating Bose Gases University of Calgary | Publication | 2007-12-01 | A. G. Morris, D. Feder |

Topological entropy of quantum Hall states in rotating Bose gases University of Calgary | Publication | 2009-01-01 | A. G. Morris, D. Feder |

One-way quantum computing in optical lattices with many-atom addressing University of Calgary | Publication | 2008-09-01 | T. P. Friesen, D. Feder |

Strategies for measurement-based quantum computation with cluster states transformed by stochastic local operations and classical communication University of Calgary | Publication | 2011-10-01 | A. D'Souza, D. Feder |

Bose-Hubbard model for universal quantum-walk-based computation University of Calgary | Publication | 2012-05-01 | M. S. Underwood, D. Feder |

Synthetic spin-orbit interactions and magnetic fields in ring-cavity QED University of Calgary | Publication | 2014-01-01 | F. Mivehvar, D. Feder |

Quantum search with interacting Bose-Einstein condensates University of Calgary | Publication | 2013-09-01 | M. E. Kahou, D. Feder |

One-way quantum computing in optical lattices with many atom addressing University of Calgary | Publication | 2008-01-01 | T. Friesen, D. Feder |

Cluster States from imperfect entanglement University of Calgary | Publication | 2008-01-01 | M. Garrett, D. Feder |

Stochastic one-way quantum computing with ultracold atoms in optical lattices University of Calgary | Presentation | 2006-02-25 | M. Garrett, D. Feder |

Entangled pure state classification with stabilizers University of Calgary | Presentation | 2006-06-16 | J. Briët, D. Feder |

SLOCC equivalence of graph states and Hamiltonian ground statesMeasurement-based quantum computation (MBQC) requires a massively entangled resource state (such as a cluster state) as input. Experimental efforts towards generating such states have typically focused on performing global entangling operations on uncorrelated qubits. As the states that result from this type of procedure are not generally ground states, they are very sensitive to decoherence effects. A more robust resource would be one that is in fact a ground state of some Hamiltonian that exhibits a reasonably large energy gap between the ground state and the various excited states. We discuss the possibility of finding simple two-body Hamiltonians whose ground states are equivalent to resource states for MBQC under stochastic protocols comprised solely of local operations and classical communication. University of Calgary | Presentation | 2008-02-15 | A. D'Souza, D. Feder |

Error-correcting one-way quantum computation with global entangling gates University of Calgary | Presentation | 2009-05-05 | J. Joo, D. Feder |

Quantum search by quantum cellular automataQuantum Cellular Automata provide a description of quantum systems whose evolution is periodic in space and time. The drawing feature of QCA is that evolution is described by global operations that can be decomposed into periodic components, instead of operations on individual data registers. While it has been demonstrated that QCA can be constructed that are equivalent to the circuit model, these constructions do not lend themselves easily to a physical system. However it is possible to create QCA that, while they do not correspond to a fully programmable quantum computer, can nevertheless implement quantum algorithms. By drawing on the connection between quantum walks and QCA, I demonstrate that it is possible to implement Grover's algorithm on a system that may be readily translated to a physical system. University of Calgary | Presentation | 2010-02-19 | V. D. Van, D. Feder |

Strategies for measurement-based quantum computation with SLOCC-transformed cluster statesUniversal quantum computation can be accomplished via projective single-qubit measurements on a highly entangled resource state, together with classical feedforward of the measurement results. The best-known example of such a resource state is the cluster state, on which judiciously chosen single-qubit measurements can be used to simulate an arbitrary quantum circuit with a number of measurements that is linear in the number of gates. We examine the power of the orbit of cluster states under GL(2,C), also known as the SLOCC-equivalence class, as a resource for universal computation driven strictly by projective measurements. We identify circumstances under which such states constitute resources for random-length computation, in one case quasi-deterministically and in another probabilistically. University of Calgary | Presentation | 2011-02-18 | A. D'Souza, D. Feder |

Topological entropy of quantum hall states in rotating Bose gasesUsing exact numerical simulations of a small number of harmonically trapped ultracold alkali atoms at high rotation, we calculate the von Neumann entropy of the bosonic variant of the Laughlin and Pfaffian quantum Hall states. It has recently been shown that this entropy has a linear scaling with the boundary size. The y-intercept of this scaling relation corresponds to a universal quantity known as the topological entropy that is related to the quantum Hall filling factor. Through finite size scaling, we have extracted this quantity and compare the outcome to expected results.
University of Calgary | Presentation | 2008-03-10 | A. Morris, D. Feder |

Ground states as resources for universal measurement-based quantum computingMeasurement-based quantum computation (MBQC) requires a massively entangled resource state (such as a cluster state) as input. Experimental efforts towards generating such states have typically focused on performing global entangling operations on uncorrelated qubits. As the states that result from this type of procedure are not generally ground states, they are very sensitive to decoherence effects. A more robust resource would be one that is in fact a ground state of some Hamiltonian that exhibits a reasonably large energy gap between the ground state and the various excited states. We will discuss the possibility of finding simple two-body spin Hamiltonians whose ground states are equivalent to resource states for MBQC under stochastic protocols comprised solely of local operations and classical communication.
University of Calgary | Presentation | 2008-03-11 | A. D'Souza, D. Feder |

Error-correcting one-way quantum computation with global entangling gates University of Calgary | Presentation | 2009-08-19 | J. Joo, D. Feder |

Concatenated logical cluster state using 5-qubit QECCThe highly entangled quantum states known as cluster states constitute a universal resource for measurement-based quantum computing (MBQC). How to construct a fault-tolerant protocol for MBQC is still an open question, however. We show how to build concatenated cluster states for MBQC using the five-qubit quantum error-correcting code. These states can be built by a series of single-qubit Hadamard and two-qubit controlled-phase gates. The number of operations is significantly reduced through the use of local complementation graph operations. Error thresholds are investigated and compared with current experimental capabilities. University of Calgary | Presentation | 2010-03-17 | J. Joo, D. Feder |

The theory of local complementation is useful for building concatenated error-correction codes University of Calgary | Presentation | 2010-05-26 | J. Joo, D. Feder |

Discontinuous quantum walks for universal computation University of Calgary | Presentation | 2010-07-14 | M. Underwood, D. Feder |

(Almost) No entanglement is needed for deterministic single-qubit gate teleportationComputers having access to quantum entanglement are widely believed to be more powerful than those that do not. Quantum states that are
entangled have been shown to be resources for a vast array of information processing tasks. One such task is gate teleportation, wherein arbitrary single-qubit operations can be effected
deterministically by means of local measurements on a highly entangled resource state. We will show that, under certain circumstances, deterministic gate teleportation can still be accomplished using resource states that are locally almost pure. University of Calgary | Presentation | 2010-07-16 | A. D'Souza, D. Feder |

A spatial search with quantum cellular automataQuantum Cellular Automata provide a description of quantum systems whose evolution is periodic in space and time. The salient feature of QCA is
that evolution is described by global operations that can be decomposed into local periodic components, instead of operations on individual data registers. While it has been demonstrated that QCA can be constructed that are equivalent to the circuit model, these constructions do not lend themselves easily to a physical implementation. However it is possible to create QCA that, while not corresponding to a fully programmable quantum computer, can nevertheless perform useful quantum algorithms. By drawing
on the connection between quantum walks and QCA, I demonstrate that it is possible to implement Grover's algorithm on a spin system that may be more readily translated to a physical implementation. University of Calgary | Presentation | 2010-07-16 | V. D. Van, D. Feder |

A spatial search with quantum cellular automataQuantum Cellular Automata provide a description of quantum systems whose evolution is periodic in space and time. The salient feature of QCA is that evolution is described by global operations that can be decomposed into local periodic components, instead of operations on individual data registers. While it has been demonstrated that QCA can be constructed that are equivalent to the circuit model, these constructions do not lend themselves easily to a physical implementation. However it is possible to create QCA that, while not corresponding to a fully programmable quantum computer, can nevertheless perform useful quantum algorithms. By drawing on the connection between quantum walks and QCA, I demonstrate that it is possible to implement Grover's algorithm on a spin system that may be more readily translated to a physical implementation. University of Calgary | Presentation | 2010-08-26 | V. D. Van, D. Feder |

Universal quantum computation within the Bose-Hubbard modelWe present a novel scheme for universal quantum computation based on spinless bosons hopping on a two-dimensional lattice with on-site interactions. Our setup is comprised of a $2\times n$ lattice for an $n$-qubit system; the two rows correspond to the computational basis states, and a boson in each column encodes a qubit. The system is initialized with $n$ bosons occupying the $n$ sites of the $|0\rangle$ row, and the lattice deep enough to prevent tunneling. Arbitrary single-qubit $X$ rotations are implemented by tuning the tunneling strength between the $|0\rangle$ and $|1\rangle$ sites of the appropriate column, and $Z$ rotations by applying a local potential to the $|1\rangle$ site. Entanglement is generated by hopping between the $|1\rangle$ sites of adjacent qubits; by tuning the on-site interaction strength of the bosons, a non-trivial controlled phase is acquired if these two qubits are in the state $|11\rangle$. Because the quantum information is encoded entirely in the lattice positions of the bosons, the encoded qubits are inherently robust against decoherence. An implementation in terms of ultracold atoms in optical lattices is suggested. University of Calgary | Presentation | 2011-03-21 | M. Underwood, D. Feder |

Ultracold atoms in a cavity: synthetic gauge fields and cavity-mediated long-range interactionsThe collective coupling of ultracold neutral atoms to electromagnetic fields in cavity QED results in cavity-mediated long-range atom-atom interactions, paving the way for the realization of strongly correlated states and collective phenomena. That said, quantum Hall and topological insulator states are not directly accessible in these environments because they require the coupling of the particles' center-of-mass motion to external magnetic fields and to internal spin degrees of freedom, respectively. In this work, we show that coupling three-level atoms to two counter-propagating ring-cavity modes in the Λ scheme can give rise to synthetic spin-orbit interactions and large synthetic magnetic fields. In the presence of an additional optical lattice, the Hamiltonian in the weak-coupling regime corresponds to an effective spin-orbit coupled Hubbard model for the atoms in the first Bloch band, including a variety of long-range atom-atom interactions. The eigenstates of this model are explored for various choices of the parameters. University of Calgary | Presentation | 2014-03-06 | F. Mivehvar, D. Feder |

Hard-core lattice bosons: new insights from algebraic graph theory University of Calgary | Presentation | 2014-03-07 | R. W. Squires, D. Feder |

Winding numbers in rotating Bose gasesThe exact ground states of zero-temperature rotating Bose gases confined in quasi-two-dimensional harmonic traps are investigated numerically, for small numbers of alkali atoms. As the rotation frequency increases, the interacting Bose gas undergoes a series of transitions from one quantum Hall state to another. By tracking the change in ground state energy with an applied phase twist, we are able to calculate the winding (Chern) number characterizing the topological nature of the various bosonic quantum Hall states.
University of Calgary | Presentation | 2006-03-15 | A. Morris, D. Feder |

Stochastic one-way quantum computing with ultracold atoms in optical latticesThe one-way model of quantum computation has the advantage over conventional approaches of allowing all entanglement to be prepared in a single initial step prior to any logical operations, generating the so-called cluster state. One of the most promising experimental approaches to the formation of such a highly entangled resource employs a gas of ultracold atoms confined in an optical lattice. Starting with a Mott insulator state of pseudospin-1/2 bosons at unit filling, an Ising-type interaction can be induced by allowing weak nearest-neighbor tunneling, resulting in the formation of a cluster state. An alternate approach is to prepare each spin state in its own sublattice, and induce collisional phase shifts by varying the laser polarizations. In either case, however, there is a systematic phase error which is likely to arise, resulting in the formation of imperfect cluster states. We will present various approaches to one-way quantum computation using imperfect cluster states, and show that the algorithms are necessarily stochastic if the error syndrome is not known.
University of Calgary | Presentation | 2006-03-16 | M. Garrett, D. Feder |

Exact Calculations for Ultracold Rotating Bose GasesThrough the use of exact diagonalization, we have investigated general properties of harmonically trapped, rotating ultracold bose gases having both attractive and repulsive interactions. We have calculated the low energy spectrum for a small number of bosons and have used the similarities between fermions in a strong magnetic field and bosons subjected to rotation in order to identify different bosonic fractional quantum states which may be used to perform topological quantum computations. University of Calgary | Presentation | 2005-03-22 | A. Morris, D. Feder |

Quantum walks with ultracold atoms in optical latticesThe behavior of several ultracold atoms (bosons or fermions) undergoing a quantum walk in a one-dimensional optical lattice is investigated numerically. Both discrete and continuous time quantum walks are implemented, the latter within the context of a tight-binding model. Because the quantum statistics place constraints on the overlap between different many-particle states, the Hamiltonian generates a one-particle quantum walk on a graph with vertices of higher degree. The results will be used to make predictions for experiments with ultracold atoms in optical lattices, as well as to explore fundamental issues related to quantum information, such as graph covering and the role of entanglement. University of Calgary | Presentation | 2005-03-23 | S. van der Lee, D. Feder |

Using custom potentials to access quantum Hall states in rotating Bose gasesThe exact ground states of zero-temperature rotating Bose gases confined in quasi-two-dimensional harmonic traps are studied numerically, for small numbers of alkali atoms. As the rotation frequency increases, the interacting Bose gas undergoes a series of transitions from one quantum Hall state to another. We have investigated the possibility of facilitating access to specific quantum Hall states through the addition of customized potentials to the existing trapping potential. For the right choice of potential, we show that creation of predetermined quantum Hall states in rotating Bose gases should be possible using current experimental setups. (Research supported by NSERC, iCORE and CFI)
University of Calgary | Presentation | 2007-03-05 | A. Morris, D. Feder |

Perfect GHZ states from imperfect cluster states in optical latticesCluster states form a class of non-separable multipartite graph states, the entanglement of which is exceptionally persistent against the effects of single-qubit measurements. One of the most promising experimental approaches to the formation of cluster states employs a gas of ultracold atoms confined in an optical lattice. Starting with a Mott insulator state of pseudospin-1/2 bosons at unit filling, cluster states can be generated efficiently by preparing each spin state in its own sublattice, and inducing collisional phase shifts by varying the laser polarizations. In practice, systematic phase errors are expected to arise during this entangling process, resulting in the formation of imperfect cluster states. In this poster, we present a technique for using imperfect cluster states to distill perfect GHZ states. Applications include fault-tolerant quantum computing, open-destination quantum teleportation, quantum cryptography, Heisenberg-limited spectroscopy, and atomic clocks University of Calgary | Presentation | 2007-03-06 | M. Garrett, D. Feder |

One-way quantum computing in optical lattices with many atom measurementsIn one-way quantum computation single qubit measurements on a highly entangled state, known as a cluster state, are sufficient to perform universal quantum computation. One of the most promising approaches for generating the cluster state is to manipulate ultracold atoms in optical lattices. Unfortunately, the small lattice spacing places severe constraints on the ability to sequentially measure the states of individual atoms by external lasers, a crucial requirement for one-way computing. With current technology, we are generally limited to many atom measurements. We have developed a deterministic protocol for one-way quantum computing based on many atom measurements on an optical lattice cluster state, requiring only polynomial classical overhead. Our scheme opens the way toward concrete experimental quantum computing in neutral atom systems. \r\n University of Calgary | Presentation | 2007-03-07 | T. Friesen, D. Feder |

Fermionic resources for quantum teleportationThe measurement-based quantum computing (MBQC) model requires the
creation of a massively entangled ``resource state,'' on which
computation proceeds via single-qubit measurements. Although 2D
resource states are believed necessary for universal MBQC, 1D states
can serve as resources for certain tasks as well, such as quantum
teleportation. One possible route to a resource state is to cool a
gapped, two-body system whose ground state encodes the resource. I
will discuss our recent work in this area, in which we investigate
candidate fermionic systems using the Density Matrix Renormalization
Group method and the Matrix Product States description of highly
entangled 1D states. University of Calgary | Presentation | 2010-03-18 | A. D'Souza, D. Feder |

Quantum walks in momentum spaceIt has recently been shown that universal quantum computation can be achieved via quantum walks, both continuous [1] and discrete [2]. In analogy to the standard circuit model for quantum algorithms, these quantum walk-based proposals require a `rail' for each computational basis state, meaning that the number of these rails must grow exponentially with the number of qubits. The quantum walker travels from left to right along the rails, and gates are enacted via additions to the rails or connections among them. While these methods employ large numbers of spatial states for even simple gates on small numbers of qubits, they only require a small number of momentum eigenstates. With this in mind, we explore the promise of performing quantum walks in momentum space to drastically reduce the number of required resources. \\[4pt] [1] Childs. Phys.\ Rev.\ Lett.\ \textbf{102} 180501 (2009) \\[0pt] [2] Lovett et al. arXiv:0910.1024v2 [quant-ph] (2009) University of Calgary | Presentation | 2010-03-15 | M. Underwood, D. Feder |

Deterministic random-length computation with weakly entangled cluster statesUniversal quantum computation can be accomplished via single-qubit measurements on a highly entangled resource state, together with classical feedforward of the measurement results. The best-known example of such a resource state is the cluster state, on which judiciously chosen single-qubit measurements can be used to simulate an arbitrary quantum circuit with a number of measurements that is linear in the number of gates. We examine the power of the orbit of the cluster states under GL(2,C), also known as the SLOCC equivalence class of the cluster state, as a resource for deterministic universal computation. We find that, under certain circumstances, these states do indeed constitute resources for such computations, but of random length. University of Calgary | Presentation | 2011-03-21 | A. D'Souza, D. Feder |

Single-qubit unitary gates by graph scattering University of Calgary | Publication | 2011-12-01 | B. A. Blumer, M. S. Underwood, D. Feder |

Fermionized photons in the ground state of one-dimensional coupled cavities University of Calgary | Publication | 2013-01-01 | A. D'Souza, B. C. Sanders, D. Feder |

Nonlinear phase shifts of light trapped in a two-component Bose-Einstein condensate University of Calgary | Publication | 2014-01-01 | C. Trail, K. Almutairi, D. Feder, B. C. Sanders |

SLOCC-Equivalence of Pure States and Graph StatesMeasurement-based quantum computation (MBQC) is a model of quantum computing allowing for information processing by means of adaptive local measurements on a resource state. This resource state is a massively entangled many-body state, the best known example of which is the cluster state. While the cluster is not itself a non-degenerate ground state of a realistic Hamiltonian, other resources that are equivalent to the cluster under stochastic local operations and classical communication (SLOCC) may be. We describe a protocol for determining SLOCC-equivalence between arbitrary pure states and graph states, a generalization of cluster states. University of Calgary | Presentation | 2010-02-19 | A. D'Souza, J. Briët, D. Feder |

Superfluid to Mott-Insulator Transition in Thermodynamic Limit of 1D Coupled Cavity Array University of Calgary | Presentation | 2012-02-29 | A. D'Souza, B. C. Sanders, D. Feder |

Single-qubit gates by graph scatteringContinuous-time quantum walkers with tightly peaked momenta can simulate quantum computations by scattering off finite graphs. We enumerate all single-qubit gates that can be enacted by scattering off a single graph on up to $n=9$ vertices at certain momentum values, and provide numerical evidence that the number of such gates grows exponentially with $n$. The single-qubit rotations are about axes distributed roughly uniformly on the Bloch sphere, and rotations by both rational and irrational multiples of $\pi$ are found. University of Calgary | Presentation | 2012-03-02 | M. Underwood, B. Blumer, D. Feder |

Tonks-Girardeau phase in 1D coupled cavity arrays University of Calgary | Presentation | 2012-05-29 | A. D'Souza, B. C. Sanders, D. Feder |

Microscopic Structure of a Vortex Line in a Dilute Superfluid Fermi Gas University of Calgary | Publication | 2003-05-01 | N. Nygaard, G. M. Bruun, C. W. Clark, D. Feder |

Watching Dark Solitons Decay into Vortex Rings in a Bose-Einstein Condensate University of Calgary | Publication | 2001-04-01 | B. P. Anderson, P. C. Haljan, C. A. Regal, D. Feder, L. A. Collins, C. W. Clark, E. A. Cornell |

Time-Dependent Computational Methods for Matter Under Extreme Conditions University of Calgary | Publication | 2014-12-01 | B. I. Schneider, K. R. Bartschat, X. Guan, D. Feder |

Vortex line in a neutral finite-temperature superfluid Fermi gas University of Calgary | Publication | 2004-05-01 | N. Nygaard, G. Bruun, B. Schneider, C. Clark, D. Feder |

Detecting topological transitions in two dimensions by Hamiltonian evolution University of Calgary | Publication | 2017-01-01 | W. Zhang, B. C. Sanders, S. Apers, S. Goyal, D. Feder |