## Profile
## Outputs
Title | Category | Date | Authors |
Fermi-Frenet coordinates for space-like curves University of Calgary | Publication | 2010-01-01 | M. Underwood, K. -. Marzlin | Geometric phase in optical fibres University of Calgary | Publication | 2006-01-01 | M. Underwood, K. -. Marzlin | Fermi-Frenet coordinates for space-like curves We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's world line, to a coordinate system in a neighbourhood of the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are fixed using a covariant Frenet triad, analogous to that of classical differential geometry, so that the metric can be expressed in terms of the curvature and torsion of the spatial curve. This construction is used to analyze the covariant definition of inertial forces felt by an observer constrained to motion upon the worldsheet. We also consider the application of these coordinates to examining photon propagation in arbitrarily-curved optical fibres. University of Calgary | Presentation | 2007-06-18 | M. Underwood, K. Marzlin | Manipulation and storage of qubits via CRIB We present a new technique for using a quantum memory device to perform arbitrary rotations of qubits living in the two-dimensional Hilbert space spanned by the time-bin states |early〉 and |late〉. The CRIB protocol [1, 2, 3, 4] (controlled and reversible inhomogeneous broadening) allows the quantum information encoded in a photon state to be stored in the atomic coherences of a collection of rare-earth ions in a doped crystal or optical ﬁbre. This is achieved by artificially broadening the inhomogeneous line width of an atomic transition within the medium in a reversible manner such that all Fourier components of the input light ﬁeld can be absorbed. When this is the case one can show that later reversing the applied detuning (i.e. letting Δ→−Δ) and applying a phase-matching operation allows the equations of motion for a forward-propagating pulse to be transformed into a time-reversed copy of the equations of motion for a backward-moving pulse. When done correctly this causes the atomic coherences to evolve back to their initial state and the input pulse to be re-emitted in the opposite direction. A modification to this protocol allows an input pulse in a well-defined time bin to be recalled in a superposition of |early> and |late>, or more than two different states. We have numerically simulated the Maxwell-Bloch equations describing the interaction of a classical electric ﬁeld with an ensemble of two-level systems. In the modified version of the CRIB protocol we perform the rephasing operation on the absorbing medium at different times for two spatially distinct sections. This results in two output pulses. By modifying the relative size of the two spatial sections being rephased we are able to tailor the ratio of the amplitudes of the output pulses. The time difference between the pulses is easily controlled, so by associating the ﬁrst (second) pulse with the early (late) time bin we have eﬀectively rotated the initial pulse into a superposition state with coefficients that depend on the amplitudes of the output pulses. We investigate a number of variations on this theme including different input pulse shapes and detuning proﬁles. We look at different coherence times and temporal separations of the output pulses, and consider output in both the forward and backward directions. In each case the recall efficiency provides a ﬁgure of merit.
**References** [1] S. A. Moiseev and S. Kröll, Phys. Rev. Lett. **87**, 173601 (2001) [2] M. Nilsson and S. Kröll, Opt. Commun. **247** 292 (2005) [3] B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll, and J. I. Cirac, Phys. Rev. A. **73**,\\r\\n020302(R) (2006) [4] A. L. Alexander, J. J. Longdell, N. B. Manson, and M. J. Sellars, Phys. Rev. Lett. **96**, 043602 (2006) University of Calgary, The University of Calgary | Presentation | 2008-01-26 | M. Underwood, K. Marzlin, W. Tittel | Adapting CRIB-based memories to photon state manipulation University of Calgary, The University of Calgary | Presentation | 2008-08-21 | M. Underwood, K. Marzlin, S. Moiseev, W. Tittel | Discontinuous quantum walks for universal computation University of Calgary | Presentation | 2010-07-14 | M. Underwood, 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 | 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 | 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 | Universal quantum computation by discontinuous quantum walk University of Calgary | Publication | 2010-01-01 | M. Underwood | Relaxing symmetry in CRIB: Combining quantum state storage with data transformationRelaxing symmetry in CRIB: Combining quantum state storage with data
transformation
A. Delfan1, C. La Mela1, M. S. Underwood1, K.-P. Marzlin1, S. Moiseev1,2, and W. Tittel1
1Institute for Quantum Information Science, University of Calgary, Canada
2Kazan Physical-Technical Institute, Russian Academy of Science, Russia
Quantum repeater [1], based on sources of entangled photons, quantum memory, and
single and two qubit gates plus measurements, promise overcoming the distance barrier
of quantum communication protocols. We investigate extensions of a recent quantum
memory protocol based on controlled, reversible, inhomogeneous broadening (CRIB) [2-
5] for combining quantum state storage with transformation of the absorbed quantum
data. More precisely, we relax the symmetry requirement between inhomogeneous
broadening during quantum state absorption and recall, as required for perfectly timereversed
quantum dynamics. We will discuss possibilities for single qubit rotations based
on sequential rephrasing [3], and propose an experiment based on stimulated photon
echoes [4], which serves as a test-bed for the more efficient, CRIB based realization.
Other types of quantum (or classical) data transformation arise from asymmetry in the
rate of de-and rephasing, leading to data compression or decompression [5].
[1] H. Briegel, W. DÃ¼r, I. Cirac, P. Zoller, Phys. Rev. Lett. 81, 5932(1998)
[2] S. A. Moiseev and S. KrÃ¶ll, Phys Rev Lett. 87, 173601(2001),
[3] M. Nilsson and S. KrÃ¶ll, Opt. Commun. 247, 292 (2005),
[4]} A. L. Alexander, J. J. Longdell, N. B. Manson, and M. J. Sellars Phys. Rev. Lett. 96,
043602 (2006).
[5] B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kroll, and J. I. Cirac, Phys. Rev. A. 73,
020302(R) (2006).
[6] see contribution by M.S.Underwood et al.
[7] see contribution by A. Delfan et al.
[8] see contribution by S. Moiseev et al. University of Calgary, The University of Calgary | Presentation | 2008-01-25 | A. Delfan, C. La Mela, M. Underwood, K. Marzlin, S. Moiseev, W. Tittel | Beyond CRIB-based memory: combining storage with data manipulation University of Calgary, The University of Calgary | Presentation | 2008-03-18 | A. Delfan, C. La Mela, M. Underwood, K. Marzlin, S. Moiseev, W. Tittel | Combining quantum memory with state manipulation University of Calgary, The University of Calgary | Presentation | 2008-07-02 | A. Delfan, C. La Mela, M. Underwood, K. Marzlin, S. Moiseev, W. Tittel | Quantum communication in the QC2 lab University of Calgary, The University of Calgary | Presentation | 2007-09-26 | F. Bussières, P. Chan, A. Delfan, S. Hosier, C. La Mela, I. Lucio Martinez, X. Mo, J. Nguyen, A. Rubenok, E. Saglamyurek, J. Slater, M. Underwood, W. Tittel | Quantum communication in the QC2 lab University of Calgary, The University of Calgary | Presentation | 2007-09-26 | F. Bussières, P. Chan, A. Delfan, S. Hosier, C. La Mela, I. Lucio Martinez, X. Mo, J. Nguyen, A. Rubenok, E. Saglamyurek, J. Slater, M. Underwood, W. Tittel | Quantum cryptography in the QC2 lab University of Calgary, The University of Calgary | Presentation | 2007-11-28 | F. Bussières, P. Chan, A. Delfan, S. Hosier, C. La Mela, I. Lucio Martinez, X. Mo, J. Nguyen, A. Rubenok, E. Saglamyurek, N. Sinclair, J. Slater, M. Underwood, W. Tittel |
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