1,581 research outputs found
Quantum walks on general graphs
Quantum walks, both discrete (coined) and continuous time, on a general graph
of N vertices with undirected edges are reviewed in some detail. The resource
requirements for implementing a quantum walk as a program on a quantum computer
are compared and found to be very similar for both discrete and continuous time
walks. The role of the oracle, and how it changes if more prior information
about the graph is available, is also discussed.Comment: 8 pages, v2: substantial rewrite improves clarity, corrects errors
and omissions; v3: removes major error in final section and integrates
remainder into other sections, figures remove
Bounds for mixing time of quantum walks on finite graphs
Several inequalities are proved for the mixing time of discrete-time quantum
walks on finite graphs. The mixing time is defined differently than in
Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for
particular examples of walks on a cycle, a hypercube and a complete graph,
quantum walks provide no speed-up in mixing over the classical counterparts. In
addition, non-unitary quantum walks (i.e., walks with decoherence) are
considered and a criterion for their convergence to the unique stationary
distribution is derived.Comment: This is the journal version (except formatting); it is a significant
revision of the previous version, in particular, it contains a new result
about the convergence of quantum walks with decoherence; 16 page
Coherent transport on Apollonian networks and continuous-time quantum walks
We study the coherent exciton transport on Apollonian networks generated by
simple iterative rules. The coherent exciton dynamics is modeled by
continuous-time quantum walks and we calculate the transition probabilities
between two nodes of the networks. We find that the transport depends on the
initial nodes of the excitation. For networks less than the second generation
the coherent transport shows perfect revivals when the initial excitation
starts at the central node. For networks of higher generation, the transport
only shows partial revivals. Moreover, we find that the excitation is most
likely to be found at the initial nodes while the coherent transport to other
nodes has a very low probability. In the long time limit, the transition
probabilities show characteristic patterns with identical values of limiting
probabilities. Finally, the dynamics of quantum transport are compared with the
classical transport modeled by continuous-time random walks.Comment: 5 pages, 6 figues. Submitted to Phys. ReV.
Conditional Quantum Walk and Iterated Quantum Games
Iterated bipartite quantum games are implemented in terms of the
discrete-time quantum walk on the line. Our proposal allows for conditional
strategies, as two rational agents make a choice from a restricted set of
two-qubit unitary operations. Several frequently used classical strategies give
rise to families of corresponding quantum strategies. A quantum version of the
Prisoner's Dilemma in which both players use mixed strategies is presented as a
specific example. Since there are now quantum walk physical implementations at
a proof-of principle stage, this connection may represent a step towards the
experimental realization of quantum games.Comment: Revtex 4, 6 pages, 3 figures. Expanded version with one more figure
and updated references. Abstract was rewritte
Effects of non-local initial conditions in the Quantum Walk on the line
We report an enhancement of the decay rate of the survival probability when
non-local initial conditions in position space are considered in the Quantum
Walk on the line. It is shown how this interference effect can be understood
analytically by using previously derived results. Within a restricted position
subspace, the enhanced decay is correlated with a maximum asymptotic
entanglement level while the normal decay rate corresponds to initial relative
phases associated to a minimum entanglement level.Comment: 5 pages, 1 figure, Elsevier style, to appear in Physica
Continuous-time quantum walks on one-dimension regular networks
In this paper, we consider continuous-time quantum walks (CTQWs) on
one-dimension ring lattice of N nodes in which every node is connected to its
2m nearest neighbors (m on either side). In the framework of the Bloch function
ansatz, we calculate the spacetime transition probabilities between two nodes
of the lattice. We find that the transport of CTQWs between two different nodes
is faster than that of the classical continuous-time random walk (CTRWs). The
transport speed, which is defined by the ratio of the shortest path length and
propagating time, increases with the connectivity parameter m for both the
CTQWs and CTRWs. For fixed parameter m, the transport of CTRWs gets slow with
the increase of the shortest distance while the transport (speed) of CTQWs
turns out to be a constant value. In the long time limit, depending on the
network size N and connectivity parameter m, the limiting probability
distributions of CTQWs show various paterns. When the network size N is an even
number, the probability of being at the original node differs from that of
being at the opposite node, which also depends on the precise value of
parameter m.Comment: Typos corrected and Phys. ReV. E comments considered in this versio
Encoded Universality for Generalized Anisotropic Exchange Hamiltonians
We derive an encoded universality representation for a generalized
anisotropic exchange Hamiltonian that contains cross-product terms in addition
to the usual two-particle exchange terms. The recently developed algebraic
approach is used to show that the minimal universality-generating encodings of
one logical qubit are based on three physical qubits. We show how to generate
both single- and two-qubit operations on the logical qubits, using suitably
timed conjugating operations derived from analysis of the commutator algebra.
The timing of the operations is seen to be crucial in allowing simplification
of the gate sequences for the generalized Hamiltonian to forms similar to that
derived previously for the symmetric (XY) anisotropic exchange Hamiltonian. The
total number of operations needed for a controlled-Z gate up to local
transformations is five. A scalable architecture is proposed.Comment: 11 pages, 4 figure
Perdeuterated cyanobiphenyl liquid crystals for infrared applications
Perdeuterated 4'-pentyl-4-cyanobiphenyl (D5CB) was synthesized and its physical properties evaluated and compared to those of 5CB. D5CB retains physical properties similar to those of 5CB, such as phase transition temperatures, dielectric constants, and refractive indices. An outstanding feature of D5CB is that it exhibits a much cleaner and reduced infrared absorption. Perdeuteration, therefore, extends the usable range of liquid crystals to the mid infrared by significantly reducing the absorption in the near infrared, which is essential for telecom applications
Simulating adiabatic evolution of gapped spin systems
We show that adiabatic evolution of a low-dimensional lattice of quantum
spins with a spectral gap can be simulated efficiently. In particular, we show
that as long as the spectral gap \Delta E between the ground state and the
first excited state is any constant independent of n, the total number of
spins, then the ground-state expectation values of local operators, such as
correlation functions, can be computed using polynomial space and time
resources. Our results also imply that the local ground-state properties of any
two spin models in the same quantum phase can be efficiently obtained from each
other. A consequence of these results is that adiabatic quantum algorithms can
be simulated efficiently if the spectral gap doesn't scale with n. The
simulation method we describe takes place in the Heisenberg picture and does
not make use of the finitely correlated state/matrix product state formalism.Comment: 13 pages, 2 figures, minor change
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