6,669 research outputs found

### Searching via walking: How to find a marked subgraph of a graph using quantum walks

We show how a quantum walk can be used to find a marked edge or a marked
complete subgraph of a complete graph. We employ a version of a quantum walk,
the scattering walk, which lends itself to experimental implementation. The
edges are marked by adding elements to them that impart a specific phase shift
to the particle as it enters or leaves the edge. If the complete graph has N
vertices and the subgraph has K vertices, the particle becomes localized on the
subgraph in O(N/K) steps. This leads to a quantum search that is quadratically
faster than a corresponding classical search. We show how to implement the
quantum walk using a quantum circuit and a quantum oracle, which allows us to
specify the resource needed for a quantitative comparison of the efficiency of
classical and quantum searches -- the number of oracle calls.Comment: 4 pages, 2 figure

### Quantum searches on highly symmetric graphs

We study scattering quantum walks on highly symmetric graphs and use the
walks to solve search problems on these graphs. The particle making the walk
resides on the edges of the graph, and at each time step scatters at the
vertices. All of the vertices have the same scattering properties except for a
subset of special vertices. The object of the search is to find a special
vertex. A quantum circuit implementation of these walks is presented in which
the set of special vertices is specified by a quantum oracle. We consider the
complete graph, a complete bipartite graph, and an $M$-partite graph. In all
cases, the dimension of the Hilbert space in which the time evolution of the
walk takes place is small (between three and six), so the walks can be
completely analyzed analytically. Such dimensional reduction is due to the fact
that these graphs have large automorphism groups. We find the usual quadratic
quantum speedups in all cases considered.Comment: 11 pages, 6 figures; major revision

### Continuous-variable blind quantum computation

Blind quantum computation is a secure delegated quantum computing protocol
where Alice who does not have sufficient quantum technology at her disposal
delegates her computation to Bob who has a fully-fledged quantum computer in
such a way that Bob cannot learn anything about Alice's input, output, and
algorithm. Protocols of blind quantum computation have been proposed for
several qubit measurement-based computation models, such as the graph state
model, the Affleck-Kennedy-Lieb-Tasaki model, and the
Raussendorf-Harrington-Goyal topological model. Here, we consider blind quantum
computation for the continuous-variable measurement-based model. We show that
blind quantum computation is possible for the infinite squeezing case. We also
show that the finite squeezing causes no additional problem in the blind setup
apart from the one inherent to the continuous-variable measurement-based
quantum computation.Comment: 20 pages, 8 figure

### Non-Markovian decoherence in the adiabatic quantum search algorithm

We consider an adiabatic quantum algorithm (Grover's search routine) weakly
coupled to a rather general environment, i.e., without using the Markov
approximation. Markovian errors generally require high-energy excitations (of
the reservoir) and tend to destroy the scalability of the adiabatic quantum
algorithm. We find that, under appropriate conditions (such as low
temperatures), the low-energy (i.e., non-Markovian) modes of the bath are most
important. Hence the scalability of the adiabatic quantum algorithm depends on
the infra-red behavior of the environment: a reasonably small coupling to the
three-dimensional electromagnetic field does not destroy the scaling behavior,
whereas phonons or localized degrees of freedom can be problematic. PACS:
03.67.Pp, 03.67.Lx, 03.67.-a, 03.65.Yz

### Searches on star graphs and equivalent oracle problems

We examine a search on a graph among a number of different kinds of objects
(vertices), one of which we want to find. In a standard graph search, all of
the vertices are the same, except for one, the marked vertex, and that is the
one we wish to find. We examine the case in which the unmarked vertices can be
of different types, so the background against which the search is done is not
uniform. We find that the search can still be successful, but the probability
of success is lower than in the uniform background case, and that probability
decreases with the number of types of unmarked vertices. We also show how the
graph searches can be rephrased as equivalent oracle problems

### Upper bounds on entangling rates of bipartite Hamiltonians

We discuss upper bounds on the rate at which unitary evolution governed by a
non-local Hamiltonian can generate entanglement in a bipartite system. Given a
bipartite Hamiltonian H coupling two finite dimensional particles A and B, the
entangling rate is shown to be upper bounded by c*log(d)*norm(H), where d is
the smallest dimension of the interacting particles, norm(H) is the operator
norm of H, and c is a constant close to 1. Under certain restrictions on the
initial state we prove analogous upper bound for the ancilla-assisted
entangling rate with a constant c that does not depend upon dimensions of local
ancillas. The restriction is that the initial state has at most two distinct
Schmidt coefficients (each coefficient may have arbitrarily large
multiplicity). Our proof is based on analysis of a mixing rate -- a functional
measuring how fast entropy can be produced if one mixes a time-independent
state with a state evolving unitarily.Comment: 14 pages, 4 figure

### Universal quantum computation by discontinuous quantum walk

Quantum walks are the quantum-mechanical analog of random walks, in which a
quantum `walker' evolves between initial and final states by traversing the
edges of a graph, either in discrete steps from node to node or via continuous
evolution under the Hamiltonian furnished by the adjacency matrix of the graph.
We present a hybrid scheme for universal quantum computation in which a quantum
walker takes discrete steps of continuous evolution. This `discontinuous'
quantum walk employs perfect quantum state transfer between two nodes of
specific subgraphs chosen to implement a universal gate set, thereby ensuring
unitary evolution without requiring the introduction of an ancillary coin
space. The run time is linear in the number of simulated qubits and gates. The
scheme allows multiple runs of the algorithm to be executed almost
simultaneously by starting walkers one timestep apart.Comment: 7 pages, revte

### Universal computation by multi-particle quantum walk

A quantum walk is a time-homogeneous quantum-mechanical process on a graph
defined by analogy to classical random walk. The quantum walker is a particle
that moves from a given vertex to adjacent vertices in quantum superposition.
Here we consider a generalization of quantum walk to systems with more than one
walker. A continuous-time multi-particle quantum walk is generated by a
time-independent Hamiltonian with a term corresponding to a single-particle
quantum walk for each particle, along with an interaction term. Multi-particle
quantum walk includes a broad class of interacting many-body systems such as
the Bose-Hubbard model and systems of fermions or distinguishable particles
with nearest-neighbor interactions. We show that multi-particle quantum walk is
capable of universal quantum computation. Since it is also possible to
efficiently simulate a multi-particle quantum walk of the type we consider
using a universal quantum computer, this model exactly captures the power of
quantum computation. In principle our construction could be used as an
architecture for building a scalable quantum computer with no need for
time-dependent control

### Structural lineaments in the southern Sierra Nevada, California

The author has identified the following significant results. Several lineaments observed in ERTS-1 MSS imagery over the southern Sierra Nevada of California have been studied in the field in an attempt to explain their geologic origins and significance. The lineaments are expressed topographically as alignments of linear valleys, elongate ridges, breaks in slope or combinations of these. Natural outcrop exposures along them are characteristically poor. Two lineaments were found to align with foliated metamorphic roof pendants and screens within granitic country rocks. Along other lineaments, the most consistant correlations were found to be alignments of diabase dikes of Cretaceous age, and younger cataclastic shear zones and minor faults. The location of several Pliocene and Pleistocene volcanic centers at or near lineament intersections suggests that the lineaments may represent zones of crustal weakness which have provided conduits for rising magma

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