3,881 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
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
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
Crustal extension and transform faulting in the southern Basin Range Province
The author has identified the following significant results. Field reconnaissance and study of geologic literature guided by analysis of ERTS-1 MSS imagery have led to a hypothesis of tectonic control of Miocene volcanism, plutonism, and related mineralization in part of the Basin Range Province of southern Nevada and northwestern Arizona. The easterly trending right-lateral Las Vegas Shear Zone separates two volcanic provinces believed to represent areas of major east-west crustal extension. One volcanic province is aligned along the Colorado River south of the eastern termination of the Las Vegas Shear Zone; the second province is located north of the western termination of the shear zone in southern Nye County, Nevada. Geochronologic, geophysical, and structural evidence suggests that the Las Vegas Shear Zone may have formed in response to crustal extension in the two volcanic provinces in a manner similar to the formation of a ridge-ridge transform fault, as recognized in ocean floor tectonics
Numerical Analysis of the Capacities for Two-Qubit Unitary Operations
We present numerical results on the capacities of two-qubit unitary
operations for creating entanglement and increasing the Holevo information of
an ensemble. In all cases tested, the maximum values calculated for the
capacities based on the Holevo information are close to the capacities based on
the entanglement. This indicates that the capacities based on the Holevo
information, which are very difficult to calculate, may be estimated from the
capacities based upon the entanglement, which are relatively straightforward to
calculate.Comment: 9 pages, 10 figure
Architectures for a quantum random access memory
A random access memory, or RAM, is a device that, when interrogated, returns
the content of a memory location in a memory array. A quantum RAM, or qRAM,
allows one to access superpositions of memory sites, which may contain either
quantum or classical information. RAMs and qRAMs with n-bit addresses can
access 2^n memory sites. Any design for a RAM or qRAM then requires O(2^n)
two-bit logic gates. At first sight this requirement might seem to make large
scale quantum versions of such devices impractical, due to the difficulty of
constructing and operating coherent devices with large numbers of quantum logic
gates. Here we analyze two different RAM architectures (the conventional fanout
and the "bucket brigade") and propose some proof-of-principle implementations
which show that in principle only O(n) two-qubit physical interactions need
take place during each qRAM call. That is, although a qRAM needs O(2^n) quantum
logic gates, only O(n) need to be activated during a memory call. The resulting
decrease in resources could give rise to the construction of large qRAMs that
could operate without the need for extensive quantum error correction.Comment: 10 pages, 7 figures. Updated version includes the answers to the
Refere
Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations
In principle a quantum system could be used to simulate another quantum
system. The purpose of such a simulation would be to obtain information about
problems which cannot be simulated with a classical computer due to the
exponential increase of the Hilbert space with the size of the system and which
cannot be measured or controlled in an actual experiment. The system will
interact with the surrounding environment, with the other particles in the
system and be implemented using imperfect controls making it subject to noise.
It has been suggested that noise does not need to be controlled to the same
extent as it must be for general quantum computing. However the effects of
noise in quantum simulations and how to treat them are not completely
understood. In this paper we study an existing quantum algorithm for the
one-dimensional Fano-Anderson model to be simulated using a liquid-state NMR
device. We calculate the evolution of different initial states in the original
model, and then we add interacting spins to simulate a more realistic
situation. We find that states which are entangled with their environment, and
sometimes correlated but not necessarily entangled have an evolution which is
described by maps which are not completely positive. We discuss the conditions
for this to occur and also the implications.Comment: Revtex 4-1, 14 pages, 21 figures, version 2 has typos corrected and
acknowledgement adde
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