8,362 research outputs found
Quantum phase estimation algorithms with delays: effects of dynamical phases
The unavoidable finite time intervals between the sequential operations
needed for performing practical quantum computing can degrade the performance
of quantum computers. During these delays, unwanted relative dynamical phases
are produced due to the free evolution of the superposition wave-function of
the qubits. In general, these coherent "errors" modify the desired quantum
interferences and thus spoil the correct results, compared to the ideal
standard quantum computing that does not consider the effects of delays between
successive unitary operations. Here, we show that, in the framework of the
quantum phase estimation algorithm, these coherent phase "errors", produced by
the time delays between sequential operations, can be avoided by setting up the
delay times to satisfy certain matching conditions.Comment: 10 pages, no figur
On Quantum Algorithms
Quantum computers use the quantum interference of different computational
paths to enhance correct outcomes and suppress erroneous outcomes of
computations. In effect, they follow the same logical paradigm as
(multi-particle) interferometers. We show how most known quantum algorithms,
including quantum algorithms for factorising and counting, may be cast in this
manner. Quantum searching is described as inducing a desired relative phase
between two eigenvectors to yield constructive interference on the sought
elements and destructive interference on the remaining terms.Comment: 15 pages, 8 figure
Black hole state counting in loop quantum gravity
The two ways of counting microscopic states of black holes in the U(1)
formulation of loop quantum gravity, one counting all allowed spin network
labels j,m and the other only m labels, are discussed in some detail. The
constraints on m are clarified and the map between the flux quantum numbers and
m discussed. Configurations with |m|=j, which are sometimes sought after, are
shown to be important only when large areas are involved. The discussion is
extended to the SU(2) formulation.Comment: 5 page
Quantum Multi-object Search Algorithm with the Availability of Partial Information
Consider the unstructured search of an unknown number l of items in a large
unsorted database of size N. The multi-object quantum search algorithm consists
of two parts. The first part of the algorithm is to generalize Grover's
single-object search algorithm to the multi-object case and the second part is
to solve a counting problem to determine l.
In this paper, we study the multi-object quantum search algorithm (in
continuous time), but in a more structured way by taking into account the
availability of partial information. The modeling of available partial
information is done simply by the combination of several prescribed, possibly
overlapping, information sets with varying weights to signify the reliability
of each set. The associated statistics is estimated and the algorithm
efficiency and complexity are analyzed.
Our analysis shows that the search algorithm described here may not be more
efficient than the unstructured (generalized) multi-object Grover search if
there is ``misplaced confidence''. However, if the information sets have a
``basic confidence'' property in the sense that each information set contains
at least one search item, then a quadratic speedup holds on a much smaller data
space, which further expedite the quantum search for the first item.Comment: 17 pages, 1 figur
Preparing ground states of quantum many-body systems on a quantum computer
Preparing the ground state of a system of interacting classical particles is
an NP-hard problem. Thus, there is in general no better algorithm to solve this
problem than exhaustively going through all N configurations of the system to
determine the one with lowest energy, requiring a running time proportional to
N. A quantum computer, if it could be built, could solve this problem in time
sqrt(N). Here, we present a powerful extension of this result to the case of
interacting quantum particles, demonstrating that a quantum computer can
prepare the ground state of a quantum system as efficiently as it does for
classical systems.Comment: 7 pages, 1 figur
Quantum enhancement of N-photon phase sensitivity by interferometric addition of down-converted photon pairs to weak coherent light
It is shown that the addition of down-converted photon pairs to coherent
laser light enhances the N-photon phase sensitivity due to the quantum
interference between components of the same total photon number. Since most of
the photons originate from the coherent laser light, this method of obtaining
non-classical N-photon states is much more efficient than methods based
entirely on parametrically down-converted photons. Specifically, it is possible
to achieve an optimal phase sensitivity of about delta phi^2=1/N^(3/2), equal
to the geometric mean of the standard quantum limit and the Heisenberg limit,
when the average number of down-converted photons contributing to the N-photon
state approaches (N/2)^(1/2).Comment: 21 pages, including 6 figures. Extended version gives more details on
down-conversion efficiencies and clarifies the relation between phase
sensitivity and squeezing. The title has been changed in order to avoid
misunderstandings regarding these concept
Quantum state estimation
New algorithm for quantum state estimation based on the maximum likelihood
estimation is proposed. Existing techniques for state reconstruction based on
the inversion of measured data are shown to be overestimated since they do not
guarantee the positive definiteness of the reconstructed density matrix.Comment: 4 pages, twocolumn Revte
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