8,333 research outputs found
Improved quantum algorithms for the ordered search problem via semidefinite programming
One of the most basic computational problems is the task of finding a desired
item in an ordered list of N items. While the best classical algorithm for this
problem uses log_2 N queries to the list, a quantum computer can solve the
problem using a constant factor fewer queries. However, the precise value of
this constant is unknown. By characterizing a class of quantum query algorithms
for ordered search in terms of a semidefinite program, we find new quantum
algorithms for small instances of the ordered search problem. Extending these
algorithms to arbitrarily large instances using recursion, we show that there
is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433
log_2 N queries, which improves upon the previously best known exact algorithm.Comment: 8 pages, 4 figure
A Semidefinite Programming Approach to Optimal Unambiguous Discrimination of Quantum States
In this paper we consider the problem of unambiguous discrimination between a
set of linearly independent pure quantum states. We show that the design of the
optimal measurement that minimizes the probability of an inconclusive result
can be formulated as a semidefinite programming problem. Based on this
formulation, we develop a set of necessary and sufficient conditions for an
optimal quantum measurement. We show that the optimal measurement can be
computed very efficiently in polynomial time by exploiting the many well-known
algorithms for solving semidefinite programs, which are guaranteed to converge
to the global optimum.
Using the general conditions for optimality, we derive necessary and
sufficient conditions so that the measurement that results in an equal
probability of an inconclusive result for each one of the quantum states is
optimal. We refer to this measurement as the equal-probability measurement
(EPM). We then show that for any state set, the prior probabilities of the
states can be chosen such that the EPM is optimal.
Finally, we consider state sets with strong symmetry properties and equal
prior probabilities for which the EPM is optimal. We first consider
geometrically uniform state sets that are defined over a group of unitary
matrices and are generated by a single generating vector. We then consider
compound geometrically uniform state sets which are generated by a group of
unitary matrices using multiple generating vectors, where the generating
vectors satisfy a certain (weighted) norm constraint.Comment: To appear in IEEE Transactions on Information Theor
Constructive Multiuser Interference in Symbol Level Precoding for the MISO Downlink Channel
This paper investigates the problem of interference among the simultaneous
multiuser transmissions in the downlink of multiple antennas systems. Using
symbol level precoding, a new approach towards the multiuser interference is
discussed along this paper. The concept of exploiting the interference between
the spatial multiuser transmissions by jointly utilizing the data information
(DI) and channel state information (CSI), in order to design symbol-level
precoders, is proposed. In this direction, the interference among the data
streams is transformed under certain conditions to useful signal that can
improve the signal to interference noise ratio (SINR) of the downlink
transmissions. We propose a maximum ratio transmission (MRT) based algorithm
that jointly exploits DI and CSI to glean the benefits from constructive
multiuser interference. Subsequently, a relation between the constructive
interference downlink transmission and physical layer multicasting is
established. In this context, novel constructive interference precoding
techniques that tackle the transmit power minimization (min power) with
individual SINR constraints at each user's receivers is proposed. Furthermore,
fairness through maximizing the weighted minimum SINR (max min SINR) of the
users is addressed by finding the link between the min power and max min SINR
problems. Moreover, heuristic precoding techniques are proposed to tackle the
weighted sum rate problem. Finally, extensive numerical results show that the
proposed schemes outperform other state of the art techniques.Comment: Submitted to IEEE Transactions on Signal Processin
Cognitive Beamforming for Multiple Secondary Data Streams With Individual SNR Constraints
In this paper, we consider cognitive beamforming for multiple secondary data
streams subject to individual signal-to-noise ratio (SNR) requirements for each
secondary data stream. In such a cognitive radio system, the secondary user is
permitted to use the spectrum allocated to the primary user as long as the
caused interference at the primary receiver is tolerable. With both secondary
SNR constraint and primary interference power constraint, we aim to minimize
the secondary transmit power consumption. By exploiting the individual SNR
requirements, we formulate this cognitive beamforming problem as an
optimization problem on the Stiefel manifold. Both zero forcing beamforming
(ZFB) and nonzero forcing beamforming (NFB) are considered. For the ZFB case,
we derive a closed form beamforming solution. For the NFB case, we prove that
the strong duality holds for the nonconvex primal problem and thus the optimal
solution can be easily obtained by solving the dual problem. Finally, numerical
results are presented to illustrate the performance of the proposed cognitive
beamforming solutions.Comment: This is the longer version of a paper to appear in the IEEE
Transactions on Signal Processin
Quantum Circuits Architecture
We present a method for optimizing quantum circuits architecture. The method
is based on the notion of "quantum comb", which describes a circuit board in
which one can insert variable subcircuits. The method allows one to efficiently
address novel kinds of quantum information processing tasks, such as
storing-retrieving, and cloning of channels.Comment: 10 eps figures + Qcircuit.te
Asynchronous Distributed Optimization over Lossy Networks via Relaxed ADMM: Stability and Linear Convergence
In this work we focus on the problem of minimizing the sum of convex cost
functions in a distributed fashion over a peer-to-peer network. In particular,
we are interested in the case in which communications between nodes are prone
to failures and the agents are not synchronized among themselves. We address
the problem proposing a modified version of the relaxed ADMM, which corresponds
to the Peaceman-Rachford splitting method applied to the dual. By exploiting
results from operator theory, we are able to prove the almost sure convergence
of the proposed algorithm under general assumptions on the distribution of
communication loss and node activation events. By further assuming the cost
functions to be strongly convex, we prove the linear convergence of the
algorithm in mean to a neighborhood of the optimal solution, and provide an
upper bound to the convergence rate. Finally, we present numerical results
testing the proposed method in different scenarios.Comment: To appear in IEEE Transactions on Automatic Contro
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