16,278 research outputs found
Equilibrium bandwidth and buffer allocations for elastic traffics
Consider a set of users sharing a network node under an allocation scheme that provides each user with a fixed minimum and a random extra amount of bandwidth and buffer. Allocations and prices are adjusted to adapt to resource availability and user demands. Equilibrium is achieved when all users optimize their utility and demand equals supply for nonfree resources. We analyze two models of user behavior. We show that at equilibrium expected return on purchasing variable resources can be higher than that on fixed resources. Thus users must balance the marginal increase in utility due to higher return on variable resources and the marginal decrease in utility due to their variability. For the first user model we further show that at equilibrium where such tradeoff is optimized all users hold strictly positive amounts of variable bandwidth and buffer. For the second model we show that if both variable bandwidth and buffer are scarce then at equilibrium every user either holds both variable resources or none
Hamiltonian Simulation by Qubitization
We present the problem of approximating the time-evolution operator
to error , where the Hamiltonian is the
projection of a unitary oracle onto the state created by
another unitary oracle. Our algorithm solves this with a query complexity
to both oracles that is optimal
with respect to all parameters in both the asymptotic and non-asymptotic
regime, and also with low overhead, using at most two additional ancilla
qubits. This approach to Hamiltonian simulation subsumes important prior art
considering Hamiltonians which are -sparse or a linear combination of
unitaries, leading to significant improvements in space and gate complexity,
such as a quadratic speed-up for precision simulations. It also motivates
useful new instances, such as where is a density matrix. A key
technical result is `qubitization', which uses the controlled version of these
oracles to embed any in an invariant subspace. A large
class of operator functions of can then be computed with optimal
query complexity, of which is a special case.Comment: 23 pages, 1 figure; v2: updated notation; v3: accepted versio
A new approach to service provisioning in ATM networks
The authors formulate and solve a problem of allocating resources among competing services differentiated by user traffic characteristics and maximum end-to-end delay. The solution leads to an alternative approach to service provisioning in an ATM network, in which the network offers directly for rent its bandwidth and buffers and users purchase freely resources to meet their desired quality. Users make their decisions based on their own traffic parameters and delay requirements and the network sets prices for those resources. The procedure is iterative in that the network periodically adjusts prices based on monitored user demand, and is decentralized in that only local information is needed for individual users to determine resource requests. The authors derive the network's adjustment scheme and the users' decision rule and establish their optimality. Since the approach does not require the network to know user traffic and delay parameters, it does not require traffic policing on the part of the network
Electronic marking and identification techniques to discourage document copying
Modern computer networks make it possible to distribute documents quickly and economically by electronic means rather than by conventional paper means. However, the widespread adoption of electronic distribution of copyrighted material is currently impeded by the ease of illicit copying and dissemination. In this paper we propose techniques that discourage illicit distribution by embedding each document with a unique codeword. Our encoding techniques are indiscernible by readers, yet enable us to identify the sanctioned recipient of a document by examination of a recovered document. We propose three coding methods, describe one in detail, and present experimental results showing that our identification techniques are highly reliable, even after documents have been photocopied
The Red Queen visits Minkowski Space
When Alice went `Through the Looking Glass' [1], she found herself in a
situation where she had to run as fast as she could in order to stay still. In
accordance with the dictum that truth is stranger than fiction, we will see
that it is possible to find a situation in special relativity where running
towards one's target is actually counter-productive. Although the situation is
easily analysed algebraically, the qualitative properties of the analysis are
greatly illuminated by the use of space-time diagrams
Quantum imaging by coherent enhancement
Conventional wisdom dictates that to image the position of fluorescent atoms
or molecules, one should stimulate as much emission and collect as many photons
as possible. That is, in this classical case, it has always been assumed that
the coherence time of the system should be made short, and that the statistical
scaling defines the resolution limit for imaging time .
However, here we show in contrast that given the same resources, a long
coherence time permits a higher resolution image. In this quantum regime, we
give a procedure for determining the position of a single two-level system, and
demonstrate that the standard errors of our position estimates scale at the
Heisenberg limit as , a quadratic, and notably optimal, improvement
over the classical case.Comment: 4 pages, 4 figue
Quantum Inference on Bayesian Networks
Performing exact inference on Bayesian networks is known to be #P-hard.
Typically approximate inference techniques are used instead to sample from the
distribution on query variables given the values of evidence variables.
Classically, a single unbiased sample is obtained from a Bayesian network on
variables with at most parents per node in time
, depending critically on , the probability the
evidence might occur in the first place. By implementing a quantum version of
rejection sampling, we obtain a square-root speedup, taking
time per sample. We exploit the Bayesian
network's graph structure to efficiently construct a quantum state, a q-sample,
representing the intended classical distribution, and also to efficiently apply
amplitude amplification, the source of our speedup. Thus, our speedup is
notable as it is unrelativized -- we count primitive operations and require no
blackbox oracle queries.Comment: 8 pages, 3 figures. Submitted to PR
Fixed-point quantum search with an optimal number of queries
Grover's quantum search and its generalization, quantum amplitude
amplification, provide quadratic advantage over classical algorithms for a
diverse set of tasks, but are tricky to use without knowing beforehand what
fraction of the initial state is comprised of the target states. In
contrast, fixed-point search algorithms need only a reliable lower bound on
this fraction, but, as a consequence, lose the very quadratic advantage that
makes Grover's algorithm so appealing. Here we provide the first version of
amplitude amplification that achieves fixed-point behavior without sacrificing
the quantum speedup. Our result incorporates an adjustable bound on the failure
probability, and, for a given number of oracle queries, guarantees that this
bound is satisfied over the broadest possible range of .Comment: 4 pages plus references, 2 figure
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