30,585 research outputs found
On Finding Quantum Multi-collisions
A -collision for a compressing hash function is a set of distinct
inputs that all map to the same output. In this work, we show that for any
constant , quantum
queries are both necessary and sufficient to achieve a -collision with
constant probability. This improves on both the best prior upper bound
(Hosoyamada et al., ASIACRYPT 2017) and provides the first non-trivial lower
bound, completely resolving the problem
Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision
The quantum query complexity of Boolean matrix multiplication is typically
studied as a function of the matrix dimension, n, as well as the number of 1s
in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values
of \ell. This is an improvement over previous algorithms for all values of
\ell. On the other hand, we show that for any \eps < 1 and any \ell <= \eps
n^2, there is an \Omega(n\sqrt{\ell}) lower bound for this problem, showing
that our algorithm is essentially tight.
We first reduce Boolean matrix multiplication to several instances of graph
collision. We then provide an algorithm that takes advantage of the fact that
the underlying graph in all of our instances is very dense to find all graph
collisions efficiently
Net-charge probability distributions in heavy ion collisions at chemical freeze-out
We explore net charge probability distributions in heavy ion collisions
within the hadron resonance gas model. The distributions for strangeness,
electric charge and baryon number are derived. We show that, within this model,
net charge probability distributions and the resulting fluctuations can be
computed directly from the measured yields of charged and multi-charged
hadrons. The influence of multi-charged particles and quantum statistics on the
shape of the distribution is examined. We discuss the properties of the net
proton distribution along the chemical freeze-out line. The model results
presented here can be compared with data at RHIC energies and at the LHC to
possibly search for the relation between chemical freeze-out and QCD cross-over
lines in heavy ion collisions.Comment: 21 pages, 6 figure
Transverse momentum spectra of identified particles in high energy collisions with statistical hadronisation model
A detailed analysis is performed of transverse momentum spectra of several
identified hadrons in high energy collisions within the framework of the
statistical model of hadronisation. The effect of the decay chain following
hadron generation is accurately taken into account. The considered
centre-of-mass energies range from ~ 10 to 30 GeV in hadronic collisions (pi+
p, pp and Kp) and from ~ 15 to 45 GeV in e+e- collisions. A clear consistency
is found between the temperature parameter extracted from the present analysis
and that obtained from fits to average hadron multiplicities in the same
collision systems. This finding indicates that in the hadronisation, the
production of different particle species and their momentum spectra are two
closely related phenomenons governed by one parameter.Comment: Talk given by F. Becattini in "Correlations and Fluctuations 2000",
12 pp., 11 figure
The quantum complexity of approximating the frequency moments
The 'th frequency moment of a sequence of integers is defined as , where is the number of times that occurs in the
sequence. Here we study the quantum complexity of approximately computing the
frequency moments in two settings. In the query complexity setting, we wish to
minimise the number of queries to the input used to approximate up to
relative error . We give quantum algorithms which outperform the best
possible classical algorithms up to quadratically. In the multiple-pass
streaming setting, we see the elements of the input one at a time, and seek to
minimise the amount of storage space, or passes over the data, used to
approximate . We describe quantum algorithms for , and
in this model which substantially outperform the best possible
classical algorithms in certain parameter regimes.Comment: 22 pages; v3: essentially published versio
Element Distinctness, Frequency Moments, and Sliding Windows
We derive new time-space tradeoff lower bounds and algorithms for exactly
computing statistics of input data, including frequency moments, element
distinctness, and order statistics, that are simple to calculate for sorted
data. We develop a randomized algorithm for the element distinctness problem
whose time T and space S satisfy T in O (n^{3/2}/S^{1/2}), smaller than
previous lower bounds for comparison-based algorithms, showing that element
distinctness is strictly easier than sorting for randomized branching programs.
This algorithm is based on a new time and space efficient algorithm for finding
all collisions of a function f from a finite set to itself that are reachable
by iterating f from a given set of starting points. We further show that our
element distinctness algorithm can be extended at only a polylogarithmic factor
cost to solve the element distinctness problem over sliding windows, where the
task is to take an input of length 2n-1 and produce an output for each window
of length n, giving n outputs in total. In contrast, we show a time-space
tradeoff lower bound of T in Omega(n^2/S) for randomized branching programs to
compute the number of distinct elements over sliding windows. The same lower
bound holds for computing the low-order bit of F_0 and computing any frequency
moment F_k, k neq 1. This shows that those frequency moments and the decision
problem F_0 mod 2 are strictly harder than element distinctness. We complement
this lower bound with a T in O(n^2/S) comparison-based deterministic RAM
algorithm for exactly computing F_k over sliding windows, nearly matching both
our lower bound for the sliding-window version and the comparison-based lower
bounds for the single-window version. We further exhibit a quantum algorithm
for F_0 over sliding windows with T in O(n^{3/2}/S^{1/2}). Finally, we consider
the computations of order statistics over sliding windows.Comment: arXiv admin note: substantial text overlap with arXiv:1212.437
- …