50,756 research outputs found
Quantum differential cryptanalysis to the block ciphers
Differential cryptanalysis is one of the most popular methods in attacking
block ciphers. However, there still some limitations in traditional
differential cryptanalysis. On the other hand, researches of quantum algorithms
have made great progress nowadays. This paper proposes two methods to apply
quantum algorithms in differential cryptanalysis, and analysis their
efficiencies and success probabilities. One method is using quantum algorithm
in the high probability differential finding period for every S-Box. The second
method is taking the encryption as a whole, using quantum algorithm in this
process.Comment: 11 pages, no figure
A quantum algorithm to approximate the linear structures of Boolean functions
We present a quantum algorithm for approximating the linear structures of a
Boolean function . Different from previous algorithms (such as Simon's and
Shor's algorithms) which rely on restrictions on the Boolean function, our
algorithm applies to every Boolean function with no promise. Here, our methods
are based on the result of the Bernstein-Vazirani algorithm which is to
identify linear Boolean functions and the idea of Simon's period-finding
algorithm. More precisely, how the extent of approximation changes over the
time is obtained, and meanwhile we also get some quasi linear structures if
there exists. Next, we obtain that the running time of the quantum algorithm to
thoroughly determine this question is related to the relative differential
uniformity of . Roughly speaking, the smaller the is,
the less time will be needed.Comment: 16 page
A quantum algorithm for approximating the influences of Boolean functions and its applications
We investigate the influences of variables on a Boolean function based on
the quantum Bernstein-Vazirani algorithm. A previous paper (Floess et al. in
Math. Struct. in Comp. Science 23: 386, 2013) has proved that if a -variable
Boolean function does not depend on an input variable
, using the Bernstein-Vazirani circuit to will always obtain an output
that has a in the th position. We generalize this result and show
that after one time running the algorithm, the probability of getting a 1 in
each position is equal to the dependence degree of on the variable
, i.e. the influence of on . On this foundation, we give an
approximation algorithm to evaluate the influence of any variable on a Boolean
function. Next, as an application, we use it to study the Boolean functions
with juntas, and construct probabilistic quantum algorithms to learn certain
Boolean functions. Compared with the deterministic algorithms given by Floess
et al., our probabilistic algorithms are faster.Comment: 13 page
Investigating the linear structure of Boolean functions based on Simon's period-finding quantum algorithm
It is believed that there is no efficient classical algorithm to determine
the linear structure of Boolean function. We investigate an extension of
Simon's period-finding quantum algorithm, and propose an efficient quantum
algorithm to determine the linear structure of Boolean function.Comment: 13 pages, 2 figure
Quantum Zeno and anti-Zeno effect in atom-atom entanglement induced by non-Markovian environment
The dynamic behavior of the entanglement for two two-level atoms coupled to a
common lossy cavity is studied. We find that the speed of disentanglement is a
decreasing (increasing) function of the damping rate of the cavity for on/near
(far-off) resonant couplings. The quantitative explanations for these phenomena
are given, and further, it is shown that they are related to the quantum Zeno
and anti-Zeno effect induced by the non-Markovian environment.Comment: 4 pages, 2 figure
A mathematical model of demand-supply dynamics with collectability and saturation factors
We introduce a mathematical model on the dynamics of demand and supply
incorporating collectability and saturation factors. Our analysis shows that
when the fluctuation of the determinants of demand and supply is strong enough,
there is chaos in the demand-supply dynamics. Our numerical simulation shows
that such a chaos is not an attractor (i.e. dynamics is not approaching the
chaos), instead a periodic attractor (of period 3 under the Poincar\'e period
map) exists near the chaos, and co-exists with another periodic attractor (of
period 1 under the Poincar\'e period map) near the market equilibrium. Outside
the basins of attraction of the two periodic attractors, the dynamics
approaches infinity indicating market irrational exuberance or flash crash. The
period 3 attractor represents the product's market cycle of growth and
recession, while period 1 attractor near the market equilibrium represents the
regular fluctuation of the product's market. Thus our model captures more
market phenomena besides Marshall's market equilibrium. When the fluctuation of
the determinants of demand and supply is strong enough, a three leaf danger
zone exists where the basins of attraction of all attractors intertwine and
fractal basin boundaries are formed. Small perturbations in the danger zone can
lead to very different attractors. That is, small perturbations in the danger
zone can cause the market to experience oscillation near market equilibrium,
large growth and recession cycle, and irrational exuberance or flash crash
Variational study of the one dimensional t-J model
We find the Gutzwiller projected Fermi sea wave function(GWF) has the correct
phase structure to describe the kink nature of the doped holes in the ground
state of the one dimensional model. We find the failure of the GWF for
general value of and electron density can be attributed to the
residual charge correlation in the ground state. We find such residual charge
correlation is well described by a XXZ-type effective Hamiltonian. Based on
these observations, a Pfaffian-type variational wave function is proposed and
is found to reproduce correctly the global phase diagram and corresponding
correlation functions of the one dimensional model, including the
Luther-Emery phase in the low electron density and large region.Comment: 8 pages, 8 figure
Spin Charge Recombination in Projected Wave Functions
We find spin charge recombination is a generic feature of projected wave
functions. We find this effect is responsible for a series of differences
between mean field theory prediction and the result from projected wave
functions. We also find spin charge recombination plays an important role in
determining the dissipation of supercurrent, the quasiparticle properties and
the hole - hole correlation.Comment: 13 pages,7 figure
Topological Order in Projected Wave Functions and Effective Theories of Quantum Antiferromagnets
We study the topological order in RVB state derived from Gutzwiller
projection of BCS-like mean field state. We propose to construct the
topological excitation on the projected RVB state through Gutzwiller projection
of mean field state with inserted flux tube. We prove that all
projected RVB states derived from bipartite effective theories, no matter the
gauge structure in the mean field ansatz, are positive definite in the sense of
the Marshall sign rule, which provides a universal origin for the absence of
topological order in such RVB state.Comment: 5 pages, 1 figure
The Hellberg-Mele Jastrow factor as a variational wave function for the one dimensional XXZ model
We find the Jastrow factor introduced by Hellberg and Mele in their study of
the one dimensional t-J model provides an exceedingly good variational
description of the one dimensional XXZ model.Comment: 3 pages, 2 figure
- β¦