10,235 research outputs found
Recursive n-gram hashing is pairwise independent, at best
Many applications use sequences of n consecutive symbols (n-grams). Hashing
these n-grams can be a performance bottleneck. For more speed, recursive hash
families compute hash values by updating previous values. We prove that
recursive hash families cannot be more than pairwise independent. While hashing
by irreducible polynomials is pairwise independent, our implementations either
run in time O(n) or use an exponential amount of memory. As a more scalable
alternative, we make hashing by cyclic polynomials pairwise independent by
ignoring n-1 bits. Experimentally, we show that hashing by cyclic polynomials
is is twice as fast as hashing by irreducible polynomials. We also show that
randomized Karp-Rabin hash families are not pairwise independent.Comment: See software at https://github.com/lemire/rollinghashcp
Detecting entanglement of two electron spin qubits with witness operators
We propose a scheme for detecting entanglement between two electron spin
qubits in a double quantum dot using an entanglement witness operator. We first
calculate the optimal configuration of the two electron spins, defined as the
position in the energy level spectrum where, averaged over the nuclear spin
distribution, 1) the probability to have two separated electrons, and 2) the
degree of entanglement of the quantum state quantified by the concurrence are
both large. Using a density matrix approach, we then calculate the evolution of
the expectation value of the witness operator for the two-spin singlet state,
taking into account the effect of decoherence due to quantum charge
fluctuations modeled as a boson bath. We find that, for large interdot
coupling, it is possible to obtain a highly entangled and robust ground state.Comment: 4 pages, 3 figure
Quantum Dissipation due to the Interaction with Chaos
We discuss the possibility of having "quantum dissipation" due to the
interaction with chaotic degrees of freedom. We define the conditions that
should be satisfied in order to have a dissipative effect similar to the one
due to an interaction with a (many body) bath. We also compare with the case
where the environment is modeled by a random matrix model. In case of
interaction with "chaos" we observe a regime where the relaxation process is
non-universal, and reflects the underlaying semiclassical dynamics. As an
example we consider a two level system (spin) that interacts with a two
dimensional anharmonic oscillator.Comment: 5 pages, 1 figure, final improved version, to be published as Phys
Rev. E Rapid Communicatio
Effect of random interactions in spin baths on decoherence
We study the decoherence of a central spin 1/2 induced by a spin bath with
intrabath interactions. Since we are interested in the cumulative effect of
interaction and disorder, we study baths comprising Ising spins with random
ferro- and antiferromagnetic interactions between the spins. Using the
resolvent operator method which goes beyond the standard Born-Markov master
equation approach, we show that, in the weak coupling regime, the decoherence
of the central spin at all times is entirely determined by the local-field
distribution or equivalently, the dynamical structure factor of the Ising bath.
We present analytic results for the Ising spin chain bath at arbitrary
temperature for different distributions of the intrabath interaction strengths.
We find clear evidence of non-Markovian behavior in the low temperature regime.
We also consider baths described by Ising models on higher-dimensional
lattices. We find that interactions lead to a significant reduction of the
decoherence. An important feature of interacting spinbaths is the saturation of
the asymptotic Markovian decay rate at high temperatures, as opposed to the
conventional Ohmic boson bath.Comment: 13 page
Entanglement spectroscopy of a driven solid-state qubit and its detector
We study the asymptotic dynamics of a driven quantum two level system coupled
via a quantum detector to the environment. We find multi-photon resonances
which are due to the entanglement of the qubit and the detector. Different
regimes are studied by employing a perturbative Floquet-Born-Markov approach
for the qubit+detector system, as well as non-perturbative real-time path
integral schemes for the driven spin-boson system. We find analytical results
for the resonances, including the red and the blue sidebands. They agree well
with those of exact ab-initio calculations.Comment: 4 pages, 4 figure
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