16,451 research outputs found
A Foundation of Programming a Multi-Tape Quantum Turing machine
The notion of quantum Turing machines is a basis of quantum complexity
theory. We discuss a general model of multi-tape, multi-head Quantum Turing
machines with multi final states that also allow tape heads to stay still.Comment: A twelve page version is to appear in the Proceedings of the 24th
International Symposium on Mathematical Foundations of Computer Science in
September, 1999. LNC
Fast quantum algorithm for numerical gradient estimation
Given a blackbox for f, a smooth real scalar function of d real variables,
one wants to estimate the gradient of f at a given point with n bits of
precision. On a classical computer this requires a minimum of d+1 blackbox
queries, whereas on a quantum computer it requires only one query regardless of
d. The number of bits of precision to which f must be evaluated matches the
classical requirement in the limit of large n.Comment: additional references and minor clarifications and corrections to
version
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Optimization of the neutron yield in fusion plasmas produced by Coulomb explosions of deuterium clusters irradiated by a petawatt laser
The kinetic energy of hot (multi-keV) ions from the laser-driven Coulomb explosion of deuterium clusters and the resulting fusion yield in plasmas formed from these exploding clusters has been investigated under a variety of conditions using the Texas Petawatt laser. An optimum laser intensity was found for producing neutrons in these cluster fusion plasmas with corresponding average ion energies of 14 keV. The substantial volume (1-10 mm(3)) of the laser-cluster interaction produced by the petawatt peak power laser pulse led to a fusion yield of 1.6x10(7) neutrons in a single shot with a 120 J, 170 fs laser pulse. Possible effects of prepulses are discussed. DOI: 10.1103/PhysRevE.87.023106Glenn Focht Memorial FellowshipNNSA DE-FC52-08NA28512DOE Office of Basic Energy SciencesPhysic
On the role of entanglement in quantum computational speed-up
For any quantum algorithm operating on pure states we prove that the presence
of multi-partite entanglement, with a number of parties that increases
unboundedly with input size, is necessary if the quantum algorithm is to offer
an exponential speed-up over classical computation. Furthermore we prove that
the algorithm can be classically efficiently simulated to within a prescribed
tolerance \eta even if a suitably small amount of global entanglement
(depending on \eta) is present. We explicitly identify the occurrence of
increasing multi-partite entanglement in Shor's algorithm. Our results do not
apply to quantum algorithms operating on mixed states in general and we discuss
the suggestion that an exponential computational speed-up might be possible
with mixed states in the total absence of entanglement. Finally, despite the
essential role of entanglement for pure state algorithms, we argue that it is
nevertheless misleading to view entanglement as a key resource for quantum
computational power.Comment: Main proofs simplified. A few further explanatory remarks added. 22
pages, plain late
Third-order cosmological perturbations of zero-pressure multi-component fluids: Pure general relativistic nonlinear effects
Present expansion stage of the universe is believed to be mainly governed by
the cosmological constant, collisionless dark matter and baryonic matter. The
latter two components are often modeled as zero-pressure fluids. In our
previous work we have shown that to the second-order cosmological
perturbations, the relativistic equations of the zero-pressure, irrotational,
multi-component fluids in a spatially near flat background effectively coincide
with the Newtonian equations. As the Newtonian equations only have quadratic
order nonlinearity, it is practically interesting to derive the potential
third-order perturbation terms in general relativistic treatment which
correspond to pure general relativistic corrections. Here, we present pure
general relativistic correction terms appearing in the third-order
perturbations of the multi-component zero-pressure fluids. We show that, as in
a single component situation, the third-order correction terms are quite small
(~ 5 x10^{-5} smaller compared with the relativistic/Newtonian second-order
terms) due to the weak level anisotropy of the cosmic microwave background
radiation. Still, there do exist pure general relativistic correction terms in
third-order perturbations which could potentially become important in future
development of precision cosmology. We include the cosmological constant in all
our analyses.Comment: 20 pages, no figur
On bit-commitment based quantum coin flipping
In this paper, we focus on a special framework for quantum coin flipping
protocols,_bit-commitment based protocols_, within which almost all known
protocols fit. We show a lower bound of 1/16 for the bias in any such protocol.
We also analyse a sequence of multi-round protocol that tries to overcome the
drawbacks of the previously proposed protocols, in order to lower the bias. We
show an intricate cheating strategy for this sequence, which leads to a bias of
1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and
also demonstrates that a cleverer proof technique may be required to show this
optimality.Comment: The lower bound shown in this paper is superceded by a result of
Kitaev (personal communication, 2001
Anti-Proton Evolution in Little Bangs and Big Bang
The abundances of anti-protons and protons are considered within
momentum-integrated Boltzmann equations describing Little Bangs, i.e.,
fireballs created in relativistic heavy-ion collisions. Despite of a large
anti-proton annihilation cross section we find a small drop of the ratio of
anti-protons to protons from 170 MeV (chemical freeze-out temperature) till 100
MeV (kinetic freeze-out temperature) for CERN-SPS and BNL-RHIC energies thus
corroborating the solution of the previously exposed "ani-proton puzzle". In
contrast, the Big Bang evolves so slowly that the anti-baryons are kept for a
long time in equilibrium resulting in an exceedingly small fraction. The
adiabatic path of cosmic matter in the phase diagram of strongly interacting
matter is mapped out
Quantum Algorithms for Learning and Testing Juntas
In this article we develop quantum algorithms for learning and testing
juntas, i.e. Boolean functions which depend only on an unknown set of k out of
n input variables. Our aim is to develop efficient algorithms:
- whose sample complexity has no dependence on n, the dimension of the domain
the Boolean functions are defined over;
- with no access to any classical or quantum membership ("black-box")
queries. Instead, our algorithms use only classical examples generated
uniformly at random and fixed quantum superpositions of such classical
examples;
- which require only a few quantum examples but possibly many classical
random examples (which are considered quite "cheap" relative to quantum
examples).
Our quantum algorithms are based on a subroutine FS which enables sampling
according to the Fourier spectrum of f; the FS subroutine was used in earlier
work of Bshouty and Jackson on quantum learning. Our results are as follows:
- We give an algorithm for testing k-juntas to accuracy that uses
quantum examples. This improves on the number of examples used
by the best known classical algorithm.
- We establish the following lower bound: any FS-based k-junta testing
algorithm requires queries.
- We give an algorithm for learning -juntas to accuracy that
uses quantum examples and
random examples. We show that this learning algorithms is close to optimal by
giving a related lower bound.Comment: 15 pages, 1 figure. Uses synttree package. To appear in Quantum
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