3,013 research outputs found
Almost-Everywhere Superiority for Quantum Computing
Simon as extended by Brassard and H{\o}yer shows that there are tasks on
which polynomial-time quantum machines are exponentially faster than each
classical machine infinitely often. The present paper shows that there are
tasks on which polynomial-time quantum machines are exponentially faster than
each classical machine almost everywhere.Comment: 16 page
The Road to Quantum Computational Supremacy
We present an idiosyncratic view of the race for quantum computational
supremacy. Google's approach and IBM challenge are examined. An unexpected
side-effect of the race is the significant progress in designing fast classical
algorithms. Quantum supremacy, if achieved, won't make classical computing
obsolete.Comment: 15 pages, 1 figur
New quantum algorithm for studying NP-complete problems
Ordinary approach to quantum algorithm is based on quantum Turing machine or
quantum circuits. It is known that this approach is not powerful enough to
solve NP-complete problems. In this paper we study a new approach to quantum
algorithm which is a combination of the ordinary quantum algorithm with a
chaotic dynamical system. We consider the satisfiability problem as an example
of NP-complete problems and argue that the problem, in principle, can be solved
in polynomial time by using our new quantum algorithm.Comment: 11 pages, 1 figur
Average-Case Quantum Query Complexity
We compare classical and quantum query complexities of total Boolean
functions. It is known that for worst-case complexity, the gap between quantum
and classical can be at most polynomial. We show that for average-case
complexity under the uniform distribution, quantum algorithms can be
exponentially faster than classical algorithms. Under non-uniform distributions
the gap can even be super-exponential. We also prove some general bounds for
average-case complexity and show that the average-case quantum complexity of
MAJORITY under the uniform distribution is nearly quadratically better than the
classical complexity.Comment: 14 pages, LaTeX. Some parts rewritten. This version to appear in the
Journal of Physics
Succinctness of two-way probabilistic and quantum finite automata
We prove that two-way probabilistic and quantum finite automata (2PFA's and
2QFA's) can be considerably more concise than both their one-way versions
(1PFA's and 1QFA's), and two-way nondeterministic finite automata (2NFA's). For
this purpose, we demonstrate several infinite families of regular languages
which can be recognized with some fixed probability greater than by
just tuning the transition amplitudes of a 2QFA (and, in one case, a 2PFA) with
a constant number of states, whereas the sizes of the corresponding 1PFA's,
1QFA's and 2NFA's grow without bound. We also show that 2QFA's with mixed
states can support highly efficient probability amplification. The weakest
known model of computation where quantum computers recognize more languages
with bounded error than their classical counterparts is introduced.Comment: A new version, 21 pages, late
Bulk and surface energetics of lithium hydride crystal: benchmarks from quantum Monte Carlo and quantum chemistry
We show how accurate benchmark values of the surface formation energy of
crystalline lithium hydride can be computed by the complementary techniques of
quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry.
To demonstrate the high accuracy of the QMC techniques, we present a detailed
study of the energetics of the bulk LiH crystal, using both pseudopotential and
all-electron approaches. We show that the equilibrium lattice parameter agrees
with experiment to within 0.03 %, which is around the experimental uncertainty,
and the cohesive energy agrees to within around 10 meV per formula unit. QMC in
periodic slab geometry is used to compute the formation energy of the LiH (001)
surface, and we show that the value can be accurately converged with respect to
slab thickness and other technical parameters. The quantum chemistry
calculations build on the recently developed hierarchical scheme for computing
the correlation energy of a crystal to high precision. We show that the
hierarchical scheme allows the accurate calculation of the surface formation
energy, and we present results that are well converged with respect to basis
set and with respect to the level of correlation treatment. The QMC and
hierarchical results for the surface formation energy agree to within about 1
%.Comment: 16 pages, 4 figure
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