2,597 research outputs found
Quantum annealing with Jarzynski equality
We show a practical application of the Jarzynski equality in quantum
computation. Its implementation may open a way to solve combinatorial
optimization problems, minimization of a real single-valued function, cost
function, with many arguments. We consider to incorpolate the Jarzynski
equality into quantum annealing, which is one of the generic algorithms to
solve the combinatorial optimization problem. The ordinary quantum annealing
suffers from non-adiabatic transitions whose rate is characterized by the
minimum energy gap of the quantum system under
consideration. The quantum sweep speed is therefore restricted to be extremely
slow for the achievement to obtain a solution without relevant errors. However,
in our strategy shown in the present study, we find that such a difficulty
would not matter.Comment: 4 pages, to appear in Phys. Rev. Let
Quantum annealing with antiferromagnetic fluctuations
We introduce antiferromagnetic quantum fluctuations into quantum annealing in
addition to the conventional transverse-field term. We apply this method to the
infinite-range ferromagnetic p-spin model, for which the conventional quantum
annealing has been shown to have difficulties to find the ground state
efficiently due to a first-order transition. We study the phase diagram of this
system both analytically and numerically. Using the static approximation, we
find that there exists a quantum path to reach the final ground state from the
trivial initial state that avoids first-order transitions for intermediate
values of p. We also study numerically the energy gap between the ground state
and the first excited state and find evidence for intermediate values of p that
the time complexity scales polynomially with the system size at a second-order
transition point along the quantum path that avoids first-order transitions.
These results suggest that quantum annealing would be able to solve this
problem with intermediate values of p efficiently in contrast to the case with
only simple transverse-field fluctuations.Comment: 19 pages, 11 figures; Added references; To be published in Physical
Review
Geometries for universal quantum computation with matchgates
Matchgates are a group of two-qubit gates associated with free fermions. They
are classically simulatable if restricted to act between nearest neighbors on a
one-dimensional chain, but become universal for quantum computation with
longer-range interactions. We describe various alternative geometries with
nearest-neighbor interactions that result in universal quantum computation with
matchgates only, including subtle departures from the chain. Our results pave
the way for new quantum computer architectures that rely solely on the simple
interactions associated with matchgates.Comment: 6 pages, 4 figures. Updated version includes an appendix extending
one of the result
On the complexity of the multiple stack TSP, kSTSP
The multiple Stack Travelling Salesman Problem, STSP, deals with the collect
and the deliverance of n commodities in two distinct cities. The two cities are
represented by means of two edge-valued graphs (G1,d2) and (G2,d2). During the
pick-up tour, the commodities are stored into a container whose rows are
subject to LIFO constraints. As a generalisation of standard TSP, the problem
obviously is NP-hard; nevertheless, one could wonder about what combinatorial
structure of STSP does the most impact its complexity: the arrangement of the
commodities into the container, or the tours themselves? The answer is not
clear. First, given a pair (T1,T2) of pick-up and delivery tours, it is
polynomial to decide whether these tours are or not compatible. Second, for a
given arrangement of the commodities into the k rows of the container, the
optimum pick-up and delivery tours w.r.t. this arrangement can be computed
within a time that is polynomial in n, but exponential in k. Finally, we
provide instances on which a tour that is optimum for one of three distances
d1, d2 or d1+d2 lead to solutions of STSP that are arbitrarily far to the
optimum STSP
Jarzynski Equality for an Energy-Controlled System
The Jarzynski equality (JE) is known as an exact identity for nonequillibrium
systems. The JE was originally formulated for isolated and isothermal systems,
while Adib reported an JE extended to an isoenergetic process. In this paper,
we extend the JE to an energy-controlled system. We make it possible to control
the instantaneous value of the energy arbitrarily in a nonequilibrium process.
Under our extension, the new JE is more practical and useful to calculate the
number of states and the entropy than the isoenergetic one. We also show
application of our JE to a kind of optimization problems.Comment: 6 pages, 1 figur
On the Complexity of Local Search for Weighted Standard Set Problems
In this paper, we study the complexity of computing locally optimal solutions
for weighted versions of standard set problems such as SetCover, SetPacking,
and many more. For our investigation, we use the framework of PLS, as defined
in Johnson et al., [JPY88]. We show that for most of these problems, computing
a locally optimal solution is already PLS-complete for a simple neighborhood of
size one. For the local search versions of weighted SetPacking and SetCover, we
derive tight bounds for a simple neighborhood of size two. To the best of our
knowledge, these are one of the very few PLS results about local search for
weighted standard set problems
First order phase transition in the Quantum Adiabatic Algorithm
We simulate the quantum adiabatic algorithm (QAA) for the exact cover problem
for sizes up to N=256 using quantum Monte Carlo simulations incorporating
parallel tempering. At large N we find that some instances have a discontinuous
(first order) quantum phase transition during the evolution of the QAA. This
fraction increases with increasing N and may tend to 1 for N -> infinity.Comment: 5 pages, 3 figures. Replaced with published version; two figures
slightly changed and some small changes to the tex
On the Complexity of Searching in Trees: Average-case Minimization
We focus on the average-case analysis: A function w : V -> Z+ is given which
defines the likelihood for a node to be the one marked, and we want the
strategy that minimizes the expected number of queries. Prior to this paper,
very little was known about this natural question and the complexity of the
problem had remained so far an open question.
We close this question and prove that the above tree search problem is
NP-complete even for the class of trees with diameter at most 4. This results
in a complete characterization of the complexity of the problem with respect to
the diameter size. In fact, for diameter not larger than 3 the problem can be
shown to be polynomially solvable using a dynamic programming approach.
In addition we prove that the problem is NP-complete even for the class of
trees of maximum degree at most 16. To the best of our knowledge, the only
known result in this direction is that the tree search problem is solvable in
O(|V| log|V|) time for trees with degree at most 2 (paths).
We match the above complexity results with a tight algorithmic analysis. We
first show that a natural greedy algorithm attains a 2-approximation.
Furthermore, for the bounded degree instances, we show that any optimal
strategy (i.e., one that minimizes the expected number of queries) performs at
most O(\Delta(T) (log |V| + log w(T))) queries in the worst case, where w(T) is
the sum of the likelihoods of the nodes of T and \Delta(T) is the maximum
degree of T. We combine this result with a non-trivial exponential time
algorithm to provide an FPTAS for trees with bounded degree
Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling
In this paper, we design a supervisor to prevent vehicle collisions at
intersections. An intersection is modeled as an area containing multiple
conflict points where vehicle paths cross in the future. At every time step,
the supervisor determines whether there will be more than one vehicle in the
vicinity of a conflict point at the same time. If there is, then an impending
collision is detected, and the supervisor overrides the drivers to avoid
collision. A major challenge in the design of a supervisor as opposed to an
autonomous vehicle controller is to verify whether future collisions will occur
based on the current drivers choices. This verification problem is particularly
hard due to the large number of vehicles often involved in intersection
collision, to the multitude of conflict points, and to the vehicles dynamics.
In order to solve the verification problem, we translate the problem to a
job-shop scheduling problem that yields equivalent answers. The job-shop
scheduling problem can, in turn, be transformed into a mixed-integer linear
program when the vehicle dynamics are first-order dynamics, and can thus be
solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201
Ferric iron reduction by bacteria associated with the roots of freshwater and marine macrophytes
In vitro assays of washed, excised roots revealed maximum potential ferric iron reduction rates of \u3e100 μmol g (dry weight)-1 day-1 for three freshwater macrophytes and rates between 15 and 83 μmol (dry weight)-1 day-1 for two marine species. The rates varied with root morphology but not consistently (fine root activity exceeded smooth root activity in some but not all cases). Sodium molybdate added at final concentrations of 0.2 to 20 mM did not inhibit iron reduction by roots of marine macrophytes (Spartina alterniflora and Zostera marina). Roots of a freshwater macrophyte, Sparganium eurycarpum, that were incubated with an analog of humic acid precursors, anthroquinone disulfate (AQDS), reduced freshly precipitated iron oxyhydroxide contained in dialysis bags that excluded solutes with molecular weights of \u3e 1,000; no reduction occurred in the absence of AQDS. Bacterial enrichment cultures and isolates from freshwater and marine roots used a variety of carbon and energy sources (e.g., acetate, ethanol, succinate, toluene, and yeast extract) and ferric oxyhydroxide, ferric citrate, uranate, and AQDS as terminal electron acceptors. The temperature optima for a freshwater isolate and a marine isolate were equivalent (approximately 32°C). However, iron reduction by the freshwater isolate decreased with increasing salinity, while reduction by the marine isolate displayed a relatively broad optimum salinity between 20 and 35 ppt. Our results suggest that by participating in an active iron cycle and perhaps by reducing humic acids, iron reducers in the rhizoplane of aquatic macrophytes limit organic availability to other heterotrophs (including methanogens) in the rhizosphere and bulk sediments
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