Search results for " Computational"
showing 10 items of 661 documents
Superlinear advantage for exact quantum algorithms
2012
A quantum algorithm is exact if, on any input data, it outputs the correct answer with certainty (probability 1). A key question is: how big is the advantage of exact quantum algorithms over their classical counterparts: deterministic algorithms. For total Boolean functions in the query model, the biggest known gap was just a factor of 2: PARITY of N inputs bits requires $N$ queries classically but can be computed with N/2 queries by an exact quantum algorithm. We present the first example of a Boolean function f(x_1, ..., x_N) for which exact quantum algorithms have superlinear advantage over the deterministic algorithms. Any deterministic algorithm that computes our function must use N qu…
Quantum Computation With Devices Whose Contents Are Never Read
2010
In classical computation, a "write-only memory" (WOM) is little more than an oxymoron, and the addition of WOM to a (deterministic or probabilistic) classical computer brings no advantage. We prove that quantum computers that are augmented with WOM can solve problems that neither a classical computer with WOM nor a quantum computer without WOM can solve, when all other resource bounds are equal. We focus on realtime quantum finite automata, and examine the increase in their power effected by the addition of WOMs with different access modes and capacities. Some problems that are unsolvable by two-way probabilistic Turing machines using sublogarithmic amounts of read/write memory are shown to…
A Quantum Lovasz Local Lemma
2012
The Lovasz Local Lemma (LLL) is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of "weakly dependent" criteria. We show that the LLL extends to a much more general geometric setting, where events are replaced with subspaces and probability is replaced with relative dimension, which allows to lower bound the dimension of the intersection of vector spaces under certain independence conditions. Our result immediately applies to the k-QSAT problem: For instance we show that any collection of rank 1 projectors with the property that each qubit appears in at most $2^k/(e \cdot k)$ of them, has a joint satisfiable state. We then …
Sensitivity versus block sensitivity of Boolean functions
2010
Determining the maximal separation between sensitivity and block sensitivity of Boolean functions is of interest for computational complexity theory. We construct a sequence of Boolean functions with bs(f) = 1/2 s(f)^2 + 1/2 s(f). The best known separation previously was bs(f) = 1/2 s(f)^2 due to Rubinstein. We also report results of computer search for functions with at most 12 variables.
Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions
2021
We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead, our method uses standard time-discretised approximations of diffusions, such as the Euler--Maruyama scheme. Our approach is based on particle marginal Metropolis--Hastings, a particle filter, randomised multilevel Monte Carlo, and importance sampling type correction of approximate Markov chain Monte Carlo. The resulting estimator leads to inference without a bias from the time-discretisation as the number of Markov chain iterations increases. We give conver…
Reliability analysis of processes with moving cracked material
2015
Abstract The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected to homogeneous tension acting in the travelling direction. For tension, two models are studied: (i) tension is constant with respect to time, and (ii) tension varies temporally according to an Ornstein–Uhlenbeck process. Cracks of random length are assumed to occur in the material according to a stochastic counting process. For a general counting process, a representation of the nonfracture probability of the system is obtained that exploits condi…
Proving The Power Of Postselection
2011
It is a widely believed, though unproven, conjecture that the capability of postselection increases the language recognition power of both probabilistic and quantum polynomial-time computers. It is also unknown whether polynomial-time quantum machines with postselection are more powerful than their probabilistic counterparts with the same resource restrictions. We approach these problems by imposing additional constraints on the resources to be used by the computer, and are able to prove for the first time that postselection does augment the computational power of both classical and quantum computers, and that quantum does outperform probabilistic in this context, under simultaneous time an…
Forrelation
2014
We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly correlated with the Fourier transform of a second function. This problem can be solved using 1 quantum query, yet we show that any randomized algorithm needs Ω(√(N)log(N)) queries (improving an Ω(N[superscript 1/4]) lower bound of Aaronson). Conversely, we show that this 1 versus Ω(√(N)) separation is optimal: indeed, any t-query quantum algorithm whatsoever can be simulated by an O(N[superscript 1-1/2t])-query randomized algorithm. Thus, resolving an open questi…
Exact affine counter automata
2017
We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las Vegas affine finite automata. Lastly, we show that how a counter helps for affine finite automata by showing that the language MANYTWINS, which is conjectured not to be recognized by affin…
A rule‐based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts
2019
Rule-based methods are often used for assigning fiber orientation to cardiac anatomical models. However, existing methods have been developed using data mostly from the left ventricle. As a consequence, fiber information obtained from rule-based methods often does not match histological data in other areas of the heart such as the right ventricle, having a negative impact in cardiac simulations beyond the left ventricle. In this work, we present a rule-based method where fiber orientation is separately modeled in each ventricle following observations from histology. This allows to create detailed fiber orientation in specific regions such as the endocardium of the right ventricle, the inter…