Related papers: A Quadratic Lower Bound for Simulation
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods to find optimal values for these parameters. Solving a quantum computational problem with such…
We prove lower bounds for higher-order methods in smooth non-convex finite-sum optimization. Our contribution is threefold: We first show that a deterministic algorithm cannot profit from the finite-sum structure of the objective, and that…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
Simulation Optimization (SO) refers to the optimization of an objective function subject to constraints, both of which can be evaluated through a stochastic simulation. To address specific features of a particular simulation---discrete or…
In this paper, we define the upper (resp. lower) covariance under multiple probabilities via a corresponding max-min-max (resp. min-max-min) optimization problem and the related properties of covariances are obtained. In particular, we…
This is a companion note to our recent study of the weak convergence properties of constrained emphatic temporal-difference learning (ETD) algorithms from a theoretic perspective. It supplements the latter analysis with simulation results…
We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…
We derive lower bounds on the time needed for a quantum annealer to prepare the ground state of a target Hamiltonian. These bounds do not depend on the annealing schedule and can take the local structure of the Hamiltonian into account.…
We investigate the time T a quantum computer requires to factorize a given number dependent on the number of bits L required to represent this number. We stress the fact that in most cases one has to take into account that the execution…
We study quadratic optimization with indicator variables and an M-matrix, i.e., a PSD matrix with non-positive off-diagonal entries, which arises directly in image segmentation and portfolio optimization with transaction costs, as well as a…
We study (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly one-counter automata. We describe generic methods for proving…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
Strongly simulating a quantum circuit, that is, computing an output amplitude, amounts to summing the circuit's Feynman paths, a weighted count over assignments to the Boolean ``path'' variables. The circuit's gates induce correlations…
We introduce a systematic study of "symmetric quantum circuits", a new restricted model of quantum computation that preserves the symmetries of the problems it solves. This model is well-adapted for studying the role of symmetry in quantum…
Similarity learning is a general problem to elicit useful representations by predicting the relationship between a pair of patterns. This problem is related to various important preprocessing tasks such as metric learning, kernel learning,…
Quantum computing is a hotspot technology for its potential to accelerate specific applications by exploiting quantum parallelism. However, current physical quantum computers are limited to a relatively small scale, simulators based on…