Related papers: Almost all decision trees do not allow significant…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structural and ancestral constraints within a rigorous mathematical…
Although quantum control typically relies on greedy (local) optimization, traps (irregular critical points) in the control landscape can make optimization hard by foiling local search strategies. We demonstrate the failure of greedy…
Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in…
Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex…
We study possible advantages of randomized and quantum computing over deterministic computing for scalar initial-value problems for ordinary differential equations of order k. For systems of equations of the first order this question has…
The subcube partition model of computation is at least as powerful as decision trees but no separation between these models was known. We show that there exists a function whose deterministic subcube partition complexity is asymptotically…
Efficiently counting or detecting defective items is a crucial task in various fields ranging from biological testing to quality control to streaming algorithms. The \emph{group testing estimation problem} concerns estimating the number of…
We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of…
We consider quantum-classical hybrid machine learning in which large-scale input channels remain classical and small-scale working channels process quantum operations conditioned on classical input data. This does not require the conversion…
We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…
In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation.…
Treedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a $2^{O(k^2)} n$-time exact algorithm and a polynomial-time $O(\text{OPT} \log^{3/2}…
The quantum query complexity of evaluating any read-once formula with n black-box input bits is Theta(sqrt(n)). However, the corresponding problem for read-many formulas (i.e., formulas in which the inputs have fanout) is not well…
Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically,…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
When trying to use quantum-enhanced methods for optimization problems, the sheer number of options inhibits its adoption by industrial end users. Expert knowledge is required for the formulation and encoding of the use case, the selection…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
A number of recent works have employed decision trees for the construction of explainable partitions that aim to minimize the $k$-means cost function. These works, however, largely ignore metrics related to the depths of the leaves in the…