Related papers: On query complexity measures and their relations f…
We prove a new lower bound on the parity decision tree complexity $\mathsf{D}_{\oplus}(f)$ of a Boolean function $f$. Namely, granularity of the Boolean function $f$ is the smallest $k$ such that all Fourier coefficients of $f$ are integer…
Boolean matching is significant to digital integrated circuits design. An exhaustive method for Boolean matching is computationally expensive even for functions with only a few variables, because the time complexity of such an algorithm for…
For any Boolean function $f:\{0,1\}^n \to \{0,1\}$ with a complexity measure having value $k \ll n$, is it possible to restrict the function $f$ to $\Theta(k)$ variables while keeping the complexity preserved at $\Theta(k)$? This question,…
We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations and…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum…
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…
We introduce a new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem. This problem encompasses both, the computation of partial or total functions and the preparation of target…
Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…
The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum…
We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct…
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…
We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional…
We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra~(SICOMP 2018) for Boolean functions to the case of real-valued functions $f \colon \{0,1\}^d\to\mathbb{R}$. Our main tool in the proof of the generalized…
We study the query complexity of Bayesian Private Learning: a learner wishes to locate a random target within an interval by submitting queries, in the presence of an adversary who observes all of her queries but not the responses. How many…
Given a Boolean function $f:\{0,1\}^n\to\{0,1\}$, the goal in the usual query model is to compute $f$ on an unknown input $x \in \{0,1\}^n$ while minimizing the number of queries to $x$. One can also consider a "distinguishing" problem…
This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication…
We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates…