Related papers: Monte Carlo to Las Vegas for Recursively Composed …

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…

We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at…

The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values of…

We study when partial Boolean functions can (and cannot) exhibit superpolynomial quantum query speedups, and develop a general framework for ruling out such speedups via two complementary lenses: promise-aware complexity measures and…

It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…

We show that for a relation $f\subseteq \{0,1\}^n\times \mathcal{O}$ and a function $g:\{0,1\}^{m}\times \{0,1\}^{m} \rightarrow \{0,1\}$ (with $m= O(\log n)$), $$\mathrm{R}_{1/3}(f\circ g^n) = \Omega\left(\mathrm{R}_{1/3}(f) \cdot…

We study Boolean functions of an arbitrary number of input variables that can be realized by simple iterative constructions based on constant-size primitives. This restricted type of construction needs little global coordination or control…

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…

We use the venerable "fooling set" method to prove new lower bounds on the quantum communication complexity of various functions. Let f:X x Y-->{0,1} be a Boolean function, fool^1(f) its maximal fooling set size among 1-inputs, Q_1^*(f) its…

Fix a positive integer $N$. Select an additive composition $\xi$ of $N$ uniformly out of $2^{N-1}$ possibilities. The interplay between the number of parts in $\xi$ and the maximum part in $\xi$ is our focus. It is not surprising that…

In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded…

The {\em Total Influence} ({\em Average Sensitivity) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influence of a monotone Boolean function \ifnum\plusminus=1 $f: \{\pm1\}^n…

A long-investigated problem in circuit complexity theory is to decompose an $n$-input or $n$-variable Majority Boolean function (call it $M_n$) using $k$-input ones ($M_k$), $k < n$, where the objective is to achieve the decomposition using…

We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…

We study the computational power of randomized computations on infinite objects, such as real numbers. In particular, we introduce the concept of a Las Vegas computable multi-valued function, which is a function that can be computed on a…

In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…

In this work, we unify several quantum algorithmic frameworks for boolean functions that are based on the quantum adversary bound. First, we show that the $st$-connectivity framework subsumes the (adaptive/extended) learning graph…

We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…

We determine sufficient conditions under which certain recursively defined functions are well defined for all real inputs. Given a function $f:\mathbb R\to\mathbb R$, call a decreasing sequence $x_1>x_2>x_3>\cdots$ "$f$-bad" if…

Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…