Related papers: All Classical Adversary Methods are Equivalent for…
The quantum adversary method is a versatile method for proving lower bounds on quantum algorithms. It yields tight bounds for many computational problems, is robust in having many equivalent formulations, and has natural connections to…
The quantum adversary method is one of the most versatile lower-bound methods for quantum algorithms. We show that all known variants of this method are equivalent: spectral adversary (Barnum, Saks, and Szegedy, 2003), weighted adversary…
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…
We investigate the relation between the block sensitivity $\text{bs}(f)$ and fractional block sensitivity $\text{fbs}(f)$ complexity measures of Boolean functions. While it is known that $\text{fbs}(f) = O(\text{bs}(f)^2)$, the best known…
The (negative-weighted) quantum adversary bound is a tight characterisation of the quantum query complexity for any partial function. We analyse the extent to which this bound can be generalised. Ambainis et al. [arXiv:1012.2112] and Lee et…
We introduce two new complexity measures for Boolean functions, or more generally for functions of the form f:S->T. We call these measures sumPI and maxPI. The quantity sumPI has been emerging through a line of research on quantum query…
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using…
We present a new variant of the quantum adversary method. All adversary methods give lower bounds on the quantum query complexity of a function by bounding the change of a progress function caused by one query. All previous variants…
We introduce the notion of classical fractional query algorithms, which generalize decision trees in the average-case setting, and can potentially perform better than them. We show that the limiting run-time complexity of a natural class of…
The quantum adversary method is one of the most successful techniques for proving lower bounds on quantum query complexity. It gives optimal lower bounds for many problems, has application to classical complexity in formula size lower…
We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1. We show that the classical adversary bound lifts to a lower bound on randomized communication…
The sensitivity conjecture of Nisan and Szegedy [CC '94] asks whether for any Boolean function $f$, the maximum sensitivity $s(f)$, is polynomially related to its block sensitivity $bs(f)$, and hence to other major complexity measures.…
We consider adversarially robust classification in a multiclass setting under arbitrary loss functions and derive dual and barycentric reformulations of the corresponding learner-agnostic robust risk minimization problem. We provide…
In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function $f$ on $n$ variables that only depends on $k$ variables, and, when restricted to them, equals some predefined…
We show an equivalence between 1-query quantum algorithms and representations by degree-2 polynomials. Namely, a partial Boolean function $f$ is computable by a 1-query quantum algorithm with error bounded by $\epsilon<1/2$ iff $f$ can be…
The general adversary bound is a semi-definite program (SDP) that lower-bounds the quantum query complexity of a function. We turn this lower bound into an upper bound, by giving a quantum walk algorithm based on the dual SDP that has query…
Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been…
The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the…
We study classical query algorithms with post-selection, and find that they are closely connected to rational functions with nonnegative coefficients. We show that the post-selected classical query complexity of a Boolean function is equal…
Ben Reichardt showed in a series of results that the general adversary bound of a function characterizes its quantum query complexity. This survey seeks to aggregate the background and definitions necessary to understand the proof. Notable…