Related papers: On query complexity measures and their relations f…
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…
The negative weight adversary method, $\mathrm{ADV}^\pm(g)$, is known to characterize the bounded-error quantum query complexity of any Boolean function $g$, and also obeys a perfect composition theorem $\mathrm{ADV}^\pm(f \circ g^n) =…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
The Boolean satisfiability problem (SAT) is of central importance in both theory and practice. Yet, most provable guarantees for quantum algorithms rely exclusively on Grover-type methods that cap the possible advantage at only quadratic…
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list,…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to…
In this paper, we inaugurate the field of quantum fair machine learning. We undertake a comparative analysis of differences and similarities between classical and quantum fair machine learning algorithms, specifying how the unique features…
We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main…
There are two main attack models considered in the adversarial robustness literature: black-box and white-box. We consider these threat models as two ends of a fine-grained spectrum, indexed by the number of queries the adversary can ask.…
We use critical block sensitivity, a new complexity measure introduced by Huynh and Nordstr\"om (STOC 2012), to study the communication complexity of search problems. To begin, we give a simple new proof of the following central result of…
In this work, we study the phase estimation problem. We show an alternative, simpler and self-contained proof of query lower bounds. Technically, compared to the previous proofs [NW99, Bes05], our proof is considerably elementary.…
Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from d-dimensional classical systems…
This note complements the paper "One-Way Ticket to Las Vegas and the Quantum Adversary" (arxiv:2301.02003). I develop the ideas behind the adversary bound - universal algorithm duality therein in a different form, using the same perspective…
Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques such as $k$-center clustering and agglomerative hierarchical clustering. These techniques…
In this paper, we consider lower bounds on the query complexity for testing CSPs in the bounded-degree model. First, for any ``symmetric'' predicate $P:{0,1}^{k} \to {0,1}$ except \equ where $k\geq 3$, we show that every (randomized)…
We present general methods for proving lower bounds on the query complexity of nonadaptive quantum algorithms. Our results are based on the adversary method of Ambainis.
Compiling Bell games under cryptographic assumptions replaces the need for physical separation, allowing nonlocality to be probed with a single untrusted device. While Kalai et al. (STOC'23) showed that this compilation preserves quantum…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…