Related papers: Quantum advantage and lower bounds in parallel que…
Random access codes have provided many examples of quantum advantage in communication, but concern only one kind of information retrieval task. We introduce a related task - the Torpedo Game - and show that it admits greater quantum…
We show that any boolean function can be evaluated optimally by a quantum query algorithm that alternates a certain fixed, input-independent reflection with a second reflection that coherently queries the input string. Originally introduced…
The rapid evolution of quantum devices fuels concerted efforts to experimentally establish quantum advantage over classical computing. Many demonstrations of quantum advantage, however, rely on computational assumptions and face…
We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…
A contemporary technological milestone is to build a quantum device performing a computational task beyond the capability of any classical computer, an achievement known as quantum adversarial advantage. In what ways can the entanglement…
In Exact Quantum Query model, almost all of the Boolean functions for which non-trivial query algorithms exist are symmetric in nature. The most well known techniques in this domain exploit parity decision trees, in which the parity of two…
Aaronson and Ambainis (SICOMP `18) showed that any partial function on $N$ bits that can be computed with an advantage $\delta$ over a random guess by making $q$ quantum queries, can also be computed classically with an advantage $\delta/2$…
The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity…
One of the central problems in the study of quantum resource theories is to provide a given resource with an operational meaning, characterizing physical tasks in which the resource can give an explicit advantage over all resourceless…
Quantum parallelism is the main feature of quantum computation. In 1985 D. Deutsch showed that a single quantum computation may be sufficient to state whether a two-valued function of a two-valued variable is constant or not. Though the…
Quantum mechanical search induces polynomial speed up in an unsorted database search process. In case of classical linear search the computational time increases with the dimensionality of the query. However, quantum parallelism, inherent…
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…
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which…
Priority queues with parallel access are an attractive data structure for applications like prioritized online scheduling, discrete event simulation, or greedy algorithms. However, a classical priority queue constitutes a severe bottleneck…
We deal with the problem, initiated in [8], of finding randomized and quantum complexity of initial-value problems. We showed in [8] that a speed-up in both settings over the worst-case deterministic complexity is possible. In the present…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
We derive a device-independent quantum key distribution protocol based on synchronous correlations and their Bell inequalities. This protocol offers several advantages over other device-independent schemes including symmetry between the two…
Motivated by notions of quantum heuristics and by average-case rather than worst-case algorithmic analysis, we define quantum computational advantage in terms of individual problem instances. Inspired by the classical notions of Kolmogorov…