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We give a new upper bound on the quantum query complexity of deciding $st$-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation…

Quantum Physics · Physics 2019-12-19 Stacey Jeffery , Shelby Kimmel

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…

Quantum Physics · Physics 2015-02-24 Stacey Jeffery , Frederic Magniez , Ronald de Wolf

Let $R_\epsilon(\cdot)$ stand for the bounded-error randomized query complexity with error $\epsilon > 0$. For any relation $f \subseteq \{0,1\}^n \times S$ and partial Boolean function $g \subseteq \{0,1\}^m \times \{0,1\}$, we show that…

Computational Complexity · Computer Science 2018-11-28 Dmitry Gavinsky , Troy Lee , Miklos Santha , Swagato Sanyal

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…

Quantum Physics · Physics 2007-05-23 Alp Atici , Rocco A. Servedio

We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of…

Quantum Physics · Physics 2007-05-23 Harry Buhrman , Wim van Dam

This paper studies the gap between quantum one-way communication complexity $Q(f)$ and its classical counterpart $C(f)$, under the {\em unbounded-error} setting, i.e., it is enough that the success probability is strictly greater than 1/2.…

Quantum Physics · Physics 2007-09-18 Kazuo Iwama , Harumichi Nishimura , Rudy Raymond , Shigeru Yamashita

In this paper, we study quantum Ordered Binary Decision Diagrams($OBDD$) model; it is a restricted version of read-once quantum branching programs, with respect to "width" complexity. It is known that the maximal gap between deterministic…

Quantum Physics · Physics 2022-04-25 Kamil Khadiev , Aliya Khadieva , Alexander Knop

Despite years of effort, the quantum machine learning community has only been able to show quantum learning advantages for certain contrived cryptography-inspired datasets in the case of classical data. In this note, we discuss the…

Quantum Physics · Physics 2023-07-06 Casper Gyurik , Vedran Dunjko

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…

Quantum Physics · Physics 2016-07-01 Scott Aaronson , Andris Ambainis , Jānis Iraids , Martins Kokainis , Juris Smotrovs

In this work, we propose a new way to (non-interactively, verifiably) demonstrate quantum advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) constant degree multivariate…

Quantum Physics · Physics 2025-09-10 Pierre Briaud , Itai Dinur , Riddhi Ghosal , Aayush Jain , Paul Lou , Amit Sahai

Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…

Quantum Physics · Physics 2022-07-25 Umut Çalıkyılmaz , Sadi Turgut

The discovery of derivatives and integrals was a tremendous leap in scientific knowledge and completely revolutionized many fields, including mathematics, physics, and engineering. The existence of higher-order derivatives means better…

Quantum Physics · Physics 2023-05-16 Basanta R. Pahari , Sagar Bhat , Siri Davidi , William Oates

Facing the worldwide steady progress in building quantum computers, it is crucial for cryptographic community to design quantum-safe cryptographic primitives. To achieve this, we need to investigate the capability of cryptographic analysis…

Quantum Physics · Physics 2024-07-23 Huiqin Xie , Li Yang

We exploit symmetries to give short proofs for two prominent formula families of QBF proof complexity. On the one hand, we employ symmetry breakers. On the other hand, we enrich the (relatively weak) QBF resolution calculus Q-Res with the…

Logic in Computer Science · Computer Science 2018-04-05 Manuel Kauers , Martina Seidl

We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…

Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are…

Quantum Physics · Physics 2009-11-11 Janos A. Bergou , Mark Hillery

Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…

Quantum Physics · Physics 2017-04-11 Shota Nagayama

Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties so that certain subsets can reconstruct the secret, while unauthorized subsets obtain no information. While QSS was introduced over…

Quantum Physics · Physics 2023-05-02 Alper Çakan , Vipul Goyal , Chen-Da Liu-Zhang , João Ribeiro

We consider the Bennett-Brassard cryptographic scheme, which uses two conjugate quantum bases. An eavesdropper who attempts to obtain information on qubits sent in one of the bases causes a disturbance to qubits sent in the other basis. We…

Quantum Physics · Physics 2007-05-23 Christopher A. Fuchs , Nicolas Gisin , Robert B. Griffiths , Chi-Sheng Niu , Asher Peres

We consider the problem of private distributed multi-party multiplication. It is well-established that Shamir secret-sharing coding strategies can enable perfect information-theoretic privacy in distributed computation via the celebrated…

Information Theory · Computer Science 2025-01-20 Viveck R. Cadambe , Ateet Devulapalli , Haewon Jeong , Flavio P. Calmon