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The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…

Quantum Physics · Physics 2011-04-26 David Rosenbaum

With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…

Quantum Physics · Physics 2009-11-13 Giuseppe Castagnoli

Given a large dataset of many tuples, it is hard for users to pick out their preferred tuples. Thus, the preference query problem, which is to find the most preferred tuples from a dataset, is widely discussed in the database area. In this…

Databases · Computer Science 2024-06-03 Hao Liu , Xiaotian You , Raymond Chi-Wing Wong

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…

Quantum Physics · Physics 2021-10-19 Andrew M. Childs , Jin-Peng Liu

The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on…

Quantum Physics · Physics 2023-08-28 Michele Dall'Arno , Francesco Buscemi , Takeshi Koshiba

In order to qualify quantum algorithms for industrial NP-Hard problems, comparing them to available polynomial approximate classical algorithms and not only to exact ones -- exponential by nature -- , is necessary. This is a great challenge…

Attaining a quantum speedup in solving practically useful optimization problems has been one of the holy grails in the field of quantum computing. While prior approaches have demonstrated speedups for certain structured problem classes,…

Quantum Physics · Physics 2026-05-04 Jan Ljubas , Tim Byrnes

In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…

Quantum Physics · Physics 2024-09-10 Weitao Lin , Guojing Tian , Xiaoming Sun

Consider a function f which is defined on the integers from 1 to N and takes the values -1 and +1. The parity of f is the product over all x from 1 to N of f(x). With no further information about f, to classically determine the parity of f…

Quantum Physics · Physics 2009-01-23 E. Farhi , J. Goldstone , S. Gutmann , M. Sipser

We introduce a quantum dynamic programming framework that allows us to directly extend to the quantum realm a large body of classical dynamic programming algorithms. The corresponding quantum dynamic programming algorithms retain the same…

One of the challenges of quantum computers in the near- and mid- term is the limited number of qubits we can use for computations. Finding methods that achieve useful quantum improvements under size limitations is thus a key question in the…

Quantum Physics · Physics 2023-03-29 Mathys Rennela , Sebastiaan Brand , Alfons Laarman , Vedran Dunjko

Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…

Quantum Physics · Physics 2019-08-22 Davide Provasoli , Benjamin Nachman , Wibe A. de Jong , Christian W Bauer

A surprising 'converse to the polynomial method' of Aaronson et al. (CCC'16) shows that any bounded quadratic polynomial can be computed exactly in expectation by a 1-query algorithm up to a universal multiplicative factor related to the…

Quantum Physics · Physics 2023-12-21 Jop Briët , Francisco Escudero Gutiérrez

We study the computation complexity of Boolean functions in the quantum black box model. In this model our task is to compute a function $f:\{0,1\}\to\{0,1\}$ on an input $x\in\{0,1\}^n$ that can be accessed by querying the black box.…

Quantum Physics · Physics 2017-01-25 Andris Ambainis , Janis Iraids

In this work we first examine the hardness of solving various search problems by hybrid quantum-classical strategies, namely, by algorithms that have both quantum and classical capabilities. We then construct a hybrid quantum-classical…

Quantum Physics · Physics 2023-11-08 Alexandru Cojocaru , Juan Garay , Fang Song

Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging…

Quantum Physics · Physics 2026-05-19 Arthur G. Rattew , Po-Wei Huang , Naixu Guo , Lirandë Pira , Patrick Rebentrost

Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…

Quantum Physics · Physics 2025-08-20 Kapil Goswami , Peter Schmelcher , Rick Mukherjee

For $m,n \in \mathbb{N}$, $m\geq 1$ and a given function $f : \mathbb{R}^m\longrightarrow \mathbb{R}$ the polynomial interpolation problem (PIP) is to determine a \emph{generic node set} $P \subseteq \mathbb{R}^m$ and the coefficients of…

Numerical Analysis · Mathematics 2017-10-31 M. Hecht , B. L. Cheeseman , K. B. Hoffmann , I. F. Sbalzarini

Recently, Jordan et al. (Nature, 2025) introduced a novel quantum-algorithmic technique called Decoded Quantum Interferometry (DQI) for solving specific combinatorial optimization problems associated with classical codes. They presented a…

Quantum Physics · Physics 2026-01-22 Ansis Rosmanis

We consider the problem of recovering (that is, interpolating) and identity testing of a "hidden" monic polynomial $f$, given an oracle access to $f(x)^e$ for $x\in{\mathbb F_q}$ (extension fields access is not permitted). The naive…

Number Theory · Mathematics 2015-02-25 Gabor Ivanyos , Marek Karpinski , Miklos Santha , Nitin Saxena , Igor Shparlinski