Related papers: Quantum Algorithms for Learning and Testing Juntas
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show…
In this paper, we propose efficient probabilistic algorithms for several problems regarding the autocorrelation spectrum. First, we present a quantum algorithm that samples from the Walsh spectrum of any derivative of $f()$. Informally, the…
Quantum computers have the opportunity to be transformative for a variety of computational tasks. Recently, there have been proposals to use the unsimulatably of large quantum devices to perform regression, classification, and other machine…
We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…
This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…
Decision of whether a Boolean equation system has a solution is an NPC problem and finding a solution is NP hard. In this paper, we present a quantum algorithm to decide whether a Boolean equation system FS has a solution and compute one if…
Several classes of quantum circuits have been shown to provide a quantum computational advantage under certain assumptions. The study of ever more restricted classes of quantum circuits capable of quantum advantage is motivated by possible…
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…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum…
The Goldreich-Levin algorithm was originally proposed for a cryptographic purpose and then applied to learning. The algorithm is to find some larger Walsh coefficients of an $n$ variable Boolean function. Roughly speaking, it takes a…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
We contrast a minimalistic implementation of quantum k-means algorithm to classical k-means algorithm. With classical simulation results, we demonstrate a quantum performance, on and above par, with the classical k-means algorithm. We…
We investigate the problem of quantum searching on a noisy quantum computer. Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand.…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
A quantum algorithm is exact if, on any input data, it outputs the correct answer with certainty (probability 1). A key question is: how big is the advantage of exact quantum algorithms over their classical counterparts: deterministic…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
A new methodology is proposed to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). Our methodology successfully finds all optimized approximated solutions for Boolean problems,…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…