Related papers: Characterization of exact one-query quantum algori…
One-way quantum computing is an important and novel approach to quantum computation. By exploiting the existing particle-particle interactions, we report the first experimental realization of the complete process of deterministic one-way…
This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication…
In this paper we discuss an efficient technique that can implement any given Boolean function as a quantum circuit. The method converts a truth table of a Boolean function to the corresponding quantum circuit using a minimal number of…
Let $f$ be a real-valued, degree-$d$ Boolean function defined on the $n$-dimensional Boolean cube $\{\pm 1\}^{n}$, and $f(x) = \sum_{S \subset \{1,\ldots,d\}} \widehat{f}(S) \prod_{k \in S} x_k$ its Fourier-Walsh expansion. The main result…
Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…
The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in…
We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the maximal subproblem that can be solved without entanglement, and show that the algorithm…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
In Weighted Model Counting (WMC) we assign weights to Boolean literals and we want to compute the sum of the weights of the models of a Boolean function where the weight of a model is the product of the weights of its literals. WMC was…
Quantum formulas, defined by Yao [FOCS '93], are the quantum analogs of classical formulas, i.e., classical circuits in which all gates have fanout one. We show that any read-once quantum formula over a gate set that contains all…
We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…
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 prove a characterization of $t$-query quantum algorithms in terms of the unit ball of a space of degree-$2t$ polynomials. Based on this, we obtain a refined notion of approximate polynomial degree that equals the quantum query…
Although quantum computers are capable of solving problems like factoring exponentially faster than the best-known classical algorithms, determining the resources responsible for their computational power remains unclear. An important class…
In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state. The choices of bases for these measurements as well as the structure of the…
{\it Learning finite automata} (termed as {\it model learning}) has become an important field in machine learning and has been useful realistic applications. Quantum finite automata (QFA) are simple models of quantum computers with finite…
The von Neumann and quantum R\'enyi entropies characterize fundamental properties of quantum systems and lead to theoretical and practical applications in many fields. Quantum algorithms for estimating quantum entropies, using a quantum…