Related papers: A better lower bound for quantum algorithms search…
It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity $O(\sqrt{GT})$ where $T$ is…
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.…
We consider the problem of sorting $n$ items, given the outcomes of $m$ pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in $O(m + \log T)$ time and does $O(\log T)$ comparisons, where $T$ is the…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…
We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
We present an extension of Adiabatic Quantum Computing (AQC) algorithm for the unstructured search to the case when the number of marked items is unknown. The algorithm maintains the optimal Grover speedup and includes a small counting…
In this work, we study the phase estimation problem. We show an alternative, simpler and self-contained proof of query lower bounds. Technically, compared to the previous proofs [NW99, Bes05], our proof is considerably elementary.…
Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately square-root of N queries to a quantum oracle, thus achieving a square-root speed-up over classical…
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
Quantum computing technology is advancing rapidly. Yet, even accounting for these trends, a quantum leap would be needed for quantum computers to meaningfully impact deep learning over the coming decade or two. We arrive at this conclusion…
As quantum computing technology improves and quantum computers with a small but non-trivial number of N > 100 qubits appear feasible in the near future the question of possible applications of small quantum computers gains importance. One…
Despite the advent of Grover's algorithm for the unstructured search, its successful implementation on near-term quantum devices is still limited. We apply three strategies to reduce the errors associated with implementing quantum search…
Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexity theory and many other areas in theoretical computer…
Quantum search is a technique for searching N possibilities in only O(sqrt(N)) steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum…