0000000000161216
AUTHOR
Taisia Mischenko-slatenkova
Quantum Queries on Permutations
K. Iwama and R. Freivalds considered query algorithms where the black box contains a permutation. Since then several authors have compared quantum and deterministic query algorithms for permutations. It turns out that the case of \(n\)-permutations where \(n\) is an odd number is difficult. There was no example of a permutation problem where quantization can save half of the queries for \((2m+1)\)-permutations if \(m\ge 2\). Even for \((2m)\)-permutations with \(m\ge 2\), the best proved advantage of quantum query algorithms is the result by Iwama/Freivalds where the quantum query complexity is \(m\) but the deterministic query complexity is \((2m-1)\). We present a group of \(5\)-permutati…
Quantum Query Algorithms for Conjunctions
Every Boolean function can be presented as a logical formula in conjunctive normal form. Fast algorithm for conjunction plays significant role in overall algorithm for computing arbitrary Boolean function. First, we present a quantum query algorithm for conjunction of two bits. Our algorithm uses one quantum query and correct result is obtained with a probability p = 4/5, that improves the previous result. Then, we present the main result - generalization of our approach to design efficient quantum algorithms for computing conjunction of two Boolean functions. Finally, we demonstrate another kind of an algorithm for conjunction of two bits, that has a correct answer probability p = 9/10. Th…
Enlarging the gap between quantum and classical query complexity of multifunctions
Quantum computing aims to use quantum mechanical effects for the efficient performance of computational tasks. A popular research direction is enlarging the gap between classical and quantum algorithm complexity of the same computational problem. We present new results in quantum query algorithm design for multivalued functions that allow to achieve a large quantum versus classical complexity separation. To compute a basic finite multifunction in a quantum model only one query is enough while classically three queries are required. Then, we present two generalizations and a modification of the original algorithm, and obtain the following complexity gaps: Q UD (M′) ≤ N versus C UD (M′) ≥ 3N,…
High precision quantum query algorithm for computing AND-based boolean functions
Quantum algorithms can be analyzed in a query model to compute Boolean functions. Function input is provided in a black box, and the aim is to compute the function value using as few queries to the black box as possible. The complexity of the algorithm is measured by the number of queries on the worst-case input. In this paper we consider computing AND Boolean function. First, we present a quantum algorithm for AND of two bits. Our algorithm uses one quantum query and correct result is obtained with a probability p=4/5, that improves previous results. The main result is generalization of our approach to design efficient quantum algorithms for computing composite function AND(f1,f2) where fi…
An improved quantum query algorithm for computing AND Boolean function
We consider the quantum query model for computing Boolean functions. The definition of the function is known, but a black box contains the input X = (x 1 , x 2 , …, x n ). Black box can be accessed by querying x i values. The goal is to develop an algorithm, which would compute the function value for arbitrary input using as few queries to the black box as possible. We present two different quantum query algorithms for computing the basic Boolean function — logical AND of two bits. Both algorithms use only one query to determine the function value. Correct answer probability for the first algorithm is 80%, but for the second algorithm it is 90%. To compute this function with the same probab…