Related papers: Towards Optimal Separations between Quantum and Ra…
In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…
We exploit Grover operator of database search algorithm for weight decision algorithm. In this research, weight decision problem is to find an exact weight w from given two weights as w1 and w2 where w1+w2=1 and 0<w1<w2<1. Firstly, if a…
Advancements in quantum computing are fuelling emerging applications across disciplines, including finance, where quantum and quantum-inspired algorithms can now make market predictions, detect fraud, and optimize portfolios. Expanding this…
We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that…
The approximate degree of a Boolean function f is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. Approximate degree is known to be a lower bound on quantum query complexity. We resolve or nearly…
The quantum approximate optimization algorithm (QAOA) is one of the most prominent proposed applications for near-term quantum computing. Here we study the ability of QAOA to solve hard constraint satisfaction problems, as opposed to…
Discrimination of unitary operations is fundamental in quantum computation and information. A lot of quantum algorithms including the well-known Deutsch-Jozsa algorithm, Simon's algorithm, and Grover's algorithm can essentially be regarded…
We study classical query algorithms with post-selection, and find that they are closely connected to rational functions with nonnegative coefficients. We show that the post-selected classical query complexity of a Boolean function is equal…
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…
Quantum information processing offers promising advances for a wide range of fields and applications, provided that we can efficiently assess the performance of the control applied in candidate systems. That is, we must be able to determine…
We establish two results regarding the query complexity of bounded-error randomized algorithms. * Bounded-error separation theorem. There exists a total function $f : \{0,1\}^n \to \{0,1\}$ whose $\epsilon$-error randomized query complexity…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
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,…
We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…
Let X = (x_0,...,x_{n-1})$ be a sequence of n numbers. For \epsilon > 0, we say that x_i is an \epsilon-approximate median if the number of elements strictly less than x_i, and the number of elements strictly greater than x_i are each less…
The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is…
We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the…
This paper considers distributed computing on an anonymous quantum network, a network in which no party has a unique identifier and quantum communication and computation are available. It is proved that the leader election problem can…
We present a bounded-error quantum algorithm for evaluating Min-Max trees. For a tree of size N our algorithm makes N^{1/2+o(1)} comparison queries, which is close to the optimal complexity for this problem.
Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…