相关论文: A Note on the Quantum Query Complexity of the Hidd…

Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…

Eker{\aa} and H{\aa}stad have introduced a variation of Shor's algorithm for the discrete logarithm problem (DLP). Unlike Shor's original algorithm, Eker{\aa}-H{\aa}stad's algorithm solves the short DLP in groups of unknown order. In this…

We design a quantum method for classical information compression that exploits the hidden subgroup quantum algorithm. We consider sequence data in a database with a priori unknown symmetries of the hidden subgroup type. We prove that data…

In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…

Finance is one of the promising field for industrial application of quantum computing. In particular, quantum algorithms for calculation of risk measures such as the value at risk and the conditional value at risk of a credit portfolio have…

The search task is one of the most difficult when it comes to execution speed, and reducing the latter is important both when working with large data and with small samples, if they need to be processed frequently and in a limited time.…

We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup…

Quite often in database search, we only need to extract portion of the information about the satisfying item. Recently Radhakrishnan & Grover [RG] considered this problem in the following form: the database of $N$ items was divided into $K$…

Difference sets are basic combinatorial structures that have applications in signal processing, coding theory, and cryptography. We consider the problem of identifying a shifted version of the characteristic function of a (known) difference…

As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a…

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…

Advances in quantum computing make Shor's algorithm for factorising numbers ever more tractable. This threatens the security of any cryptographic system which often relies on the difficulty of factorisation. It also threatens methods based…

We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of…

We consider actions of a group or a semigroup on a set, which generalize the setup of discrete logarithm based cryptosystems. Such cryptographic group actions have gained increasing attention recently in the context of isogeny-based…

In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…

We present a quantum algorithm solving the greatest common divisor (GCD) problem. This quantum algorithm possesses similar computational complexity with classical algorithms, such as the well-known Euclidean algorithm for GCD. This…

We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…

We review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci. Rep. 3, 2773 (2013)) applied to large complex networks.…

We consider two combinatorial problems. The first we call "search with wildcards": given an unknown n-bit string x, and the ability to check whether any subset of the bits of x is equal to a provided query string, the goal is to output x.…