Related papers: Quantum Attacks without Superposition Queries: the…
In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for…
Topology optimization is a key methodology in engineering design for finding efficient and robust structures. Due to the enormous size of the design space, evaluating all possible configurations is typically infeasible. In this work, we…
We give a natural problem over input quantum oracles $U$ which cannot be solved with exponentially many black-box queries to $U$ and $U^\dagger$, but which can be solved with constant many queries to $U$ and $U^*$, or $U$ and…
In this paper, we study applications of Bernstein-Vazirani algorithm and present several new methods to attack block ciphers. Specifically, we first present a quantum algorithm for finding the linear structures of a function. Based on it,…
Can Grover's algorithm speed up search of a physical region - for example a 2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to be needed for each query, just to move amplitude across the grid. Here we show that…
Currently there is an active Post-Quantum Cryptography (PQC) solutions search, which attempts to find cryptographic protocols resistant to attacks by means of for instance Shor polynomial time algorithm for numerical field problems like…
In the emerging domain of quantum algorithms, the Grover's quantum search is certainly one of the most significant. It is relatively simple, performs a useful task and more importantly, does it in an optimal way. However, due to the success…
In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we…
The promise of quantum computation and its consequences for complexity-theoretic cryptography motivates an immediate search for cryptosystems which can be implemented with current technology, but which remain secure even in the presence of…
Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition, traditionally achieved through Hadamard gates. However, this incidentally creates an auxiliary search space consisting of nonsensical…
We present the implementation of Grover's algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation, and bitwise exclusive or. Our…
We present quantum algorithms for routing concentration assignments on full capacity fat-and-slim concentrators, bounded fat-and-slim concentrators, and regular fat-and-slim concentrators. Classically, the concentration assignment takes…
Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…
We show that the algorithmic complexity of any classical algorithm written in a Turing-complete programming language polynomially bounds the number of quantum bits that are required to run and even symbolically execute the algorithm on a…
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise…