Related papers: An Improved Query for the Hidden Subgroup Problem
We give an algorithm to solve the quantum hidden subgroup problem for maximal cyclic non-normal subgroups of the affine group of a finite field (if the field has order $q$ then the group has order $q(q-1)$) with probability $1-\varepsilon$…
The hardness to solve an unstructured quantum search problem by a standard quantum search algorithm mainly originates from the low efficiency to amplify the amplitude of the marked state by the oracle unitary operation associated with other…
Attacks on classical cryptographic protocols are usually modeled by allowing an adversary to ask queries from an oracle. Security is then defined by requiring that as long as the queries satisfy some constraint, there is some problem the…
We consider a recently proposed generalisation of the abelian hidden subgroup problem: the shifted subset problem. The problem is to determine a subset S of some abelian group, given access to quantum states of the form |S+x>, for some…
Self-supervised representation learning is a fundamental problem in computer vision with many useful applications (e.g., image search, instance level recognition, copy detection). In this paper we present a new contrastive self-supervised…
This paper introduces an extension to the Orienteering Problem (OP), called Clustered Orienteering Problem with Subgroups (COPS). In this variant, nodes are arranged into subgroups, and the subgroups are organized into clusters. A reward is…
Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the…
Given an overcomplete dictionary $A$ and a signal $b$ that is a linear combination of a few linearly independent columns of $A$, classical sparse recovery theory deals with the problem of recovering the unique sparse representation $x$ such…
It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…
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.…
The hidden subgroup problem ($\mathsf{HSP}$) has been attracting much attention in quantum computing, since several well-known quantum algorithms including Shor algorithm can be described in a uniform framework as quantum methods to address…
This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…
We are given a graph $G$ with $n$ vertices, where a random subset of $k$ vertices has been made into a clique, and the remaining edges are chosen independently with probability $\tfrac12$. This random graph model is denoted…
We propose an algorithm using a modified variant of amplitude amplification to solve combinatorial optimization problems via the use of a subdivided phase oracle. Instead of dividing input states into two groups and shifting the phase…
We study the problem of learning to cluster data points using an oracle which can answer same-cluster queries. Different from previous approaches, we do not assume that the total number of clusters is known at the beginning and do not…
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…
Anonymous Hierarchical Identity-Based Encryption (HIBE) is an extension of Identity-Based Encryption (IBE), and it provides not only a message hiding property but also an identity hiding property. Anonymous HIBE schemes can be applicable to…
The paper considers the problem of finding a given substring in a text. It is known that the complexity of a classical search query in an unordered database is linear in the length of the text and a given substring. At the same time,…
Shared control problems involve a robot learning to collaborate with a human. When learning a shared control policy, short communication between the agents can often significantly reduce running times and improve the system's accuracy. We…
It is well-known that the representation theory of the finite group of unipotent upper-triangular matrices $U_n$ over a finite field is a wild problem. By instead considering approximately irreducible representations (supercharacters), one…