Related papers: Learning and Testing Algorithms for the Clifford G…

Checklists are simple decision aids that are often used to promote safety and reliability in clinical applications. In this paper, we present a method to learn checklists for clinical decision support. We represent predictive checklists as…

An algorithm is developed for finding a close to optimal junction tree of a given graph G. The algorithm has a worst case complexity O(c^k n^a) where a and c are constants, n is the number of vertices, and k is the size of the largest…

In the oracle identification problem we have oracle access to bits of an unknown string $x$ of length $n$, with the promise that it belongs to a known set $C\subseteq\{0,1\}^n$. The goal is to identify $x$ using as few queries to the oracle…

In the context of fault-detection problems, the objective is to identify all defective items among a set of $n$ binary-state items using the minimum number of tests. The {group testing} paradigm, which allows testing a subset of items in a…

Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques such as $k$-center clustering and agglomerative hierarchical clustering. These techniques…

$\kC$ clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into $k$ clusters and come up with a representative for each cluster, so that the maximum distance between an entity…

We introduce the Non-commutative Subset Convolution - a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of…

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation…

Classical simulation of quantum circuits is a pivotal part of the quantum computing landscape, specially within the NISQ era, where the constraints imposed by available hardware are unavoidable. The Gottesman-Knill theorem further motivates…

In this contribution, the clustering procedure based on K-Means algorithm is studied as an inverse problem, which is a special case of the illposed problems. The attempts to improve the quality of the clustering inverse problem drive to…

We have generalized the well-known statement that the Clifford group is a unitary 3-design into symmetric cases by extending the notion of unitary design. Concretely, we have proven that a symmetric Clifford group is a symmetric unitary…

The Clifford hierarchy is a nested sequence of sets of quantum gates that can be fault-tolerantly performed using gate teleportation within standard quantum error correction schemes. The groups of Pauli and Clifford gates constitute the…

We introduce a low-overhead approach for detecting errors in arbitrary Clifford circuits on arbitrary qubit connectivities. Our method is based on the framework of spacetime codes, and is particularly suited to near-term hardware since it…

The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…

Machine learning methods must be trusted to make appropriate decisions in real-world environments, even when faced with out-of-distribution (OOD) samples. Many current approaches simply aim to detect OOD examples and alert the user when an…

Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…

Linear combination of unitaries (LCU for short) is one of the most important techniques in designing quantum algorithms. In this paper, we propose a new quantum algorithm in three different forms to achieve LCU. Different from previous…

Let $G$ be a finite group, $N$ a normal subgroup of $G$, and $k$ a field of characteristic $p>0$. In this paper, we formulate the brick version of Clifford's theorem under suitable assumptions and prove it by using the theory of wide…

Schur-Weyl duality is a ubiquitous tool in quantum information. At its heart is the statement that the space of operators that commute with the tensor powers of all unitaries is spanned by the permutations of the tensor factors. In this…

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…