Related papers: From optimal measurement to efficient quantum algo…
We show that the general Heisenberg Hamiltonian with non-uniform couplings can be characterised by mapping the entanglement it generates as a function of time. Identification of the Hamiltonian in this way is possible as the coefficients of…
Testing efficiently whether a finite set with a binary operation over it, given as an oracle, is a group is a well-known open problem in the field of property testing. Recently, Friedl, Ivanyos and Santha have made a significant step in the…
Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For…
The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…
We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical…
We consider deterministic algorithms for the well-known hidden subgroup problem ($\mathsf{HSP}$): for a finite group $G$ and a finite set $X$, given a function $f:G \to X$ and the promise that for any $g_1, g_2 \in G, f(g_1) = f(g_2)$ iff…
An important task for quantum information processing is optimal discrimination between two non-orthogonal quantum states, which until now has only been realized optically. Here, we present and compare experimental realizations of optimal…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete…
Let $G$ be a finite group, $N$ a nilpotent normal subgroup of $G$ and let $\mathrm{V}(\mathbb{\Z} G, N)$ denote the group formed by the units of the integral group ring $\mathbb{\Z} G$ of $G$ which map to the identity under the natural…
The group isomorphism problem asks whether two finite groups given by their Cayley tables are isomorphic or not. Although there are polynomial-time algorithms for some specific group classes, the best known algorithm for testing isomorphism…
Let $P$ be a generalized laplacian on $R^{2n+1}$. It is known that $P$ is the generating functional of semigroups of measures $\mu_{t}$ on the Heisenberg group $H^{n}$ and $\nu_{t}$ on the Abelian group $R^{2n+1}$. Under some smoothness and…
We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient variational quantum/classical computations. We establish a robust connection between…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
Monitoring machine learning systems post deployment is critical to ensure the reliability of the systems. Particularly importance is the problem of monitoring the performance of machine learning systems across all the data subgroups…
We describe a new algorithm for computing the ideal class group, the regulator and a system of fundamental units in number fields under the generalized Riemann hypothesis. We use sieving techniques adapted from the number field sieve…
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…
We consider the problem of grouping items into clusters based on few random pairwise comparisons between the items. We introduce three closely related algorithms for this task: a belief propagation algorithm approximating the Bayes optimal…
Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum…