Related papers: Building manifolds from quantum codes
We address the "inverse problem" for discrete geometry, which consists in determining whether, given a discrete structure of a type that does not in general imply geometrical information or even a topology, one can associate with it a…
We introduce a general procedure called `reverse engineering' that can be used to construct infinite families of smooth 4-manifolds in a given homeomorphism type. As one of the applications of this technique, we produce an infinite family…
Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
A major hurdle to the deployment of quantum linear systems algorithms and recent quantum simulation algorithms lies in the difficulty to find inexpensive reversible circuits for arithmetic using existing hand coded methods. Motivated by…
We consider the simultaneous control of the relative phase and populations of two-level quantum systems by an external field. We apply a reverse engineering approach, which allows obtaining an analytical expression for the control field…
We use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or Renyi…
Quantum cryptography leverages many unique features of quantum information in order to construct cryptographic primitives that are oftentimes impossible classically. In this work, we build on the no-cloning principle of quantum mechanics…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
The inverse design of molecules has challenged chemists for decades. In the past years, machine learning and artificial intelligence have emerged as new tools to generate molecules tailoring desired properties, but with the limit of relying…
In this article we extend the computational geometric curve reconstruction approach to curves in Riemannian manifolds. We prove that the minimal spanning tree, given a sufficiently dense sample, correctly reconstructs the smooth arcs and…
We construct noncommutative `Riemannian manifold' structures on dual quasitriangular Hopf algebras such as $C_q[SU_2]$ with its standard bicovariant differential calculus, using the quantum frame bundle formalism introduced previously. The…
We propose a new algorithm MARINLINGA for reverse line graph computation, i.e., constructing the original graph from a given line graph. Based on the completely new and simpler principle of link relabeling and endnode recognition,…
We present a recipe for rendering a submanifold normally hyperbolic and invariant within a stability basin. The construction includes the ability to choose the asymptotic phase map. We are motivated by the notion of "templates and anchors"…
Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing…
A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
In this work, we report on a novel quantum state reconstruction process based on the disentanglement algorithm. Using variational quantum circuits, we disentangle the quantum state to a product of computational zero states. Inverse…
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.