Related papers: Random Quantum Maps and Their Associated Quantum M…
Quantum supremacy in many applications using well-known quantum algorithms rely on availability of data in quantum format. Quantum Random Access Memory (QRAM), an equivalent of classical Random Access Memory (RAM), fulfills this…
Supermaps between quantum channels (completely positive trace-preserving (CPTP) maps of matrix algebras) were introduced in [Chiribella et al., EPL 83(3) (2008)]. In this work we generalise to supermaps between channels of any type; by…
Man\v{c}inska and Roberson introduced quantum graph homomorphisms as the existence of perfect quantum strategies for graph homomorphism games. The resulting relation is a quasi-order on finite graphs, and hence gives a partial order after…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
We introduce quantum versions of Manin pairs and Manin triples and define quantum moment maps in this context. This provides a framework that incorporates quantum moment maps for actions of Lie algebras and quantum groups for any quantum…
We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
Symmetries are a central concept in our understanding of physics. In quantum theories, a quantum reference frame (QRF) can be used to distinguish between observables related by a symmetry. The framework of operational QRFs provides a means…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
We argue that the quantum-theoretical structures studied in several recent lines of research cannot be adequately described within the standard framework of quantum circuits. This is in particular the case whenever the combination of…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and…
We introduce the notion of a quantum locally compact metric space, which is the noncommutative analogue of a locally compact metric space, and generalize to the nonunital setting the notion of quantum metric spaces introduced by Rieffel. We…
We present a strong connection between quantum information and quantum permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups, and then show…
The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures --such as triad and area operators-- exhibit a non-commutativity. At first…
Random feature mapping (RFM) is a popular method for speeding up kernel methods at the cost of losing a little accuracy. We study kernel ridge regression with random feature mapping (RFM-KRR) and establish novel out-of-sample error upper…
Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank-$D$…
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections…
Consider a Hamiltonian action of a compact connected Lie group $G$ on an aspherical symplectic manifold $(M,\omega)$. Under some assumptions on $(M,\omega)$ and the action, D. A. Salamon conjectured that counting gauge equivalence classes…