Related papers: Classical feature map surrogates and metrics for q…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
Quantum Machine Learning (QML) is fundamentally limited by two challenges: barren plateaus (exponentially vanishing gradients) and the fragility of parameterized quantum circuits under noise. Despite extensive empirical studies, a unified…
We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to $c=1$ matter. Our motivation is to understand whether some form of…
In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions…
Parameterized quantum circuits (PQCs) are a central component of many variational quantum algorithms, yet there is a lack of understanding of how their parameterization impacts algorithm performance. We initiate this discussion by using…
We show how quantum discreteness of spatial area is consistent with a unitary implementation of Lorentz boosts in an LQG type quantization of a diffeomorphism invariant reformulation of free scalar field theory on 2d flat spacetime known as…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
Equilibrium statistical ensembles impose stringent constraints on phases of quantum matter. For example, the Mermin-Wagner theorem prohibits long-range order in low-dimensional systems beyond the ground state. Here, we show that quantum…
An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the…
We revisit the mean field parametrization of shallow neural networks, using signed measures on unbounded parameter spaces and duality pairings that take into account the regularity and growth of activation functions. This setting directly…
Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…
In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, { which acts on the spin network states modifying both…
Parameterized quantum circuits used as variational ans\"atze are emerging as promising tools to tackle complex problems ranging from quantum chemistry to combinatorial optimization. These variational quantum circuits can suffer from the…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…
The theory of embedded random surfaces, equivalent to two--dimensional quantum gravity coupled to matter, is reviewed, further developed and partly generalized to four dimensions. It is shown that the action of the Liouville field theory…
Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…
We show the relationship between the Fourier coefficients and the barren plateau problem emerging in parameterized quantum circuits. In particular, the sum of squares of the Fourier coefficients is exponentially restricted concerning the…
Under ideal conditions, quantum metrology promises a precision gain over classical techniques scaling quadratically with the number of probe particles. At the same time, no-go results have shown that generic, uncorrelated noise limits the…
In finance, predictive models must balance accuracy and interpretability, particularly in credit risk assessment, where model decisions carry material consequences. We present a quantum neural network (QNN) based on a single qudit, in which…
We present a systematic study of how quantum circuit design, specifically the depth of the variational ansatz and the choice of quantum feature mapping, affects the performance of hybrid quantum-classical neural networks on a causal…