Related papers: Fermionic Gaussian states: an introduction to nume…
Gaussian quantum mechanics is a powerful tool regularly used in quantum optics to model linear and quadratic Hamiltonians efficiently. Recent interest in qubit-CV hybrid models has revealed a simple, yet important gap in our knowledge,…
A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using…
To analyze quantum many-body Hamiltonians, recently, machine learning techniques have been shown to be quite useful and powerful. However, the applicability of such machine learning solvers is still limited. Here, we propose schemes that…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
The anticommuting analysis with Grassmann variables is applied to the two-dimensional Ising model in statistical mechanics. The discussion includes the transformation of the partition function into a Gaussian fermionic integral, the…
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation…
In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In…
Understanding the computational complexity of quantum states is a central challenge in quantum many-body physics. In qubit systems, fermionic Gaussian states can be efficiently simulated on classical computers and hence can be employed as a…
Simulating quantum states on a classical computer is hard, typically requiring prohibitive resources in terms of memory and computational power. Efficient simulation, however, can be achieved for certain classes of quantum states, in…
Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…
We discuss the inclusion of fermionic loops contributions in Numerical Stochastic Perturbation Theory for Lattice Gauge Theories. We show how the algorithm implementation is in principle straightforward and report on the status of the…
In this work we present a formal solution of the extended version of the Friedrichs Model. The Hamiltonian consists of discrete and continuum bosonic states, which are coupled to fermions. The simultaneous treatment of the couplings of the…
Quantum state tomography is an essential tool for the characterization and verification of quantum states. However, as it cannot be directly applied to systems with more than a few qubits, efficient tomography of larger states on mid-sized…
Detecting when a quantum state leaves the efficiently simulable fermionic Gaussian regime is a central task for benchmarking quantum devices and certifying fermionic magic resources. We develop practical tests and witnesses based on…
The Julia package FuzzifiED aims at simplifying the numerical calculations on the fuzzy sphere. It supports exact diagonalisation (ED) and density matrix renormalisation group (DMRG) calculations. FuzzifiED can also apply to generic…
We consider the optimization problem (ground energy search) for fermionic Hamiltonians with classical interactions. This QMA-hard problem is motivated by the Coulomb electron-electron interaction being diagonal in the position basis, a…
We present a novel approach to Gaussian Berezin correlation functions. A formula well known in the literature expresses these quantities in terms of submatrices of the inverse matrix appearing in the Gaussian action. By using a recently…
We present a stochastic method for the simulation of the time evolution in systems which obey generalized statistics, namely fractional exclusion statistics and Gentile's statistics. The transition rates are derived in the framework of…