In this article, we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.
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http://dx.doi.org/10.3390/e20070485 | DOI Listing |
Phys Rev Lett
August 2024
Physics Department and Research Center OPTIMAS, University of Kaiserslautern-Landau, 67663 Kaiserslautern, Germany.
We investigate the generic transport in a one-dimensional strongly correlated fermionic chain beyond linear response. Starting from a Gaussian wave packet with positive momentum on top of the ground state, we find that the numerical time evolution splits the signal into at least three distinct fractional charges moving with different velocities. A fractional left-moving charge is expected from conventional Luttinger liquid theory, but for the prediction of the two separate right-moving packets the nonlinearity of the dispersion must also be taken into account.
View Article and Find Full Text PDFNat Commun
August 2024
Max-Planck-Institut für Quantenoptik, Garching, Germany.
Several quantum hardware platforms, while being unable to perform fully fault-tolerant quantum computation, can still be operated as analogue quantum simulators for addressing many-body problems. However, due to the presence of errors, it is not clear to what extent those devices can provide us with an advantage with respect to classical computers. In this work, we make progress on this problem for noisy analogue quantum simulators computing physically relevant properties of many-body systems both in equilibrium and undergoing dynamics.
View Article and Find Full Text PDFPhys Rev E
June 2024
Instituto de Fisica, Universidade Federal Fluminense, Campus da Praia Vermelha Sao Domingos, 24210-346 Niteroi-RJ, Brasil.
Determinants are useful to represent the state of an interacting system of (effectively) repulsive and independent elements, like fermions in a quantum system and training samples in a learning problem. A computationally challenging problem is to compute the sum of powers of principal minors of a matrix which is relevant to the study of critical behaviors in quantum fermionic systems and finding a subset of maximally informative training data for a learning algorithm. Specifically, principal minors of positive square matrices can be considered as statistical weights of a random point process on the set of the matrix indices.
View Article and Find Full Text PDFRep Prog Phys
June 2024
Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China.
The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian. Since the topological classification of such Hamiltonians depends on their symmetry classes, a primary issue we address is determining the requirement for the Lindbladian operators, under which the modular Hamiltonian can preserve its symmetry class during the dynamical evolution.
View Article and Find Full Text PDFNat Commun
June 2024
DeepMind, London, N1C 4DJ, UK.
Quantum chemical calculations of the ground-state properties of positron-molecule complexes are challenging. The main difficulty lies in employing an appropriate basis set for representing the coalescence between electrons and a positron. Here, we tackle this problem with the recently developed Fermionic neural network (FermiNet) wavefunction, which does not depend on a basis set.
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