Related papers: Circuit Complexity in Fermionic Field Theory
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the locality of the operators comes at the expense of increasing the Hilbert space with auxiliary degrees of freedom. In order to…
Dynamic equations that are the simplest conformally invariant generalization of Einstein equations with cosmological term are considered. Dimensions and Weyl weights of the additional geometrical fields (the vector and the antisymmetric…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
We perform the complete bosonization of 2+1 dimensional QED with one fermionic flavor in the Hamiltonian formalism. The Fermi operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify…
We provide full details of a BV formulation of $\mathcal N=1$ supergravity in ten dimensions, to all orders in fermions, built from the generalised geometry description of the theory. In contrast to standard treatments, we introduce neither…
In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…
The pseudoparticle approach is a numerical method to compute path integrals without discretizing spacetime. The basic idea is to consider only those field configurations, which can be represented as a linear superposition of a small number…
The description of black holes in loop quantum gravity is a hard and tricky task. In this article, we focus on a minisuperspace approach based on a polymerization procedure. We consider the resulting effective metric and study the…
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a…
We construct the path integral for one-dimensional non-linear sigma models, starting from a given Hamiltonian operator and states in a Hilbert space. By explicit evaluation of the discretized propagators and vertices we find the correct…
We investigate notions of complexity of states in continuous quantum-many body systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the…
We study relativistic fermionic systems in $3+1$ spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the $i\varepsilon$ term that projects on the…
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative…
We formulate directed percolation in (1+1) dimensions in the language of a reaction-diffusion process with exclusion taking place in one space dimension. We map the master equation that describes the dynamics of the system onto a quantum…
Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…
A recently proposed path-integral bosonization scheme for massive fermions in $3$ dimensions is extended by keeping the full momentum-dependence of the one-loop vacuum polarization tensor. This makes it possible to discuss both the massive…
We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…
We present a new Python package that uses the established notion of geometric quantum complexity to numerically compute the difficulty associated with preparing a given unitary transformation on a quantum computer. The numerical procedure…
In Nielsen's geometric approach to quantum complexity, the introduction of a suitable geometrical space, based on the Lie group formed by fundamental operators, facilitates the identification of complexity through geodesic distance in the…
The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross--Neveu models with…