Related papers: Bootstrapping Lattice Vacua
We introduce a new type of boundary conditions, {\it smooth boundary conditions}, for numerical studies of quantum lattice systems. In a number of circumstances, these boundary conditions have substantially smaller finite-size effects than…
It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
Large superconducting quantum circuits have a number of important applications in quantum computing. Accurately predicting the performance of these devices from first principles is challenging, as it requires solving the many-body…
A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These…
We review the recent literature on lattice simulations for few- and many-body systems. We focus on methods and results that combine the framework of effective field theory with computational lattice methods. Lattice effective field theory…
Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified…
Compact lattice Quantum Electrodynamics is a complex quantum field theory with dynamical gauge and matter fields and it has similarities with Quantum Chromodynamics, in particular asymptotic freedom and confinement. We consider a…
String field theory is a candidate for a full non-perturbative definition of string theory. We aim to define string field theory on a space-time lattice to investigate its behaviour at the quantum level. Specifically, we look at string…
Computing the vacuum and energy spectrum in non-Abelian, interacting lattice gauge theories remains an open challenge, in part because approximating the continuum limit requires large lattices and huge Hilbert spaces. To address this…
We explore how rotational invariance is systematically recovered from calculations on hyper-cubic lattices through the use of smeared lattice operators that smoothly evolve into continuum operators with definite angular momentum as the…
The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
The encoding of lattice gauge theories onto quantum computers requires a discretization of the gauge field's Hilbert space on each link, which presents errors with respect to the Kogut--Susskind limit. In the electric basis, Hilbert space…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
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…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
For quantum lattice systems with local interactions, the Lieb-Robinson bound acts as an alternative for the strict causality of relativistic systems and allows to prove many interesting results, in particular when the energy spectrum…
The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper we review the theoretical foundations and the most basic algorithms required to implement a typical lattice…