Related papers: Interpreting Numerical Measurements in Fixed Topol…
We consider models with topological sectors, and difficulties with their Monte Carlo simulation. In particular we are concerned with the situation where a simulation has an extremely long auto-correlation time with respect to the…
In gauge theories the field configurations often occur in distinct topological sectors. In a lattice regularised system with chiral fermions, these sectors can be defined by referring to the Atiyah-Singer Index Theorem. However, if such a…
In Monte Carlo simulations with a local update algorithm, the auto-correlation with respect to the topological charge tends to become very long. In the extreme case one can only perform reliable measurements within fixed sectors. We…
For field theories with a topological charge Q, it is often of interest to measure the topological susceptibility chi_t = ( < Q^2 > - < Q >^2 ) / V. If we manage to perform a Monte Carlo simulation where Q changes frequently, chi_t can be…
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for…
Recent years have witnessed a surge of interest in performing measurements within topological phases of matter, e.g., symmetry-protected topological (SPT) phases and topological orders. Notably, measurements of certain SPT states have been…
In lattice calculations, the approach to the continuum limit is hindered by the severe freezing of the topological charge, which prevents ergodic sampling in configuration space. In order to significantly reduce the autocorrelation time of…
We report first calculations of the topological susceptibility measured using the field theoretic method on SU(3) gauge configurations produced by the UKQCD collaboration with two flavours of dynamical, improved, Wilson fermions. Using…
A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…
We construct a few parameter approximate fixed point action for SU(2) pure gauge theory and subject it to scaling tests, via Monte Carlo simulation. We measure the critical coupling for deconfinement for lattices of temporal extent $N_t=2$,…
By considering specific limits in the gauge coupling constant of pure Yang--Mills dynamics, it is shown how there exist topological quantum field theory sectors in such systems defining nonperturbative topological configurations of the…
The topological susceptibility is an important quantity in QCD, which can be computed using lattice methods. However, at a fine lattice spacing, or when using high quality chirally symmetric quarks, algorithms which proceed in small update…
We present a precise computation of the topological susceptibility $\chi_{_\mathrm{YM}}$ of SU$(N)$ Yang-Mills theory in the large $N$ limit. The computation is done on the lattice, using high-statistics Monte Carlo simulations with $N=3,…
Multimodal structures in the sampling density (e.g. two competing phases) can be a serious problem for traditional Markov Chain Monte Carlo (MCMC), because correct sampling of the different structures can only be guaranteed for infinite…
The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes…
The measurement precision of modern quantum simulators is intrinsically constrained by the limited set of measurements that can be efficiently implemented on hardware. This fundamental limitation is particularly severe for quantum…
Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the…
Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
Previous path integral treatments of Yang-Mills on a Riemann surface automatically sum over principal fiber bundles of all possible topological types in computing quantum expectations. This paper extends the path integral formulation to…