We propose an effective Hamiltonian formulation of quantum field theories using a Daubechies wavelet basis in position space. Combined with flow-equation methods of the similarity renormalization group (SRG), this approach provides an efficient framework for analyzing quantum field theories by reducing the dimensionality of the Hamiltonian and systematically decoupling degrees of freedom across scales. As an application, the free scalar field theory has been reformulated within this framework to calculate the low-lying energy spectrum of the theory. These basis elements are known to transform the free scalar field theory into a theory of coupled localized oscillators, each of which is labeled by a location and a resolution index. In this representation, the Hamiltonian is naturally organized into fixed-resolution blocks, alongside blocks associated with the interactions between different resolutions. To decouple the different resolution modes and obtain a block diagonalized Hamiltonian with each block associated with a fixed resolution, the flow equation approach of SRG is applied. Finally, we demonstrate that with increasing resolution, the low-energy spectrum can be extracted from the effective lowest-resolution block of the Hamiltonian, leading to a significant reduction in computational cost.

We present a minimal implementation of SU($N$) pure Yang-Mills theory in $3+1$ dimensions for digital quantum simulation, designed to enable quantum advantage. Building on the orbifold lattice simulation protocol with logarithmic scaling in the local Hilbert-space truncation, we introduce further simplified Hamiltonians. Furthermore, we test simple methods that improve the convergence to the infinite mass limit, thereby removing the requirement of a large scalar mass to obtain the Kogut-Susskind Hamiltonian. For the SU(2) theory, we can cut the resource requirement further by utilizing the embedding of $\mathrm{SU}(2)\cong\mathrm{S}^3$ into $\mathbb{R}^4$. Monte Carlo simulations of the Euclidean path integral were used to benchmark the accuracy of these new analytical improvements to the theory. These results provide further support for the noncompact-variable-based approach as a practical framework for quantum simulation of non-Abelian gauge theories.

We present a lattice QCD study of dilepton production in charmonium transitions, specifically focusing on the $1^{+-} \to 0^{-+}$ and $1^{++} \to 1^{--}$ processes: $h_c \to \eta_c \ell^+ \ell^-$ and $\chi_{c1} \to J/\psi \ell^+ \ell^-$, where $\ell = e, \mu$. The relevant hadronic matrix elements are computed using gauge field configurations generated by the Extended Twisted Mass Collaboration with $N_f = 2+1+1$ dynamical Wilson--Clover twisted-mass fermions at four lattice spacings. Simulations are performed at physical dynamical $u$, $d$, $s$, and $c$ quark masses, except for the coarsest lattice, where the lightest sea quark mass corresponds to a slightly heavier pion mass. A controlled continuum extrapolation is carried out. In the continuum limit for the $h_c$ decays, we obtain $\Gamma(h_c \to \eta_c e^+ e^-) = 5.45(19)~\mathrm{keV}$, and $\Gamma(h_c \to \eta_c \mu^+ \mu^-) = 0.635(22)~\mathrm{keV}$. For the $\chi_{c1}$ decays, we find: $\Gamma(\chi_{c1} \to J/\psi e^+ e^-)= 2.869(90)~\mathrm{keV}$, and $\Gamma(\chi_{c1} \to J/\psi \mu^+ \mu^-) = 0.1993(72)~\mathrm{keV}$. Our results for the $\chi_{c1}$ decays show good compatibility with experimental data. However, our prediction for the $h_c \to \eta_c e^+ e^- $ decay rate is approximately $3\sigma$ larger than the BESIII result. We also present predictions for the differential decay widths as functions of the dilepton invariant mass, $q^2$, and for angular observables sensitive to longitudinal transition form factors, which are inaccessible in radiative decays with real photon emission. These results constitute the first fully dynamical lattice QCD predictions for dilepton decay rates in $h_c$ and $\chi_{c1}$ charmonium transitions, including their differential distributions and angular observables. They provide benchmark predictions for future experimental studies.

The celebrated holographic duality posits a correspondence between a quantum gravity in a bulk spacetime and a quantum field theory (QFT) defined on its lower-dimensional boundary. This duality not only offers deep insights into the enigmatic nature of quantum gravity but also provides an efficient methodology for studying strongly correlated systems. However, despite its profound significance in modern physics, holographic duality remains a conjecture, and further experimental exploration is highly sought after. Here, we present the first experimental test of holographic duality between a three-dimensional bulk gravity and a two-dimensional boundary QFT using hyperbolic lattices. By experimentally measuring the classical scalar field propagator in hyperbolic circuits, we reproduce the equal-time two-point correlation function of the dual boundary conformal field theory (CFT), verifying its exponential dependence on the boundary separation and the conformal dimension-scalar mass relation. Furthermore, by leveraging the two-point correlation function, we reconstruct the entanglement entropy for a boundary CFT subsystem, confirming that it follows the Ryu-Takayanagi formula. These results constitute the first direct experimental evidence that quantum properties of the QFT can be holographically reproduced through its dual classical field in curved space. This heuristic experimental effort opens a new avenue for in-depth investigations on the holographic duality and extensive exploration of quantum-gravity-inspired phenomena in classical systems.