Lattice field theory, along with its algorithmic and hardware ecosystems, has been at the forefront of computational particle and nuclear physics. It continues to deliver impressive results on the hadronic spectrum, structure, decays, and reactions. Yet, this vigorous campaign has fallen short in addressing a range of problems involving dense matter and general dynamical phenomena. The reason is that such problems require an exponential scaling of computing time and space in system size. Quantum simulation, enabled by quantum-computing algorithms and hardware technology, promises a way forward by offering several polynomially efficient algorithms compared with their inefficient classical counterparts. Lattice gauge theorists have engaged in a multi-pronged program to leverage such new possibilities, and have steadily advanced the state of theory, algorithm, and hardware implementations and co-design. In this talk, I motivate the quantum-computational lattice-field-theory program; introduce the questions such a program is expected to address and the strategies it involves; report on recent progress; and end with a note on challenges and opportunities ahead.

This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data to compute rigorous upper and lower bounds on the target observable. Statistical uncertainties, including correlations, are incorporated through compatibility regions using the covariance matrix. The bounds are equivalent, via Lagrange duality, to certified bounds on the target smearing kernel. For polynomial, rational, and piecewise rational kernels, the resulting dual problems can be reduced to finite-dimensional semidefinite programs using techniques familiar, e.g., in the numerical conformal bootstrap. The present formulation clarifies the relation to moment problems, Nevanlinna--Pick interpolation, and linear kernel-reconstruction methods. Numerical examples demonstrate the method.

Neutral-current semileptonic $B$ decays are plagued by hadronic resonances across the dilepton invariant-mass squared spectrum, $q^2$. For light leptons, $\ell=e,\mu$, these resonances can be avoided with suitable $q^2$ cuts. This strategy is less straightforward for $\tau$ modes, where missing energy from the $\tau$ decay makes $q^2$ difficult to reconstruct. In fact, while Belle II is able to discriminate between different regions in $q^2$ due to its clean environment, this is not directly possible in a hadronic one. Therefore, the interpretation of $b\to s\tau^+\tau^-$ measurements from e.g. LHCb, CMS requires the description of these resonant effects. In this article, we adopt a different strategy by including the resonant contributions (in particular from $\psi(2S)$) into our predictions for $B\to K^{(*)}\tau^+\tau^-$ decays, instead of avoiding them. We provide predictions for different initial kinematic points ($4m_\tau^2, 14.18\,$GeV$^2$ and $15\,$GeV$^2$) that can be convenient for LHCb, CMS and Belle II. For this, we use a data-driven approach based on the LHCb measurements of $B\to K^{(*)}\mu^+\mu^-$ decays. Including the resonances and integrating over the full $q^2$ range substantially enhances the Standard Model predictions. However, for sufficiently large New Physics, motivated by the current tensions in $R(D^{(*)})$ and $B\to K^{(*)}\nu\nu$ decays, the short-distance contribution becomes comparable to or even exceeds the resonant one. This highlights two advantages of this strategy: it exploits the additional phase space associated with the resonant regions to probe large New Physics contributions, and it enables the use of hadron-collider data, where the resonances cannot be resolved. We further quantify how including or neglecting the resonances affects the total branching ratio as a function of New Physics contributions and, equivalently, of the experimental precision.

We present a lattice QCD study of the chiral properties of $(2\!+\!1)$-flavor QCD in background magnetic fields at zero temperature with physical pion masses. Simulations are performed using the highly improved staggered quark action across four different lattice spacings to enable a controlled continuum extrapolation. We compute the renormalized chiral condensates together with pseudoscalar meson masses and decay constants for pions, kaons, and the fictitious $\eta^0_{s\bar{s}}$ pseudoscalar as functions of the magnetic-field strength $eB$ up to $eB\simeq1.2$ $\mathrm{GeV}^2$. The chiral condensates exhibit clear magnetic catalysis, increasing monotonically with the field strength. In the meson sector, neutral pseudoscalar masses decrease steadily with $eB$, whereas charged pseudoscalar masses display a nonmonotonic response: They rise at small fields, consistent with the lowest-Landau-level expectation, but then saturate and slightly decrease at larger fields, signaling sizable internal-structure effects. At the same time, neutral pseudoscalar decay constants are strongly enhanced by the magnetic field. To quantify deviations from chiral symmetry relations, we isolate the magnetic-field-induced shift in the Gell-Mann--Oakes--Renner corrections and find it to remain small for the neutral pion but to become sizable for the neutral kaon. To elucidate the origin of the magnetic response, we separately analyze the sea- and valence-quark contributions to both neutral and charged meson masses, finding that valence effects dominate at zero temperature. These results provide new insights into the interplay between QCD chiral symmetry breaking and strong magnetic fields.

In this work, expanding on previous analyses, we employ an effective Lagrangian approach to investigate the mass spectrum of scalar and pseudoscalar mesons at finite temperature, above the (pseudo-)critical temperature $T_c$, in a "realistic" $N_f = 2 + 1$ flavor scenario with degenerate $up$ and $down$ quarks and a heavier $strange$ quark: $0 < m_u = m_d \ll m_s$. The model's predictions are then critically compared with available lattice QCD results (where meson screening masses are extracted from chiral susceptibilities, which correspond to two-point correlation functions of suitable interpolating operators), looking, in particular, for signatures of the breaking of the $U(1)$ axial symmetry above $T_c$.

A scattering event in a quantum field theory is a coherent superposition of all processes consistent with its symmetries and kinematics. While real-time simulations have progressed toward resolving individual channels, existing approaches rely on knowledge of the asymptotic particle wavefunctions. This work introduces an experimentally inspired method to isolate scattering channels in Matrix Product State simulations based on the entanglement structure of the late-time wavefunction. Schmidt decompositions at spatial bipartitions of the post-scattering state identify elastic and inelastic contributions, enabling deterministic detection of outgoing particles of specific species. This method may be used in settings beyond scattering and is applied to detect heavy particles produced in a collision in the one-dimensional Ising field theory. Natural extensions to quantum simulations of other systems and higher-order processes are discussed.