Papers

We introduce determinant quantum-quantum Monte Carlo (DQ$^2$MC), a quantum algorithm that lifts the auxiliary-field sampling and averaging at the operational core of determinant quantum Monte Carlo onto a quantum computer. A determinant oracle synthesizes the DQMC amplitudes directly from a block encoding of the single-particle action matrix via quantum singular value transformations, so that the exponentially many Hubbard-Stratonovich weights are never enumerated, precomputed, or stored. Since the fermions are free for fixed auxiliary fields, the construction operates entirely at the single-particle level, requiring $O(\log N_{\mathrm{st}})$ system qubits and no Jordan-Wigner or Bravyi-Kitaev encoding, where $N_{\mathrm{st}}$ is the space-time volume. A full-quantum protocol makes observables interference amplitudes, eliminating the Markov chain and its autocorrelation time altogether; a hybrid quantum-classical protocol retains a constant-size active block of qubits and replaces the Metropolis-Hastings acceptance step with an exact heat-bath draw, so that cluster updates of any size are rejection-free, and passes only classical information between updates, admitting parallel tempering and distributed execution across quantum processors. The circuit-depth scales more favorably with spatial volume than classical DQMC, at the price of a post-selection overhead determined exactly by the largest target probability — polynomial for smooth distributions, exponential for sharply peaked ones. Finally, the reweighting estimator underlying the fermion sign problem maps exactly onto a quantum weak value, placing the exponential cost of sign-problematic DQMC in precise correspondence with the post-selection overhead of weak-value extraction.

We introduce a renormalization-group (RG) guided machine-learning algorithm for lattice field generation based on approximate inversion of an RG transformation. A “perfect blocking” construction supplies equilibrated long-distance modes, while a conditional normalizing flow reconstructs short-distance details and brief rethermalization removes residual errors. In 2D $\phi^4$ theory at criticality, a flow trained at $L\le32$ is reused recursively in cascades reaching $L=2048$ with correct long-distance physics.

We propose an algorithm for generating lattice field configurations based on the approximate inversion of a renormalization-group blocking transformation. We optimize the blocking transformation using a “perfect blocking” condition so that the blocked lattice distribution is well approximated by a simple coarse action. The blocking is separated into an invertible smoothing transformation followed by decimation. Machine learning, in the form of a conditional normalizing flow, is used to reconstruct the short-distance degrees of freedom removed by the decimation. A short fine-action rethermalization then removes the residual mismatch. Because the coarse ensemble supplies the long-distance modes, the same blocking transformation and conditional flow can be reused recursively on larger lattices, producing a cascade of configurations from an initial small-volume ensemble. We test the method in two-dimensional $\phi^4$ theory with $\lambda=1$ at criticality and demonstrate stable cascade upscaling from $16^2$ to $2048^2$ lattices on local computational resources. Controlled rethermalization tests show that short-distance mismatches relax rapidly, whereas a deliberately introduced mismatch in the relevant thermal direction relaxes much more slowly. The construction uses ingredients that admit natural extensions to higher-dimensional systems and, ultimately, to gauge and fermionic degrees of freedom.

We prove explicitly the n-point K-identities we proposed previously in the calculation of one tensor hard string scattering amplitudes (HSSA). These K-identities were the key to obtain the stringy scaling behavior in the saddle point calculation of the n-point HSSA and, on the other hand, to consistently match with the calculation of decoupling of zero norm states. Moreover, we introduce a G function to generate an infinite set of generalized K-identities (GKI). The lowest order set of these GKI is the scattering equations (SE) used in the calculation of field theory amplitudes in the CHY formalism. The next to leading order set of these GKI is the K-identities used previously in the calculation of one tensor HSSA. We expect that the higher order sets of these GKI can find applications in calculating other HSSA.

We discuss the tension one encounters in trying to solve, simultaneously, the $U(1)$ and strong-$CP$ problems in QCD with light quarks and a small $\bar{\theta}$ angle within QCD itself. We do so by considering the low-energy expansion of a $1$PI effective action $\Gamma$, a functional of a properly chosen set of gauge-invariant (composite) operators. After enforcing Ward-identity constraints on $\Gamma$, we prove, under minor assumptions, that $CP$ violation at small non-vanishing $\bar{\theta}$ can be avoided only if the anomaly-induced contribution to the pseudoscalar mass matrix is completely negligible when compared to its non-anomalous counterpart - that is, only if the $U(1)$ problem is not solved. The topological susceptibility in QCD and a precise generalization of the one in pure Yang-Mills theory emerge as the most important players in establishing the above tension and in determining the corrections to various known results at leading order in $\bar{\theta}$.

In three-dimensional compact U(1) lattice gauge theory color confinement can be understood analytically through the dynamics of magnetic monopoles. However, its continuum limit is pathological, since the ratio of the glueball masses to the square root of the string tension vanishes as the continuum limit is approached. We investigate a simple extension of the Wilson action in which the total number of lattice monopoles is coupled to an additional parameter $\mu$. By tuning $\beta$ and $\mu$ simultaneously, we identify a line of constant physics along which the ratio of the lightest glueball mass to the square root of the string tension remains constant. We further show that the same scaling is satisfied, within numerical uncertainties, by the other low-lying glueball masses considered in this work. Along this trajectory, the string tension in lattice units decreases with increasing $\beta$, thus suggesting that the modified lattice action may provide a regularization of three-dimensional compact U(1) gauge theory with a physically well-behaved continuum limit.

We systematically investigate the magnetic moments (MMs) and radiative decay widths of S-wave doubly heavy tetraquark states based on chromomagnetic interaction (CMI). They provide a complementary probe to distinguish compact from molecule structures in addition to the mass spectrum and strong decay properties. Using the CMI eigenvectors, we compute the MMs and M1 transition rates for the tetraquarks in the compact configuration. We predict the MM of the observed $T_{cc}(3875)^+$ with $I(J^P)=0(1^+)$ to be 0.45 $\mu_N$ when treating it as a compact tetraquark state, whereas the MM of the $0(1^+)$ $DD^*$ molecule is about $-0.07\,\mu_N$. Five radiative transition channels related to the $T_{cc}(3875)^+$ are identified with widths ranging from $6.07$ keV to $306.37$ keV. Our results show that the MMs of the $J^P=1^+$ $bc\bar{q}\bar{q}^\prime$ ($q/q^\prime=u,d,s$) and $J^P=1^+$ $QQ\bar{n}\bar{s}$ ($Q=b,c; n=u,d$) states are influenced by the diquark-spin mixing. Through the analyses of radiative transitions between different tetraquark states, we find that such processes in the $QQ\bar{n}\bar{n}^\prime$, $QQ\bar{s}\bar{s}$, and $bc\bar{n}\bar{s}$ cases may serve to reveal the tetraquark structures of the initial or final states. We also define the magnetic coupling matrices characterizing the MMs of the tetraquark system with $J^P=1^+$, with which the range of MM can be constrained. The present study provides a valuable reference point for the search of exotic states in future particle physics experiments.

Finite-volume extrapolation (FVE) is essential for extracting physical observables in the lattice calculation. While rigorous FVE formulations are well established for short-range potentials in both two- and three-body systems, long-range interactions with force ranges comparable to the lattice size $L$ remain challenging. Extending a previous data-driven scheme for two-body systems, we apply symbolic regression (PySR) to uncover universal three-body FVE formulae. For short-range potentials, we reproduce the two limiting cases, i.e. $\kappa_3\gg\kappa_2$ and $\kappa_3\sim\kappa_2$. For pure long-range potentials, we obtain a dedicated analytic expression, and after incorporating short-range contributions, we uncover a unified formula consistent with the original PySR solution, which performs excellently in the intermediate force range around 1 fm. This work demonstrates that combining machine learning with physical constraints can yield novel analytical results inaccessible to conventional theoretical tools, advancing data-driven methodologies in hadron physics.

Understanding real-time flux-tube dynamics in more than one spatial dimension is key to unlocking the non-perturbative physics of confinement, and is now actively pursued by quantum computing and simulation experiments. However, describing such dynamics has proven to be extremely challenging with both experiments and state-of-the-art numerical simulations limited to small volumes and short timescales. Here we investigate flux tube statics and real-time evolution in a genuine two-dimensional $\mathbb{Z}_2$ Higgs gauge theory at system sizes and timescales order of magnitude beyond present experiments and numerics. The key enabling element is the recently introduced Clifford-augmented matrix product states (CAMPS) framework, which we demonstrate to parametrically reduce the entanglement that must be represented in the matrix product state; both in the pure-gauge limit and in the presence of dynamical matter. We benchmark this capability through stringent tests of effective string theory, including universal spectral features and flux tube roughening properties in presence of matter. We then introduce a string-pull protocol that selectively excites transverse modes and reconstructs their finite-size spectrum in real time. In the rough regime, the response is collective, and our simulations show that this is also well captured by universal effective string theory predictions. Strong confinement instead produces long-lived, lattice-locked local dynamics persisting to times $tJ \gtrsim 100$. These results provide ab initio evidence that effective string theory captures nonequilibrium string dynamics and reveal a hitherto unexplored long-lived prethermal regime of strongly confined flux tubes, providing a novel angle on how confinement dictates dynamics in more than one spatial dimension.

Maximally mixed state spectral sampling is an unbiased quantum algorithm that allows for extraction of a finite-resolution spectral distribution from a Hamiltonian over potentially the entire allowed range of energies. We show how it may be focused on any desired area of the spectrum in order to learn about the full fingerprint of the model of interest: from its ground state phenomena such as quantum criticality, obtained from the lowest lying energies, to its thermalization behavior, obtained from the mid-spectrum. We demonstrate this technique specifically on a $(1+1)d$ non-Abelian $SO(3)$ gauge theory, providing a comprehensive analysis of the steps necessary for performing this algorithm, as well as what is possible in the near-term with superconducting quantum hardware, performing simulations with circuits that are $78$ two-qubit gates deep. We show how this algorithm is able to take advantage of emerging dynamical circuit capabilities in near-term hardware to roughly halve the number required qubits, as well as how quantum readout error mitigation is trivial for this method. Along the way, we propose a novel strategy for compiling the controlled-time evolutions needed for spectral sampling by means of Pauli-frame optimizations. We illustrate two physical applications of quantum spectral sampling – disordered many-body transitions, and mid-spectrum densities of states – and what postprocessing steps they require beyond the Fourier outputs of the algorithm.

We develop a quantum algorithmic framework for the efficient simulation of Yang–Mills theories, including the $\mathrm{SU}(3)$ gauge theory in Quantum Chromodynamics (QCD). The framework uses maximal-tree gauge in terms of gauge field variables that removes all local gauge redundancies. In the resulting gauge-fixed formulation and digitization in the field-amplitude basis, we show that Hamiltonian time evolution admits an efficient implementation based on quantum singular value transformation (QSVT). We derive upper bounds on the total number of qubits and gate complexity, finding polynomial scaling with the inverse simulation precision $1/\varepsilon_s$, lattice volume $\mathcal{V}$, gauge coupling $g$, and target energy scale $E$. Our results provide a rigorous complexity-theoretic demonstration that non-Abelian Yang–Mills theories can be simulated efficiently on quantum computers, paving the way toward first-principles quantum simulations of non-perturbative QCD dynamics.

The modular commutator $J(A,B,C) = i\langle[K_{AB},K_{BC}]\rangle$ extracts the chiral central charge $c_-$ from a single bulk wavefunction of a gapped 2d state, where $3J/\pi=c_-$. Inspired by the recent developments in the field of gapless symmetry-protected topological phases, we ask: what does the modular commutator measure, if it is well-defined at all, when the 2d bulk becomes gapless? Several interesting new insights can already be obtained using the simple Haldane honeycomb model. For the critical point hosting an isolated Dirac node we find that $J$ remains sharp: it converges to a half-quantized value, with corrections that decay as a power law in the subsystem size rather than exponentially, mirroring the power-law correlations in gapless systems. We prove the half-quantization using an emergent reflection symmetry of the massless Dirac cone, and show that the half-quantized contribution comes from the other gapped cone (the massive partner of the massless one). This massive partner can be interpreted as the physical incarnation of the Pauli-Villars regulator, which is the origin of the parity-breaking level-$\frac{1}{2}$ Chern-Simons term (with half-quantized Hall conductance) and the parity anomaly. When protected chiral edge modes coexist with a bulk Dirac node we obtain $3J/\pi = c_-+\frac{1}{2}$. The half-quantization is also shown to be robust against tripartition deformation, tuning Dirac velocity and Dirac cone anisotropy. We further investigate other types of gaplessness—quadratic nodes (in contrast to linear Dirac) and the case with Fermi surface—and show that the robust half-quantization of $J$ is lost in such non-Dirac cases. These results generalize the modular commutator beyond gapped phases, and at the same time provide an information-theoretic measurement of the parity anomaly.

The predicted extent of inhomogeneous chiral phases in effective models of quantum chromodynamics is notoriously sensitive to ultraviolet regularization. We show that this sensitivity is largely artificial. In the two-flavor Nambu–Jona-Lasinio model, conventional implementations of three-dimensional cutoff, Pauli–Villars, and proper-time regularization produce strongly different finite-momentum instability regions. Once ultraviolet regulators are restricted to genuinely divergent vacuum contributions, however, all three prescriptions yield nearly identical stability diagrams. Both the onset of the moat regime and the subsequent finite-momentum instability become quantitatively robust. The apparent scheme dependence originates from regulating ultraviolet-finite medium contributions associated with the Fermi-surface response. Our results identify spatially modulated chiral correlations as a genuine property of the dense medium rather than an artifact of the ultraviolet prescription.

We calculate the radiative decay widths of $D_{s1}(2460)\to D_s\gamma$, $D_{s1}(2536)\to D_s\gamma$, $B_{s1}(5750)\to B_s\gamma$, and $B_{s1}(5830)\to B_s\gamma$ within light-cone QCD sum rules, taking into account the mixing between the $^{1}P_{1}$ and $^{3}P_{1}$ configurations. In the bottom-strange sector, we consider the experimentally established $B_{s1}(5830)$ together with the theoretically expected lower $1^+$ state, denoted $B_{s1}(5750)$. We obtain $\Gamma[D_{s1}(2460)\to D_s\gamma]=45.9^{+10.1}_{-8.5}$ keV, $\Gamma[D_{s1}(2536)\to D_s\gamma]=0.55^{+1.73}_{-0.48}$ keV, $\Gamma[B_{s1}(5750)\to B_s\gamma]=12.0^{+2.9}_{-2.3}$ keV, and $\Gamma[B_{s1}(5830)\to B_s\gamma]=8.9^{+2.4}_{-2.0}$ keV. The $D_{s1}(2460)\to D_s\gamma$ decay width is substantially larger than that of $D_{s1}(2536)\to D_s\gamma$. This difference originates from $^{1}P_{1}$-$^{3}P_{1}$ mixing: the two basis-current contributions interfere constructively for the lower state and destructively for the higher state. In the bottom-strange sector, the two widths are comparable within their uncertainties, although the higher state still exhibits destructive interference. These results show that the radiative decay pattern of strange heavy axial-vector mesons is sensitive to the mixing of the two spin configurations.

Glueball spectroscopy and real-time production with quantum computing require three distinct ingredients: a correlated gauge vacuum, a controlled construction of pure-gauge excitations, and a dynamical detector. We develop a physics-informed quantum-algorithm toolbox for these tasks in a $(2+1)$-dimensional $\mathbb{Z}_2$ lattice gauge theory. We use the term glueball-like for localized closed-flux excitations on the confining side of this Abelian model, without identifying them with the non-Abelian glueballs of QCD. A loop-gas circuit and Hamiltonian variational ansatz prepare the gauge vacuum, Wilson-loop quantum subspace expansion constructs and characterizes low-lying excitations, and eigenvector continuation imports parameter-dependent dressing without a rapidly enlarged explicit loop basis. A Bethe–Salpeter-type transition amplitude quantifies the spatial broadening of the lightest state. For dynamics, a vacuum-dressed contractible-loop counter measures excess production of localized glueball-like structures. Although demonstrated in an Abelian model, the toolbox separates preparation, construction, compression, characterization, and dynamical detection in a form that is naturally extensible to non-Abelian lattice gauge theories.

Three dimensional compact U(1) gauge theory supports a finite density of monopoles at a fixed lattice gauge coupling. After showing evidence for the expected dependence on the lattice coupling of the density of monopoles, we study the low lying spectrum of a two flavors of two-component Wilson fermions as a function of the bare Wilson mass. The Wilson-Dirac operator that realizes the two flavors are hermitian conjugate of each other to restore parity invariance and the commutativity of the two operators expected in the typical continuum limit is not the case in the presence of monopoles for all values of the lattice gauge coupling. This results in an anomalous behavior where we see clear evidence for the presence of very small eigenvalues for a wide range of a particular sign of the bare Wilson mass. These eigenmodes are typically in one-to-one correspondence with the number of monopoles as defined by the gauge field and the spectrum associated with these modes are separated by a gap from the bulk in the asymptotic regime of the lattice gauge coupling. The eigenvalues come in pairs around zero and the eigenvalues of one sign couple to the monopoles while the modes of the opposite sign couple to the anti-monopole implying flavor symmetry breaking.

Recent advancements in direct detection (DD) experiments stimulate the investigation of the interactions of dark matter (DM) with nucleons and nuclei. In the framework of Composite Higgs Models (CHMs) the lightest Dirac composite particle (LDCP) can be stable composing a significant fraction \xi of the observed DM relic abundance. We consider the elastic scattering of the LDCP on nucleons as well as on xenon (Xe) and argon (Ar) nuclei within the CHMs in which the LDCP magnetic moment, its mass and its coupling to the Higgs doublet are suppressed by an approximate U(1) symmetry. The LDCP with non-zero magnetic dipole moment can result in a substantial enhancement of the differential event rate in the DD experiments at low recoil energies of nuclei. Assuming \xi\ge 0.1, we identify the region of the parameter space where such enhancement may be potentially observable. In addition we specify some observables that can be useful in discriminating between the DM fermions with non-zero magnetic moment and other types of dark matter particles which don't have similar electromagnetic properties.

In the matrix model of two-flavor adjoint QC$_2$D, we study the low-lying states and their properties in the intermediate-to-strong (Yang-Mills) coupling regime. The model has a classical $SU(2)_R$ chiral symmetry and the eigenstates of the Hamiltonian can be organized in its irreps. We construct the energy eigenstates in presence of a chiral chemical potential $c$ using the variational techniques. We find that when $c=0$, the ground state is always a $SU(2)_R$ singlet, irrespective of the coupling strength $g$. However, as $g$ is tuned from intermediate to strong coupling, the system under goes a crossover from a unique to a doubly degenerate ground state. The degeneracy in the strong coupling regime spontaneously breaks the axial $\mathbb{Z}_8$, while preserving the chiral symmetry. When $c \neq 0$, we find that there can be level crossings which correspond to quantum phase transitions (QPTs). Depending on the ground state, there are three possible phases. The $SU(2)_R$ symmetry is spontaneously broken in only one of these phases, and this phase can only emerge for intermediate $g$ with moderate values of $c$. In the $g-c$ plane this phase corresponds to a narrow window, outside which $SU(2)_R$ is always preserved.

The energy-momentum tensor provides a unique insight into the internal gravitational structure of the proton by revealing how energy, momentum, and mechanical properties are distributed among its different QCD components. The gravitational form factors associated with different components of the QCD energy-momentum tensor allow us to investigate the individual contributions of these sectors to the gravitational properties of the proton. In this work, we calculate the photon and gluon gravitational form factors of the proton within the framework of QCD sum rules. Using the photon and gluon components of the QCD energy-momentum tensor, we derive the corresponding sum rules for four independent gravitational form factors. Their momentum transfer dependence is analyzed within the validity region of the method and extrapolated to zero momentum transfer using a multipole parametrization. The resulting parametrizations of the form factors are used to extract the mass and scalar radii associated with the photon and gluon sectors. Our results indicate that the gluon mass radius is smaller than the photon mass radius, suggesting a more localized gluonic energy distribution inside the proton. These findings provide new nonperturbative information on the gravitational structure of the proton and offer complementary theoretical results for future lattice QCD calculations and phenomenological studies.

Mapping how strongly interacting constituents are distributed within protons is a key goal of nuclear physics and a major direction of the future Electron Ion Collider program. We propose a novel space-time description of hadron structure in terms of impact-parameter Ioffe-time distributions, relating spatial density in the plane transverse to the proton momentum and the time between the probe's absorption and the product's emission in the longitudinal direction. Using lattice Quantum Chromodynamics, we perform the first calculation of the Ioffe-time-dependent mean squared proton radii and compare our results with estimates in the Goloskokov-Kroll model. We derive a relationship between the experimentally measurable Compton form factor and the generalized Ioffe-time distribution, which allows us to perform the first extraction of the Compton form factor from lattice calculations.

We present the first direct lattice QCD determination of the $\theta$-induced CP-violating pion-nucleon-nucleon coupling $\tilde g_{\pi NN}$. Using overlap valence fermions on three $2+1$-flavor domain-wall ensembles at a single lattice spacing, we calculate the forward proton matrix element of the isovector pseudoscalar density in the $\theta$-vacuum to first order in $\bar\theta$. The parity-mixing effect in the external nucleon states is included in the extraction. The cluster-decomposition error-reduction method is used to improve the statistical precision. A simultaneous extrapolation in the valence- and sea-pion masses, with model averaging over 7 forms based on the Akaike information criterion, gives $\tilde g_{\pi NN}=0.0306(56)(124)\,\bar\theta$ at the physical point. The first uncertainty includes the statistical and matrix-element-fit systematic uncertainties, whereas the second reflects the spread among the extrapolation forms. Within these uncertainties, the result is consistent with the indirect determination based on the strong neutron-proton mass splitting. The present precision is limited primarily by the extrapolation from the relatively heavy sea-pion masses.

Dynamical symmetry breaking plays a crucial role in mass and scale generation. In QCD-like theories, its dependence on the number of fermion flavours determines the phase structure and the transition to the conformal regime. In this work, we compute non-perturbative corrections relevant to this phenomenom, including momentum dependencies and field invariants essential for an adequate realisation of the global symmetries, by means of the functional renormalisation group and the generalised flow equation. We find that the critical gauge coupling required for dynamical chiral symmetry breaking acquires a strong dependence on the number of flavours and increases sharply at $N_f^\textrm{crit}\simeq 7.30$ for $N_c=3$. This establishes a new picture of the phase transition to the conformal window that disfavours Miransky/BKT scaling and walking regimes but supports a first-order quantum phase transition and a critical region with exotic dynamics and symmetric fermion mass gaps.

In this paper, we first analyze the light-cone distribution amplitudes of the pseudoscalar Glueball and point out that the two-gluon and quark-antiquark pair contributions naturally mix at the quantum loop level. Based on the $\eta-\eta'-G-\eta_c$ tetra-mixing scheme and existing experimental results, we analyze the branching ratio of $J/\psi \to P+\gamma$ with pseudoscalar meson $P$ and extract the mixing parameters of the tetra-mixing scheme. We then successfully predict the branching ratio of $\psi(2S) \to P+\gamma$, which is found to be in good agreement with experimental results. We also find that the branching ratios of $J/\psi \to X(2370)+\gamma$ and $\psi(2S) \to X(2370)+\gamma$ are highly sensitive to the Glueball-charmonium mixing angle: the destructive mixing interference in the branching ratio of $J/\psi \to X(2370)+\gamma$ occurs at $\phi_{gc}\approx0.01$, whereas that in $\psi(2S) \to X(2370)+\gamma$ occurs at $\phi_{gc}\approx 0.11$. Moreover, the $J/\psi \to X(2370)+\gamma$ branching ratio exhibits constructive mixing interference when the mixing angle is larger than $\phi_{gc}\approx 0.02$. Finally, we also study the electroproduction cross sections of pseudoscalar mesons. After excluding the resonance contributions, the theoretical calculations agree with the experimental measurements in order of magnitude, and we also present theoretical predictions for the electroproduction cross section of the $X(2370)$. These theoretical results can be readily tested by current BESIII and Belle-II experiments, and further experimental measurements will reveal the intrinsic nature of the $X(2370)$.

We incorporate the $\Delta(1232)$ resonance into pion-induced QED radiative corrections to neutron decay and inverse beta decay (IBD). Within the framework of heavy-baryon chiral perturbation theory with explicit $\Delta$ degrees of freedom, we compute additional contributions and study their impact on IBD cross sections and on the renormalization of the nucleon isovector vector and axial-vector charges. $\Delta$ resonance does not renormalize the vector charge. For the axial-vector charge, including the $\Delta$ resonance improves convergence and reduces the QED radiative correction to the experiment-over-lattice-QCD ratio $g_A/\left(g^\mathrm{QCD}_A g_V\right)$. $\Delta$ resonance increases the pion-induced QED radiative corrections to IBD by a factor $1.2$-$1.3$.

Experimental constraints on the neutron electric dipole moment (nEDM) may imply strong-CP problem in QCD, or unnatural smallness of the QCD theta angle. In this work, we present a novel determination of the neutron electric dipole moment (nEDM) $d_n$ sensitivity to theta term from nonperturbative QCD on a lattice with background electric field. Using Feynman-Hellmann theorem, we compute nEDM from the matrix element of local topological charge density between nucleon ground states spatially polarized by an electric field. These states have mixed spatial parity, and we construct them using variational analysis. We obtain statistically significant signal for the theta induced nEDM from lattices with 2+1 dynamical domain wall fermions corresponding to pion masses of 340, 420, and 576 MeV and lattice spacing $a\approx 0.11~\text{fm}$. After extrapolating to the physical point, we obtain $d_n=-0.0050(4)(8)\bar{\theta}$ e$\cdot$fm. Comparison with the current experimental bound on nEDM implies constraint $|\bar{\theta}|\lesssim 10^{-11}$, which confirms existence of the strong-CP problem in QCD. Our pioneering work demonstrates that neutron EDM can be reliably determined from the local density of topological charge with robust control of systematic effects, and can be directly extended to other CP-violating interactions.

We construct helicity-conditioned statistical states for a Whitney-discretized electromagnetic field on a closed oriented three-manifold. The simplicial de Rham complex provides exact discrete gauge symmetry, while the Whitney inner product separates exact, harmonic, and coexact sectors. The spatial Abelian Chern–Simons functional is gauge invariant and depends only on the coexact potential. After fixing harmonic modes, we introduce a helicity-biased Gaussian ensemble on the reduced electromagnetic phase space and derive explicit formulas for its admissible parameters, partition function, mean helicity, relative entropy, and Fisher information. The distribution uniquely minimizes relative entropy under a prescribed mean-helicity constraint. Its helicity susceptibility equals the variance of the discrete Chern–Simons functional and controls the local distinguishability of neighboring statistical states. Because magnetic helicity is generally not conserved under unconstrained Maxwell dynamics, these states represent conditioned inference rather than dynamical equilibrium.

One aim of neural network field theory is to put a quantum or effective field theory on a computer, with the network ensemble itself as the theory. We ask how far that aim can be pushed for a function class regular enough to be computed with. Our main result is a no-go theorem with assumptions that hold for standard network architectures. We use it to separate four versions of neural network field theory, according to whether the defining object is the finite width ensemble or its infinite width limit, and whether the target we want to compute is a quantum or an effective field theory. Neither finite width interpretation is straightforwardly consistent. For finite width ensembles with finite variance at each point, the QFT interpretation fails reflection positivity, while the EFT interpretation establishes no scale separation by which the positivity violation can be placed outside its domain of validity. Of the two limit versions, one can be simulated in full and the other only in part, as only its smeared correlators are computable with a controlled error. As such, at the level of a controlled numerical computation, the QFT and EFT versions cannot be distinguished. One dimension escapes the obstruction, yet reflection positivity is shown to still fail there at every finite width for the cosine network. Two escapes from the theorem remain, giving up either finite variance at a point or exact rotation invariance, and we discuss both of these possibilities.

Quantum algorithms for simulating quantum chromodynamics (QCD) have matured steadily since the pioneering work of Byrnes and Yamamoto [PRA 73, 022328 (2006)]. The most popular strategies for Hamiltonian simulation involve product-formula decompositions. However, the application of product-formula methods to SU($N_c$) lattice gauge theories by Byrnes and Yamamoto leads to $O(\Lambda^{8(N_c^2-1)})$ gate complexity per Trotter step, where $\Lambda$ is the bosonic cutoff in the electric (i.e., irreducible-representation) basis. A seminal work by Kan and Nam [arXiv:2107.12769 (2021)] significantly improves over such an undesirable cost and reports an $O\big(\Lambda \text{polylog}(\Lambda)\big)$ scaling, yet it still calls for an unrealistically large number of quantum gates. Here, we illuminate one of the reasons behind this high cost estimate and show that a factor of size $O(2^{4(N_c^2-1)})$ can be removed from the per-Trotter-step cost estimate by Kan and Nam. We specifically show that, by using methods developed in our past works [PRD 112, 014508 (2025); Quantum 7, 1213 (2023)], exponentiated-Hamiltonian decomposition—a necessary step in the application of product-formula algorithms—can be performed far more efficiently than previously thought. Our method reduces the T-gate cost estimate of QCD simulations using a second-order product formula by a factor of nearly $10^{14}$, independent of simulation parameters and sizes. Focusing on simulations in the electric basis, we further contrast our results with other methods: the local-multiplet basis approach of Ciavarella, Klco, and Savage [PRD 103, 094501 (2021)] and the near-optimal algorithm of Rhodes, Kreshchuk, and Pathak [PRX Quantum 5, 040347 (2024)]. This work highlights the importance of continued algorithmic improvement to bringing the quantum-simulation cost of QCD within reach of realistic quantum computers.

Quantum error mitigation (QEM) is at the very heart of near-term quantum simulations and lattice gauge theories are no exceptions, rather their physical symmetries provide natural consistency checks on noise quantum states. In this work, we exploit the parity and fermion-number symmetries of a gauge theory, the (1+1)-dimensional Schwinger model, under depolarising noise and investigate symmetry verification under digital quantum simulation. We investigate two set-ups - symmetry- sector post-selection in adiabatic state preparation followed by real-time measurements of the chiral condensate and symmetry verification within a variational quantum eigensolver (VQE). In the first case, post-selection reduces the bias in the chiral condensate consistently removing up to 60% of the quantum noise induced error in our system. Motivated by the observed regularity of the residual bias (in the low-noise regime), we further introduce a global-noise calibration obtained from classically accessible smaller lattices and implemented on larger lattices recovering noiseless chiral condensate values within statistical uncertainty. However, in VQE, symmetry verification does not seem to generally improve the optimised parameters or the fidelity of the prepared states, although it reduces the bias in the estimated ground-state energy. This demonstates that improving a noisy cost-function estimator in variational algorithms does not necessarily improve the outcome of the algorithm. Our results show the strength of symmetry verification in different approaches while establishing that its usefulness critically depends on where it is applied in the computational workflow, and provide practical guidance for symmetry-assisted quantum error mitigation in quantum simulations of lattice gauge theories.

A common approach to studying the multiquark states is to solve the few-body Schrödinger equation within a quark potential model. The multiquark states may contain quarks with several different flavors and have richer color structures than ordinary hadrons. The reliability of such an investigation requires that the underlying quark potential model can simultaneously describe the meson and baryon spectra across all flavor sectors, including orbital and radial excitations, with a single parameter set. At present, no quark potential model fully satisfies this requirement. We construct a simple nonrelativistic constituent quark potential model that includes spin–orbit and tensor interactions. We refit the model parameters to the latest experimental data. The excited light hadrons and several exotic hadron candidates are excluded from the fit. The resulting parameter set reproduces the spectra across all fitted sectors. The vast majority of deviations are below 20 MeV, while the largest deviations remain of the order of several tens of MeV, which is the typical accuracy of nonrelativistic quark potential models. Using the same parameters, we predict the spectra and internal structures of the orbitally and radially excited heavy baryons, which await further experimental determination. The excited light baryons are calculated with the same parameters. The calculated excited light baryon spectra deviate substantially from experimental values. Our refitted model does not resolve these longstanding discrepancies. The results delimit the range of validity of the nonrelativistic constituent quark potential model. By treating mesons and baryons across all flavor sectors, including both orbital and radial excitations within a unified framework, the model provides a controlled starting point for few-body calculations of multiquark states. We also urge experimental searches for the predicted states.