arXiv subjects

Julius Mildenberger

Publications and source records attributed to Julius Mildenberger.

6 recordsLinked to original sources

arXiv2025

Quantum Resources in Non-Abelian Lattice Gauge Theories: Nonstabilizerness, Multipartite Entanglement, and Fermionic Non-Gaussianity

Lattice gauge theories (LGTs) represent one of the most ambitious goals of quantum simulation. From a practical implementation perspective, non-Abelian theories present significantly tougher challenges than Abelian LGTs. However, it is unknown whether this is also reflected in increased values of quantum resources relating to the complexity of simulating quantum many-body models. Here, we compare three paradigmatic measures of quantum resources -- stabilizer R\'enyi entropy, generalized geometric measure of entanglement, and fermionic antiflatness -- for pure-gauge theories on a ladder with Abelian $\mathbb{Z}_N$ as well as non-Abelian $D_3$ and SU(2) gauge symmetries. We find that non-Abelian symmetries are not necessarily inherently harder to simulate than Abelian ones, but rather the required quantum resources depend nontrivially on the interplay between the group structure, superselection sector, and encoding of the gauge constraints. Our findings help indicate where quantum advantage could emerge in simulations of LGTs, both in NISQ and fault-tolerant eras.

quant-ph↗

arXiv2024

Symmetry verification for noisy quantum simulations of non-Abelian lattice gauge theories

Non-Abelian gauge theories underlie our understanding of fundamental forces of modern physics. Simulating them on quantum hardware is an outstanding challenge in the rapidly evolving field of quantum simulation. A key prerequisite is the protection of local gauge symmetries against errors that, if unchecked, would lead to unphysical results. While an extensive toolkit devoted to identifying, mitigating, and ultimately correcting such errors has been developed for Abelian groups, non-commuting symmetry operators complicate the implementation of similar schemes in non-Abelian theories. Here, we discuss two techniques for error mitigation through symmetry verification, tailored for non-Abelian lattice gauge theories implemented in noisy qudit hardware: dynamical post-selection (DPS), based on mid-circuit measurements without active feedback, and post-processed symmetry verification (PSV), which combines measurements of correlations between target observables and gauge transformations. We illustrate both approaches for the discrete non-Abelian group $D_3$ in 2+1 dimensions, explaining their usefulness for current NISQ devices even in the presence of fast fluctuating noise. Our results open new avenues for robust quantum simulation of non-Abelian gauge theories, for further development of error-mitigation techniques, and for measurement-based control methods in qudit platforms.

quant-ph↗

arXiv2022

Probing confinement in a $\mathbb{Z}_2$ lattice gauge theory on a quantum computer

Gauge theories describe the fundamental forces in the standard model of particle physics and play an important role in condensed matter physics. The constituents of gauge theories, for example charged matter and electric gauge field, are governed by local gauge constraints, which lead to key phenomena such as confinement of particles that are not fully understood. In this context, quantum simulators may address questions that are challenging for classical methods. While engineering gauge constraints is highly demanding, recent advances in quantum computing are beginning to enable digital quantum simulations of gauge theories. Here, we simulate confinement dynamics in a $\mathbb{Z}_2$ lattice gauge theory on a superconducting quantum processor. Tuning a term that couples only to the electric field produces confinement of charges, a manifestation of the tight bond that the gauge constraint generates between both. Moreover, we show how a modification of the gauge constraint from $\mathbb{Z}_2$ towards $\mathrm{U}(1)$ symmetry freezes the system dynamics. Our work illustrates the restriction that the underlying gauge constraint imposes on the dynamics of a lattice gauge theory, it showcases how gauge constraints can be modified and protected, and it promotes the study of other models governed by multi-body interactions.

quant-ph↗

arXiv2021

Suppressing nonperturbative gauge errors in the thermodynamic limit using local pseudogenerators

With recent progress in quantum simulations of lattice-gauge theories, it is becoming a pressing question how to reliably protect the gauge symmetry that defines such models. In a recent work [J. C. Halimeh \textit{et al.}, arXiv:2108.02203], an experimentally feasible gauge-protection scheme has been proposed that is based on the concept of a \textit{local pseudogenerator}, which is required to act identically to the full gauge-symmetry generator in the target gauge sector, but not necessarily outside of it. The scheme has been analytically and numerically shown to reliably stabilize lattice gauge theories in the presence of perturbative errors on finite-size analog quantum-simulation devices. In this work, through uniform matrix product state calculations, we demonstrate the efficacy of this scheme for nonperturbative errors in analog quantum simulators up to all accessible evolution times in the thermodynamic limit, where it is \textit{a priori} neither established nor expected that this scheme will succeed. Our results indicate the presence of an emergent gauge symmetry in an adjusted gauge theory even in the thermodynamic limit, which is beyond our analytic predictions. Additionally, we show through quantum circuit model calculations that gauge protection with local pseudogenerators also successfully suppresses gauge violations on finite quantum computers that discretize time through Trotterization. Our results firm up the robustness and feasibility of the local pseudogenerator as a viable tool for enforcing gauge invariance in modern quantum simulators and NISQ devices.

quant-ph↗

arXiv2020

Gauge-Symmetry Protection Using Single-Body Terms

Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. A major challenge is to reproduce gauge invariance, as violations of this quintessential property of lattice gauge theories can have dramatic consequences, e.g., the generation of a photon mass in quantum electrodynamics. Here, we introduce an experimentally friendly method to protect gauge invariance in $\mathrm{U}(1)$ lattice gauge theories against coherent errors in a controllable way. Our method employs only single-body energy-penalty terms, thus enabling practical implementations. As we derive analytically, some sets of penalty coefficients render undesired gauge sectors inaccessible by unitary dynamics for exponentially long times, and, for few-body error terms, with resources independent of system size. These findings constitute an exponential improvement over previously known results from energy-gap protection or perturbative treatments. In our method, the gauge-invariant subspace is protected by an emergent global symmetry, meaning it can be immediately applied to other symmetries. In our numerical benchmarks for continuous-time and digital quantum simulations, gauge protection holds for all calculated evolution times (up to $t>10^{10}/J$ for continuous time, with $J$ the relevant energy scale). Crucially, our gauge-protection technique is simpler to realize than the associated ideal gauge theory, and can thus be readily implemented in current ultracold-atom analog simulators as well as digital noisy intermediate scale quantum (NISQ) devices.

quant-ph↗

arXiv2017

Kinetic Field Theory: Effects of momentum correlations on the cosmic density-fluctuation power spectrum

In earlier work, we have developed a Kinetic Field Theory (KFT) for cosmological structure formation and showed that the non-linear density-fluctuation power spectrum known from numerical simulations can be reproduced quite well even if particle interactions are taken into account to first order only. Besides approximating gravitational interactions, we had to truncate the initial correlation hierarchy of particle momenta at the second order. Here, we substantially simplify KFT. We show that its central object, the free generating functional, can be factorized, taking the full hierarchy of momentum correlations into account. The factors appearing in the generating functional, which we identify as non-linearly evolved density-fluctuation power spectra, have a universal form and can thus be tabulated for fast access in perturbation schemes. In this paper, we focus on a complete evaluation of the free generating functional of KFT, not including particle interactions yet. This implies that the non-linearly evolved power spectra contain a damping term which reflects that structures are being wiped out at late times by free streaming. Once particle interactions will be taken into account, they will compensate this damping. If we suppress this damping in a way suggested by the fluctuation-dissipation relations of KFT, our results show that the complete hierarchy of initial momentum correlations is responsible for a large part of the characteristic non-linear deformation and the mode transport in the density-fluctuation power spectrum. Without any adjustable parameters, KFT accurately reproduces the scale at which non-linear evolution sets in. Finally, we further develop perturbation theory based on the factorization of the generating functional and propose a diagrammatic scheme for the perturbation terms.

astro-ph.CO↗