arXiv subjects

Philipp Hauke

Publications and source records attributed to Philipp Hauke.

At least 37 records · Page 2Linked 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 Rényi 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↗

arXiv2025

Quantifying non-Hermiticity using single- and many-particle quantum properties

The non-Hermitian paradigm of quantum systems displays salient features drastically different from Hermitian counterparts. In this work, we focus on one such aspect, the difference of evolving quantum ensembles under $H_{\mathrm{nh}}$ (right ensemble) versus its Hermitian conjugate, $H_{\mathrm{nh}}^{\dagger}$ (left ensemble). We propose a formalism that quantifies the (dis-)similarity of these right and left ensembles, for single- as well as many-particle quantum properties. Such a comparison gives us a scope to measure the extent to which non-Hermiticity gets translated from the Hamiltonian into physically observable properties. We test the formalism in two cases: First, we construct a non-Hermitian Hamiltonian using a set of imperfect Bell states, showing that the non-Hermiticity of the Hamiltonian does not automatically comply with the non-Hermiticity at the level of observables. Second, we study the interacting Hatano--Nelson model with asymmetric hopping as a paradigmatic quantum many-body Hamiltonian. Interestingly, we identify situations where the measures of non-Hermiticity computed for the Hamiltonian, for single-, and for many-particle quantum properties behave distinctly from each other. Thus, different notions of non-Hermiticity can become useful in different physical scenarios. Furthermore, we demonstrate that the measures can qualitatively mark the model's Parity--Time (PT) symmetry-breaking transition. Our findings can be instrumental in unveiling new exotic quantum phases of non-Hermitian quantum many-body systems as well as in preparing resourceful states for quantum technologies.

quant-ph↗

arXiv2025

Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model

Gauge-field configurations with nontrivial topology have profound consequences for the physics of Abelian and non-Abelian gauge theories. Over time, arguments have been gathering for the existence of gauge-field configurations with fractional topological charge, called fractons. Ground-state properties of gauge theories can drastically change in presence of fractons in the path integral. However, understanding the origin of such fractons is usually restricted to semiclassical argumentation. Here, we show that fractons persist in strongly correlated many-body systems, using the multiflavor Schwinger model of quantum electrodynamics as a paradigm example. Through detailed numerical tensor-network analysis, we find strong fracton signatures even in highly discretized lattice models, at sizes that are implementable on already existing quantum-simulation devices. Our work sheds light on how the nontrivial topology of gauge theories persists in challenging nonperturbative regimes, and it shows a path forward to probing it in tabletop experiments.

hep-lat↗

arXiv2025

Role of Nonstabilizerness in Quantum Optimization

Quantum optimization has emerged as a promising approach for tackling complicated classical optimization problems using quantum devices. However, the extent to which such algorithms harness genuine quantum resources and the role of these resources in their success remain open questions. In this work, we investigate the resource requirements of the Quantum Approximate Optimization Algorithm (QAOA) through the lens of the resource theory of nonstabilizerness. We demonstrate that the nonstabilizerness in QAOA increases with circuit depth before it reaches a maximum, to fall again during the approach to the final solution state -- creating a barrier that limits the algorithm's capability for shallow circuits. We find curves corresponding to different depths to collapse under a simple rescaling, and we reveal a nontrivial relationship between the final nonstabilizerness and the success probability. Finally, we identify a similar nonstabilizerness barrier also in adiabatic quantum annealing. Our results provide deeper insights into how quantum resources influence quantum optimization.

quant-ph↗

arXiv2025

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↗

arXiv2025

Unveiling Eigenstate Thermalization for Non-Hermitian systems

The eigenstate thermalization hypothesis (ETH) has been highly influential in explaining thermodynamic behavior of closed quantum systems. As of yet, it is unclear whether and how the ETH applies to non-Hermitian systems. Here, we introduce a framework that extends the ETH to non-Hermitian systems, within which expectation values of local operators reproduce statistical and scaling predictions known from Hermitian ETH. We illustrate the validity of the framework on non-Hermitian random-matrix and Sachdev-Ye-Kitaev models. Further, we show numerically how the static ETH predictions become imprinted onto the dynamics of local observables. Finally, we present a prescription for observing both ETH-obeying and ETH-violating regimes in an optical-lattice experiment that implements a disordered interacting Hatano-Nelson model. Our results generalize the celebrated ETH to the non-Hermitian setting, and they show how it affects the system dynamics, and how the salient signatures can be observed in present-day cold-atom experiments.

quant-ph↗

arXiv2025

The role of higher-order terms in trapped-ion quantum computing with magnetic gradient induced coupling

Trapped-ion hardware based on the Magnetic Gradient Induced Coupling (MAGIC) scheme is emerging as a promising platform for quantum computing. Nevertheless, in this -- as in any other -- quantum-computing platform, many technical questions still have to be resolved before large-scale and error-tolerant applications are possible. In this work, we present a thorough discussion of the structure and effects of higher-order terms in the MAGIC setup, which can occur due to anharmonicities in the external potential of the ion crystal (e.g., through Coulomb repulsion) or through curvature of the applied magnetic field. These terms generate systematic shifts in the leading-order interactions and take the form of three-spin couplings, two-spin couplings, local fields, as well as diverse phonon-phonon conversion mechanisms. We find that most of these are negligible in realistic situations, with only two contributions that need careful attention. First, there are undesired longitudinal fields contributing shifts to the resonance frequency, whose strength increases with chain length and phonon occupation numbers; while their mean effect can easily be compensated by additional $Z$ rotations, phonon number fluctuations need to be avoided for precise gate operations. Second, anharmonicities of the Coulomb interaction can lead to well-known two-to-one conversions of phonon excitations. Both of these error terms can be mitigated by sufficiently cooling the phonons to the ground-state. Our detailed analysis constitutes an important contribution on the way of making magnetic-gradient trapped-ion quantum technology fit for large-scale applications, and it may inspire new ways to purposefully design interaction terms.

quant-ph↗

arXiv2025

Boosting quantum annealing performance through direct polynomial unconstrained binary optimization

Quantum annealing aims at solving optimization problems of practical relevance using quantum-computing hardware. Problems of interest are typically formulated in terms of quadratic unconstrained binary optimization (QUBO) Hamiltonians. However, many optimization problems are much more naturally formulated in terms of polynomial unconstrained binary optimization (PUBO) functions of higher order. As we show with various problem examples, leveraging the PUBO formulation can bring considerable savings in terms of required number of qubits. Moreover, in numerical benchmarks for the paradigmatic 3-SAT problem, we find scenarios where the scaling of the minimum energy gap during the optimization sweep differs significantly, suggesting the possibility of an exponentially faster annealing time when using the PUBO as compared to the QUBO formulation. This advantage persists even when considering the overhead caused by the higher-order interactions necessary for PUBO cost Hamiltonians. As an interesting side effect, the analysis on minimum energy gaps of different 3-SAT instance generators reveals different degrees of hardness, which will be of interest also for classical benchmark calculations. Our findings show a promising path to improving the resource efficiency and sweeping speed of quantum annealing protocols on both analog and digital platforms, which are important prerequisites when aiming at solving larger optimization problems with relevance to industry.

quant-ph↗

arXiv2025

Qudit-native measurement protocol for dynamical correlations using Hadamard tests

Dynamical correlations reveal important out-of-equilibrium properties of the underlying quantum many-body system, yet they are notoriously difficult to measure in experiments. While measurement protocols for dynamical correlations based on Hadamard tests for qubit quantum devices exist, they do not straightforwardly extend to qudits. Here, we propose a modified protocol to overcome this limitation by decomposing qudit observables into unitary operations that can be implemented and probed in a quantum circuit. We benchmark our algorithm numerically at the example of quench dynamics in a spin-1 XXZ chain with finite shot noise and demonstrate advantages in terms of the signal-to-noise ratio over established protocols based on linear response. Our scheme can readily be implemented on various platforms and offers a wide range of applications like variational quantum optimization and probing thermalization in many-body systems.

quant-ph↗

arXiv2025

Symmetry-protection Zeno phase transition in monitored lattice gauge theories

Quantum measurements profoundly influence system dynamics. They lead to complex nonequilibrium phenomena like the quantum Zeno effect, and they can be used for mitigating errors in quantum simulations. Such an ability is particularly valuable for lattice gauge theories (LGTs), which require the challenging preservation of an extensive number of local conservation laws. While it is known that tailored quantum measurements can soften violations of gauge symmetry, the nature of this protection, and in particular the possibility of a threshold behavior, is still unexplored. Here, we demonstrate the existence of a sharp transition, triggered by the measurement rate, between a protected gauge-theory regime resistant to simulation errors and an irregular regime. Our results are based on the paradigmatic example of a 1+1d $\mathbb{Z}_2$ LGT. We study in detail the protection through projective measurements of ancillary qubits coupled to the local symmetry generators, and compare this approach with analog (weak) measurement protocols. We show that, while the resulting ensemble averages in the continuous-time limit share the same Liouvillian dynamics, different physical implementations of the stochastic gauge protection protocol yield trajectory unravelings with vastly different statistics. Additionally, we design an on-chip feedback mechanism that corrects bit-flip errors and significantly enhances the discrete-time scheme. Our results shed light on the dissipative criticality of strongly-interacting, highly-constrained quantum systems, and they offer valuable insights into error mitigation and correction of gauge-theory quantum simulations.

quant-ph↗

arXiv2025

Statistical Mechanics of Heteropolymers from Lattice Gauge Theory

Lattice models are valuable tools to gain insight into the statistical physics of heteropolymers. We rigorously map the partition function of these models into a vacuum expectation value of a $\mathbb{Z}_2$ lattice gauge theory (LGT), with both fermionic and bosonic degrees of freedom. Because the associated path integral expression is not affected by a sign problem, it is amenable to Monte Carlo (MC) sampling in both the sequence and structure space, unlike conventional polymer field theory. At the same time, since the LGT encoding relies on qubits, it provides a framework for future efforts to capitalize on the development of quantum computing hardware. We discuss two illustrative applications of our formalism: first, we use it to characterize the thermodynamically stable sequences and structures of small heteropolymers consisting of two types of residues. Next, we assess its efficiency to sample ensembles of compact structures, finding that the MC decorrelation time scales only linearly with the chain length.

cond-mat.stat-mech↗

arXiv2025

Genuine Multipartite Entanglement in Quantum Optimization

The ability to generate bipartite entanglement in quantum computing technologies is widely regarded as pivotal. However, the role of genuinely multipartite entanglement is much less understood than bipartite entanglement, particularly in the context of solving complicated optimization problems using quantum devices. It is thus crucial from both the algorithmic and hardware standpoints to understand whether multipartite entanglement contributes to achieving a good solution. Here, we tackle this challenge by analyzing genuine multipartite entanglement -- quantified by the generalized geometric measure -- generated in Trotterized quantum annealing and the quantum approximate optimization algorithm. Using numerical benchmarks, we analyze its occurrence in the annealing schedule in detail. We observe a multipartite-entanglement barrier, and we explore how it correlates to the algorithm's success. We also prove how multipartite entanglement provides an upper bound to the overlap of the instantaneous state with an exact solution. Vice versa, the overlaps to the initial and final product states, which can be easily measured experimentally, offer upper bounds for the multipartite entanglement during the entire schedule. Our results help to shed light on how complex quantum correlations come to bear as a resource in quantum optimization.

quant-ph↗

arXiv2025

Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to $\mathbb{D}_8$

In this work, we address the problem of a resource-efficient formulation of non-Abelian LGTs by focusing on the difficulty of simulating fermionic degrees of freedom and the Hilbert space redundancy. First, we show a procedure that removes the matter and improves the efficiency of the hardware resources. We demonstrate it for the simplest non-Abelian group addressable with this procedure, $\mathbb{D}_8$, both in the cases of one (1D) and two (2D) spatial dimensions. Then, with the objective of running a variational quantum simulation on real quantum hardware, we map the $\mathbb{D}_8$ lattice gauge theory onto qudit systems with local interactions. We propose a variational scheme for the qudit system with a local Hamiltonian, which can be implemented on a universal qudit quantum device as the one developed in $\href{https://doi.org/10.1038/s41567-022-01658-0}{[Nat. Phys. 18, 1053 (2022)]}$. Our results show the effectiveness of the matter-removing procedure, solving the redundancy problem and reducing the amount of quantum resources. This can serve as a way of simulating lattice gauge theories in high spatial dimensions, with non-Abelian gauge groups, and including dynamical fermions.

hep-lat↗

arXiv2024

Disorder-averaged Qudit Dynamics

Understanding how physical systems are influenced by disorder is a fundamental challenge in quantum science. Addressing its effects often involves numerical averaging over a large number of samples, and it is not always easy to gain an analytical handle on exploring the effect of disorder. In this work, we derive exact solutions for disorder-averaged dynamics generated by any Hamiltonian that is a periodic matrix (potentially with non-trivial base, a property also called ($p,q$)-potency). Notably, this approach is independent of the initial state, exact for arbitrary evolution times, and it holds for Hermitian as well as non-Hermitian systems. The ensemble behavior resembles that of an open quantum system, whose decoherence function or rates are determined by the disorder distribution and the periodicity of the Hamiltonian. Depending on the underlying distribution, the dynamics can display non-Markovian characteristics detectable through non-Markovian witnesses. We illustrate the scheme for qubit and qudit systems described by (products of) spin $1/2$, spin $1$, and clock operators. Our methodology offers a framework to leverage disorder-averaged exact dynamics for a range of applications in quantum-information processing and beyond.

quant-ph↗

arXiv2024

Symmetry-enhanced Counterdiabatic Quantum Algorithm for Qudits

Qubit-based variational quantum algorithms have undergone rapid development in recent years but still face several challenges. In this context, we propose a symmetry-enhanced digitized counterdiabatic quantum algorithm utilizing qudits instead of qubits. This approach offers three types of compression as compared to with respect to conventional variational circuits. First, compression in the circuit depth is achieved by counterdiabatic protocols. Second, information about the problem is compressed by replacing qubits with qudits, allowing for a more efficient representation of the problem. Lastly, the number of parameters is reduced by employing the symmetries of the system. We illustrate this approach by tackling a graph-based optimization problem Max-3-Cut and a highly-entangled state preparation, the qutrit W state. As our numerical results show, we achieve a better convergence with a lower circuit depth and less measurement overhead in all the cases considered. This work leads to a better design of shallow variational quantum circuits, improving the feasibility of their implementation on near-term qudit devices

quant-ph↗

arXiv2024

Inequality constraints in variational quantum circuits with qudits

Quantum optimization is emerging as a prominent candidate for exploiting the capabilities of near-term quantum devices. Many application-relevant optimization tasks require the inclusion of inequality constraints, usually handled by enlarging the Hilbert space through the addition of slack variables. This approach, however, requires significant additional resources especially when considering multiple constraints. Here, we study an alternative direct implementation of these constraints within the QAOA algorithm, achieved using qudit-SUM gates, and compare it to the slack variable method generalized to qudits. We benchmark these approaches on three paradigmatic optimization problems. We find that the direct implementation of the inequality penalties vastly outperforms the slack variables method, especially when studying real-world inspired problems with many constraints. Within the direct penalty implementation, a linear energy penalty for unfeasible states outperforms other investigated functional forms, such as the canonical quadratic penalty. The proposed approach may thus be an enabling step for approaching realistic industry-scale and fundamental science problems with large numbers of inequality constraints.

quant-ph↗

arXiv2024

Short-time Accuracy and Intra-electron Correlation for Nonadiabatic Quantum-Classical Mapping Approaches

Nonadiabatic quantum-classical mapping approaches have significantly gained in popularity in the past several decades because they have acceptable accuracy while remaining numerically tractable even for large system sizes. In the recent few years, several novel mapping approaches have been developed that display higher accuracy than the traditional Ehrenfest method, linearized semiclassical initial value representation (LSC-IVR), and Poisson bracket mapping equation (PBME) approaches. While various benchmarks have already demonstrated the advantages and limitations of those methods, rigorous theoretical justifications of their short-time accuracy are still demanded. In this article, we systematically examine the intra-electron correlation, as a statistical measure of electronic phase space, which has been first formally proposed for mapping approaches in the context of the generalized discrete truncated Wigner approximation (GDTWA) and which is a key ingredient for the improvement of short-time accuracy of such mapping approaches. We rigorously establish the connection between short-time accuracy and intra-electron correlation for various widely used models. We find that LSC-IVR, PBME, and Ehrenfest methods fail to correctly reproduce the intra-electron correlation. While some of the traceless Meyer--Miller--Stock--Thoss (MMST) approaches, partially linearized density matrix (PLDM) approach, and spin partially linearized density matrix (Spin-PLDM) approach are able to sample the intra-electron correlation correctly, the spin linearized semiclassical (Spin-LSC) approach and the other traceless MMST approaches sample the intra-correlation faithfully only for two-level systems. Our theoretical analysis provides insights into the short-time accuracy of semiclassical methods and presents mathematical justifications for previous numerical benchmarks.

physics.chem-ph↗

arXiv2024

Protein Design by Integrating Machine Learning with Quantum Annealing and Quantum-inspired Optimization

The protein design problem involves finding polypeptide sequences folding into a given threedimensional structure. Its rigorous algorithmic solution is computationally demanding, involving a nested search in sequence and structure spaces. Structure searches can now be bypassed thanks to recent machine learning breakthroughs, which have enabled accurate and rapid structure predictions. Similarly, sequence searches might be entirely transformed by the advent of quantum annealing machines and by the required new encodings of the search problem, which could be performative even on classical machines. In this work, we introduce a general protein design scheme where algorithmic and technological advancements in machine learning and quantum-inspired algorithms can be integrated, and an optimal physics-based scoring function is iteratively learned. In this first proof-of-concept application, we apply the iterative method to a lattice protein model amenable to exhaustive benchmarks, finding that it can rapidly learn a physics-based scoring function and achieve promising design performances. Strikingly, our quantum-inspired reformulation outperforms conventional sequence optimization even when adopted on classical machines. The scheme is general and can be easily extended, e.g., to encompass off-lattice models, and it can integrate progress on various computational platforms, thus representing a new paradigm approach for protein design.

quant-ph↗