Quantum Monte Carlo (QMC) methods are among the central numerical tools for studying strongly correlated quantum many-body systems, particularly in higher dimensions. As quantum information has introduced new information-theoretic perspectives and diagnostics into many-body physics, QMC methods have accordingly been extended beyond the measurement of conventional linear observables. This review summarizes recent progress in adapting QMC to many-body quantum-information, focusing on qubit or spin-$1/2$ systems as a concrete setting while keeping the discussion broadly applicable to qudit and bosonic systems. We present a unified perspective on the extraction of nonlinear diagnostics, including entanglement entropies and entanglement spectra, R\'enyi negativities for mixed-state entanglement, stabilizer entropies for quantum magic, and decoherence-driven phenomena such as the interplay between imaginary-time evolution and decoherence and strong-to-weak spontaneous symmetry breaking.
Quantum computers promise advantages for simulating strongly correlated quantum many-body systems, like atomic nuclei, that are beyond the reach of classical computers. Realizing this potential requires understanding the quantum complexity structure of the target problem. We investigate the time-evolution of two key indicators of quantum complexity, bipartite entanglement entropy and non-local magic (non-stabilizerness), in nuclear reaction dynamics. We analyze two representative dynamical processes: scattering in a one-dimensional model of strongly interacting fermions governed by the Negele potential, and a realistic simulation of $^{240}$Pu fission within time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. In the former case, we find that interactions dynamically generate both entanglement and non-local magic, leaving persistent signatures of quantum complexity in the outgoing states. In the latter, we observe that substantial quantum complexity survives in the spatial bipartition of daughter fragments well beyond scission. The presence of significant non-local magic and entanglement in both cases strongly indicate that quantum computers would provide substantial advantages for accurately simulating nuclear reaction dynamics.
Saurabh V. Kadam, Antonio Bjelčić, Nicolas Schunck et al.· 0 citations
Quantum Fisher Information (QFI) is a powerful spectroscopic tool to witness many-body quantum entanglement in solid state materials, but it is not always obvious how to relate it to other characteristics of condensed matter systems. In this study we elaborate on the meaning and interpretation of QFI in condensed matter by examining simple theoretical spin systems. We use finite sized spin systems to illustrate that QFI quantifies the momentum- dependent degree of quantum entanglement (that is the entanglement depth at a given wave vector) within a wave function. We subsequently use semiclassical frustrated spin models to show that, in the context of linear spin wave theory (LSWT), QFI quantifies the momentum-dependent degree of magnon squeezing in the ground state. In antiferromagnets with a zero-energy Goldstone mode, LSWT breaks down and QFI (and entanglement depth) diverges at the magnetic ordering wave vector. We also show examples of emergent quantum phases in frustrated spin systems that do not appear in classical phase diagrams. When these emergent phases are approached, QFI diverges across multiple wave vectors in momentum space. Taken together, QFI is not only helpful as a lower bound for entanglement depth, but serves as a momentum-resolved probe of entanglement that offers a novel perspective on quantum critical phenomena.
W. Simeth, P. Laurell, Allen O. Scheie· 1 citation
Strange metals exemplify highly collective quantum many-body systems that call for new means of characterization, and there is considerable potential for quantum information approaches contributing to the cause. We investigate multipartite entanglement across the quantum phase transition of a Kondo lattice model using the quantum Fisher information (QFI). We show that the QFI associated with the spin components transverse to the order parameter characterizes the destruction of heavy quasiparticles in the Kondo-destroyed magnetic-ordered phase. The physical origin of this observation is elucidated through an analysis of the antiferromagnetic Heisenberg model. We propose to test the results in terms of both unpolarized and polarized inelastic neutron scattering measurements in the ordered part of the heavy fermion phase diagram. Our findings illustrate how different operators of a many-body system can be employed to not only witness multipartite entanglement in different sectors and but also elucidate the overall physics across different parts of the phase diagram.
Yuan Fang, Lei Chen, Mounica Mahankali et al.· 1 citation
Understanding and coherently controlling the properties of interacting quantum many-body systems is a central challenge in non-equilibrium quantum physics. While in the past decades, a wide range of many-body Hamiltonians have been introduced to study quantum chaos, atypical eigenstates, and quantum resources, systematically engineering and continuously tuning these properties within a single microscopic model remains largely unexplored. Here, we employ a pulse engineering scheme to construct an effective Hamiltonian that continuously interpolates between a chaotic Heisenberg (XXX) chain with a local impurity and the ZX Hamiltonian. Along this interpolation, we identify several families of analytically tractable atypical eigenstates embedded in the excited-state spectrum with distinct entanglement and nonstabilizerness properties. In the XXX limit, these states exhibit exact plateaus in both entanglement and stabilizer R\'enyi entropy and correspond to coherent superpositions of long-range valence-bond solid (VBS) states. As the pulse strength increases, the effective Hamiltonians exhibit a hierarchy of new set of approximate entanglement plateaus in the low-energy spectrum. Interestingly, in the fully pulse-engineered ZX limit, we uncover a distinct pair of long-range entangled stabilizer eigenstates, corresponding to rainbow scar states. We further show that pulse engineering preserves the distinct chaotic and non-chaotic regimes of the original model, while that is largely absent in the dynamical generation of entanglement and nonstabilizerness. The pulse-engineered models generate nearly identical quantum resources in both regimes, revealing a partial decoupling between quantum chaos and quantum-resource generation. Our results establish pulse engineering as a versatile framework for generating many-body Hamiltonians with structured eigenstates and tunable quantum resources.
Prasant Mallik, A. Sil, Sudipto Singha Roy· 0 citations
Quantum-state complexity diagnostics provide valuable insight into many-body dynamics, information scrambling, and quantum computation. Here, we investigate the real-time dynamics of quantum complexity in $1+1$-dimensional Abelian U(1) and non-Abelian SU(2) lattice gauge theories (LGTs), focusing on the disorder-free localization (DFL) regime. Using stabilizer R\'enyi entropy, participation R\'enyi entropy, and fermionic non-Gaussianity as measures of complexity, we observe, for both theories, two main behaviors as a function of the gauge coupling: at intermediate values, a power-law relaxation towards saturation, consistent with observations in many-body localization, and, at sufficiently large values, an ultraslow double-logarithmic growth, which we substantiate with a configuration-space bound verified by exact counting. Our results not only provide deeper insight into the dynamics of DFL but also highlight the role of gauge invariance in constraining quantum resources and are relevant to recent quantum simulations of LGTs.
D. S. Bhakuni, Giovanni Cataldi, Jad C. Halimeh et al.· 2 citations
(English) The spectacular progress in controlling quantum matter has opened new avenues for studying fundamental physics. Various experimental platforms now host hundreds of quantum units, capable of quantum state engineering, Hamiltonian simulation and universal computation, already surpassing what is classically tractable. Remarkably, the versatility of such quantum simulators allows for investigating the physics from very high to very low energy scales.
While the long-term goal is to be able to perform fault-tolerant quantum computation, noisy intermediate scale quantum (NISQ) devices are prone to errors and quantum algorithms need to be tailored to the underlying physical platform by exploiting its advantages. In that regard, qudits offer enhanced Hilbert space dimension per information carrier with respect to qubits, allowing for significant reduction of costly entanglement operations. Moreover, the higher-dimensional Hilbert space of qudits natively accommodates complex many-body models, thereby minimizing algorithmic overhead.
In this thesis, we investigate the opportunities that qudit devices offer for the quantum simulation of lattice gauge theories. Being extremely successful nonperturbative framework for studying three of the four fundamental interactions--electrodynamics, the weak and the strong force-- lattice gauge theories can be formulated as many-body systems amenable to quantum simulation. This approach overcomes the intrinsic bottlenecks of classical methods, unlocking the ability to explore out-of-equilibrium phenomena and finite-density equilibrium states.
The first part of this thesis is dedicated to the development of encoding procedures for lattice gauge theories with Abelian and non-Abelian symmetry on qudit quantum hardware. Building upon advances in the understanding of the structure of the gauge-invariant Hilbert space for specific symmetry groups, we propose scalable qudit implementation of gauge theory models in arbitrary spatial dimensions and devise variational protocols for their equilibrium and out-of-equilibrium simulation. Crucially, our methods apply to gauge theories with dynamical fermionic matter, without the need for nonlocal encodings for the fermions, as they are unitarily removed in the encoding process.
In the second part of this thesis, we use quantum-inspired numerical techniques to reveal some of the plethora of physical phenomena simple many-body models with local symmetry host. Using the multi-flavour Schwinger model (quantum electrodynamics in one spatial dimension) as an example, we show how to identify signatures of fractons — gauge field configurations with fractional topological charge. Furthermore, by examining pure gauge theories with non-Abelian dihedral symmetry, we identify the importance of the central subgroup for the spectrum and the dynamics of the many-body model, relating nontrivial fusion rules to lack of confinement and presence of exotic particle excitations. Most importantly, the lattice gauge models for both examples above, due to their simplicity, are amenable to near-term implementation on qudit quantum hardware.
Ultimately, this work takes a significant step toward harnessing qudit quantum devices for the simulation of high-energy and condensed-matter systems. By detailing resource-efficient hardware implementations and outlining near-term applications, our findings provide compelling motivation for the continued symbiosis of theoretical design and experimental realization.
(Català) El progrés espectacular en el control de la matèria quàntica ha obert noves vies per a l'estudi de la física fonamental. Diverses plataformes experimentals ja integren centenars d'unitats quàntiques, capaces d'enginyar estars quàntics, simulació d'Hamiltonians i computació universal, superant ja el que és clàssicament tractable. Notablement, la versatilitat d'aquests simuladors quàntics permet investigar la física des de les escales d'energia més altes fins a les més baixes.
Tot i que l'objectiu a llarg termini és poder realitzar computació quàntica tolerant a errors, els dispositius quàntics de mida intermèdia i amb soroll (NISQ) són propensos a errors, i els algorismes quàntics han de ser adaptats a la plataforma física subjacent aprofitant els seus avantatges. En aquest sentit, els qudits ofereixen una dimensió de l'espai de Hilbert per portador d'informació major que els qubits, cosa que permet una reducció significativa de les costoses operacions d'entrellaçament. A més, l'espai de Hilbert de major dimensió dels qudits allotja de manera nativa models complexos de molts cossos, minimitzant així el cost algorítmic.
En aquesta tesi, investiguem les oportunitats que els dispositius de qudits ofereixen per a la simulació quàntica de teories de gauge a la xarxa. En ser un marc no perturbatiu extremadament reeixit per estudiar tres de les quatre interaccions fonamentals —l'electrodinàmica i les forces feble i forta—, les teories de gauge a la xarxa poden formular-se com a sistemes de molts cossos aptes per a la simulació quàntica. Aquest enfocament supera les dificultats intrínsiques dels mètodes clàssics i permet explorar fenòmens fora de l'equilibri i estats d'equilibri de densitat finita.
La primera part d'aquesta tesi està dedicada al desenvolupament de procediments de codificació per a teories de gauge a la xarxa amb simetria abeliana i no abeliana en sistema quàntic de qudits. Basant-nos en els avenços en la comprensió de l'estructura de l'espai de Hilbert invariant de gauge per a grups de simetria específics, proposem una implementació escalable de qudits per a models de teoria de gauge en dimensions espacials arbitràries i dissenyem protocols variacionals per a la seva simulació tant en equilibri com fora d'ell. Crucialment, els nostres mètodes s'apliquen a teories de gauge amb matèria fermiònica dinàmica sense necessitat de codificacions no locals per als fermions, ja que aquests s'eliminen de forma unitària en el procés de codificació.
En la segona part d'aquesta tesi, utilitzem tècniques numèriques d'inspiració quàntica per revelar part de la gran quantitat de fenòmens físics que allotgen els models senzills de molts cossos amb simetria local. Utilitzant el model de Schwinger multiflavor (electrodinàmica quàntica en una dimensió espacial) com a exemple, mostrem com identificar signatures de fractons —configuracions de camps de gauge amb càrrega toplògica fraccionària. A més, en examinar teories de gauge pures amb simetria diedral no abeliana, identifiquem la importància del subgrup central per a l'espectre i la dinàmica del model de molts cossos, relacionant regles de fusió no trivials amb la manca de confinament i la presència d'excitacions de partícules exòtiques. El més important és que els models de gauge a la xarxa per als dos exemples anteriors, a causa de la seva simplicitat, són aptes per a una implementació a curt termini en maquinari quàntic de qudits.
En última instància, aquest treball representa un pas significatiu cap a l'aprofitament dels dispositius quàntics de qudits per a la simulació de sistemes d'alta energia i de matèria condensada. En detallar implementacions de maquinari eficients en recursos i proposar aplicacions a curt termini, els nostres resultats proporcionen una motivació convincent per a la simbiosi contínua entre el disseny teòric i la realització experimental.
(Español) El progreso espectacular en el control de la materia cuántica ha abierto nuevas vías para el estudio de la física fundamental. Diversas plataformas experimentales ya integran centenares de unidades cuánticas, capaces de realizar ingeniería de estados cuánticos, simulación de Hamiltonianos y computación universal, superando ya lo que es clásicamente tratable. Notablemente, la versatilidad de estos simuladores cuánticos permite investigar la física desde las escalas de energía más altas hasta las más bajas.
Aunque el objetivo a largo plazo es poder realizar computación cuántica tolerante a errores, los dispositivos cuánticos de escala intermedia y con ruido (NISQ) son propensos a errores, y los algoritmos cuánticos deben ser adaptados a la plataforma física subyacente aprovechando sus ventajas. En este sentido, los qudits ofrecen una dimensión del espacio de Hilbert por portador de información mayor que los qubits, lo que permite una reducción significativa de las costosas operaciones de entrelazamiento. Además, el espacio de Hilbert de mayor dimensión de los qudits aloja de manera nativa modelos complejos de muchos cuerpos, minimizando así el coste algorítmico.
En esta tesis, investigamos las oportunidades que los dispositivos de qudits ofrecen para la simulación cuántica de teorías de gauge en el retículo. Al ser un marco no perturbativo extremadamente exitoso para estudiar tres de las cuatro interacciones fundamentales —la electrodinámica y las fuerzas débil y fuerte—, las teorías de gauge en el retículo pueden formularse como sistemas de muchos cuerpos aptos para la simulación cuántica. Este enfoque supera las dificultades intrínsecas de los métodos clásicos y permite explorar fenómenos fuera del equilibrio y estados de equilibrio de densidad finita.
La primera parte de esta tesis está dedicada al desarrollo de procedimientos de codificación para teorías de gauge en el retículo con simetría abeliana y no abeliana en sistemas cuánticos de qudits. Basándonos en los avances en la comprensión de la estructura del espacio de Hilbert invariante de gauge para grupos de simetría específicos, proponemos una implementación escalable de qudits para modelos de teoría de gauge en dimensiones espaciales arbitrarias y diseñamos protocolos variacionales para su simulación tanto en equilibrio como fuera de él. Crucialmente, nuestros métodos se aplican a teorías de gauge con materia fermiónica dinámica sin necesidad de codificaciones no locales para los fermiones, ya que estos se eliminan de forma unitaria en el proceso de codificación.
En la segund
Pavel P. Popov· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
