The transverse-field Ising model has attracted a lot of attention in recent years, especially in the quantum simulation and quantum computation literature. This interest is driven by many platforms for analog quantum computation, which implement the transverse-field Ising model for solving optimization problems, such as quantum annealing. However, it has remained an open question whether the Ising model with a global transverse field is equivalent to the gate model of quantum computation. Here we answer this question affirmatively for the case of a non-monotonic time-dependent transverse field. Building on a recent result by Cesa and Pichler on global control of Rydberg atoms, we provide a construction that allows simulating arbitrary quantum circuits using the Ising model with global transverse field with polynomial overhead in time, qubit number, and energy scale. Although the polynomial overheads we establish here are large relative to what is feasible on real-world quantum hardware, our result motivates the development of more sophisticated methods for simulating quantum circuits using the Ising model with a global transverse field. Additionally, under the assumption that quantum computing is strictly more powerful than classical computing, our result serves as a no-go theorem for efficient classical simulation of the transverse-field Ising model with a time-dependent global transverse field. Therefore, our finding is relevant for multiple communities, from analog quantum simulation and quantum optimization on various platforms to complexity and control theory.
This work introduces a unified measure, the magic R\'enyi entropy (MRE), to quantify computational resources in spins, bosons, and fermions on an equal footing and shows that the MRE is a resource monotone under stabilizer and Gaussian protocols involving measurements and feedforward operations.
The transverse-field Ising model is a fundamental quantum spin system that captures the competition between quantum fluctuations and interactions, playing a central role in studies of quantum phase transitions and non-equilibrium dynamics. However, classical computations of ground and excited states in large-scale or high-dimensional systems are severely limited by the exponential growth of the Hilbert space. Here, we propose a novel approach using a D-Wave quantum annealer, where a triangular-wave oscillating magnetic field is applied to induce Rabi oscillations, allowing the estimation of energy gaps between the ground and excited states. Unlike conventional quantum annealing methods limited to ground-state searches, this approach can directly access excited-state information. It is potentially applicable to larger systems, providing a new avenue for quantum-device-based simulation. The validity of the method is demonstrated through numerical simulations of relatively small systems.
Quantum computing provides a promising framework for the simulation of quantum field theories, where the computational cost depends both on the quantum algorithm employed and on the representation of the Hamiltonian. We investigate a formulation of the $\phi^4$ model based on the harmonic-oscillator basis in coordinate space. We derive the lattice $\phi^4$ Hamiltonian in this representation and analyze the structure of the resulting one-body matrix and interaction tensor. We show that both exhibit an effective band-diagonal structure, allowing controlled truncations of the Hamiltonian while preserving the low-energy spectrum. We validate this formulation by comparing low-energy observables obtained from numerical diagonalization with those computed in the standard harmonic-oscillator momentum-space representation. Finally, we estimate the resources required to encode the Hamiltonian on a quantum computer using both binary and unary boson-to-qubit mappings. By exploiting effective locality, the coordinate-space representation reduces the resources required for quantum simulation over a broad range of parameters.
Gaétan Bardy, M. Saubanère, A. Tanasa· 0 citations
The Dicke model provides a fundamental description of collective light-matter interactions and has long served as a testbed for exploring a wide range of physical phenomena in quantum optics and condensed matter physics. In this work, we develop a variational framework for investigating the finite-size Dicke model on both fully qubit-based (digital) and hybrid qubit boson based (digital-analogue) quantum computing platforms. We show that the resulting model reproduces the characteristic critical behavior of the Dicke model in the appropriate large-spin limit while remaining suitable for implementation on both classical emulators of quantum computers and actual trapped ion quantum computers, albeit in the case of latter somewhat limited by noise. Finally, we introduce a complementary hybrid qubit-bosonic variational ansatz that directly exploits the bosonic degree of freedom to reduce quantum resources and discuss its potential implementation on hybrid quantum hardware. Our results establish a scalable, symmetry-aware framework for variational quantum simulations of collective light-matter systems and provide a pathway toward efficient simulations of more general spin-boson models on near-term quantum devices.
A. Babu, Seongjin Ahn, Jing Sun et al.· 0 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
Many-body localization (MBL) is a dynamical phenomenon that describes the non-ergodicity of isolated quantum many-body systems. In contrast to thermalization, this phenomenon leads to a long-lived memory of initial states of local systems and slow growth of entanglement. In this work, we study Stark MBL in a 12-qubit correlated fermionic system described by the one-dimensional Fermi-Hubbard model using Hamiltonian simulation on an IBM superconducting qubit quantum computer. To enable such a computation on current-day noisy hardware, we combine a series of compilation steps, including the use of the spin-resolved Jordan-Wigner transformation, employing SWAP networks, and integrating a tensor-network-based quantum circuit optimization routine on top of a standard circuit optimization pipeline. As a result, there is approximately an 88$\%$ and 87$\%$ reduction in two-qubit gate count and circuit depth, respectively. Through such simulations of the real-time dynamics using Trotterized quantum circuits, we exhibit a crossover from thermalizing dynamics of the system at a weak tilt of the field to a strongly localized behavior at large tilt with short evolution times. We also benchmark our obtained results with respect to those from exact simulations.
Abdul Kalam, Prasenjit Deb, A. Sakurai et al.· 0 citations
