From the first demonstration of a quantum logic gate in 1995 to the actualizationof a “quantum advantage” over classical technology a few years ago, the field of quantum information has made remarkable progress during my lifetime. Multiple quantum technology platforms have developed to the point that companies and governments are investing heavily in the industry. A primary focus is the development of fault-tolerant error correction, a technology expected to be necessary for large-scale digital quantum computers. Meanwhile analog quantum simulators, a subclass of quantum computers that apply unitary evolutions instead of digitized gates, are at the forefront of controllable quantum system sizes. In place of algorithms, analog quantum simulators are naturally suited to study many-body physics and model certain materials and transport phenomena. In this thesis I discuss an analog quantum simulator based on trapped +Yb171 ions and its use for studying dynamics and thermalizing properties of the non-integrable long-range Ising model with system sizes near the limit of classical tractability. In addition to the technical properties of the simulator, I present three select experiments that I worked on during my PhD. The first is an observation of a phenomenon in nonequilibrium physics, a dynamical phase transition (DPT). While equilibrium phase transitions follow robust universal principles, DPTs are challenging to describe with conventional thermodynamics. We present an experimental observation and characterization of a DPT with up to 53 qubits. We also explore the system’s ability to simulate physics beyond its own by implementing a quasiparticle confinement Hamiltonian. Here we see that the natural long-range interactions present in the simulator induce an effective confining potential on pairs of domain-wall quasiparticles, which behave similarly to quarks bound into mesons. We measure post-quench dynamics to identify how confinement introduces low-energy bound states and inhibits thermalization. Lastly, we use the individual-addressing capabilities of our simulator to implement Stark many-body localization (MBL) with a linear potential gradient. Stark MBL provides a novel, disorder-free method for localizing a quantum system that would otherwise thermalize under evolution. We explore how the localized phase depends on the gradient strength and uncover the presence of correlations using interferrometric double electron-electron resonance (DEER) measurements. These experiments show the capability of our experiment to study complex quantum dynamics in systems near 50 qubits and above.
From the first demonstration of a quantum logic gate in 1995 to the actualizationof a “quantum advantage” over classical technology a few years ago, the field of quantum information has made remarkable progress during my lifetime. Multiple quantum technology platforms have developed to the point that companies and governments are investing heavily in the industry. A primary focus is the development of fault-tolerant error correction, a technology expected to be necessary for large-scale digital quantum computers. Meanwhile analog quantum simulators, a subclass of quantum computers that apply unitary evolutions instead of digitized gates, are at the forefront of controllable quantum system sizes. In place of algorithms, analog quantum simulators are naturally suited to study many-body physics and model certain materials and transport phenomena. In this thesis I discuss an analog quantum simulator based on trapped +Yb171 ions and its use for studying dynamics and thermalizing properties of the non-integrable long-range Ising model with system sizes near the limit of classical tractability. In addition to the technical properties of the simulator, I present three select experiments that I worked on during my PhD. The first is an observation of a phenomenon in nonequilibrium physics, a dynamical phase transition (DPT). While equilibrium phase transitions follow robust universal principles, DPTs are challenging to describe with conventional thermodynamics. We present an experimental observation and characterization of a DPT with up to 53 qubits. We also explore the system’s ability to simulate physics beyond its own by implementing a quasiparticle confinement Hamiltonian. Here we see that the natural long-range interactions present in the simulator induce an effective confining potential on pairs of domain-wall quasiparticles, which behave similarly to quarks bound into mesons. We measure post-quench dynamics to identify how confinement introduces low-energy bound states and inhibits thermalization. Lastly, we use the individual-addressing capabilities of our simulator to implement Stark many-body localization (MBL) with a linear potential gradient. Stark MBL provides a novel, disorder-free method for localizing a quantum system that would otherwise thermalize under evolution. We explore how the localized phase depends on the gradient strength and uncover the presence of correlations using interferrometric double electron-electron resonance (DEER) measurements. These experiments show the capability of our experiment to study complex quantum dynamics in systems near 50 qubits and above.
In recent decades, the rapid development of quantum technologies has led to a new era of programmable platforms, enabling the realizations of quantum simulation and quantum computation. This dissertation is motivated by recent experimental progress on controlling individual quantum degrees of freedom in systems such as trapped ions and Rydberg atom arrays. By tailoring the interactions in these quantum systems, we study analog quantum simulations of various physical phenomena, including non-equilibrium quantum dynamics and nontrivial topological physics. In the first part of the dissertation, we study slow quantum many-body dynamics in trapped-ion systems and Rydberg atom arrays. We first show that either the long-range interactions or an additional symmetry-breaking field can give rise to a confining potential. Such a potential can couple domain wall quasiparticles into mesonic or baryonic bound states. These confined quasiparticles strongly suppress the quantum information dynamics and lead to slow thermalization. In thelimit of strict domain-wall confinement, the full Hilbert space is fragmented into exponentially many disconnected subspaces. Furthermore, we demonstrate that thermalization can be halted by quantum engineering a uniformly increasing field in the trapped-ion quantum simulator. The second part of the dissertation focuses on topologically relevant phenomena in quantum simulators. We first study the effect of experimentally relevant disorder in 2D Rydberg atom arrays. We find that there are three distinct localization regimes due to the presence of nontrivial topological bands. We further study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We show that the interplay of anyonic statistics and interactions can give rise to spatially asymmetric quantum dynamics. Finally, we use Nielsen’s geometric approach to quantify circuit complexity in topological models. We find that the circuit complexities of ground states and non-equilibrium steady states both exhibit nonanalytical behavior at topological transition points.
While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.
One of the useful applications of a quantum computer is quantum simulation. While the quest for a universal quantum computer is still undergoing research, analog quantum simulators can study specific quantum models that are classically challenging or even intractable. These quantum simulators provide the opportunity to test particular quantum models and scale up the system size to gain insight into more exciting physics. The analog quantum simulator featured in this thesis is a cryogenic trapped-ion system. It serves the purpose of a large-scale quantum simulation by reducing the background pressure for storing a large ion chain with a long lifetime. This work presents the construction and characterization of this cryogenic apparatus and its performance as a trapped-ion quantum simulator. Quantum information is encoded in the atomic state of the ion chain. The entangling operation in trapped ions uses the collective motion of the ion chain for quantum simulation. Therefore, it is imperative to develop a cooling mechanism to prepare the ion chain to near motional ground-state for achieving high fidelity operations. Here, with this system, we explore another ground-state cooling mechanism with electromagnetically induced transparency (EIT) in a four-level system (171Yb+). EIT cooling allows simultaneous ground-state cooling across a bandwidth of motional modes, which it is useful in a large ion chain. Finally, we report the observation of magnetic domain-wall confinement in interacting spins chains. Such confinement is analogous to the color confinement in quantum chromodynamics (QCD), where hadrons are produced by quark confinement. We study the implications of such confinement in many-body spin system by observing the information propagation after applying a quantum quench of the confinement Hamiltonian. We also measure the excitation energy of domain-wall bound states from non-equilibrium quench dynamics. At the end of this experiment, we explore the number of domain wall excitations created with different quench parameters, which can be challenging to model with classical computers.
Certain classes of quantum many-body systems, including those supporting phenomena like high-Tc superconductivity and spin liquids, are believed to be fundamentally intractable to classical modeling. Quantum simulations, in which synthetic materials are engineered by inducing well-controlled quantum systems like ultracold atoms to obey many-body Hamiltonians of interest, are a promising new approach to study this type of physics. In this work, I present several advances toward this ultimate goal of large-scale, highly controllable quantum simulations of many-body spin physics. We simulate long-range Ising and XY spin models in the presence of transverse and longitudinal magnetic fields using chains of up to 18 ultracold 171Yb+ ions held in a linear Paul trap, where two hyperfine levels in each ion encode spin-1/2 states. The tunable spin-spin interactions and effective magnetic fields are engineered using laser fields, and the individual spin states are directly imaged with state-dependent fluorescence. The results in this thesis address several of the ongoing challenges in the development of synthetic quantum matter platforms. One such challenge is establishing more flexible capabilities in the sorts of Hamiltonians we can model. By observing suppression of the ground state spin ordering, we have demonstrated our ability to continuously tune the interaction range in a power-law interaction pattern, and hence the amount of frustration present in the spin system. We have additionally begun developing tools to study particles of higher spin, which could eventually be used to create and study topological phases of matter. Another challenge is the necessity of identifying problems that the next generation of experiments, with flexible (but not arbitrary) controls and classically intractable (but not infinitely large) system sizes, can feasibly shed new light on. We have made measurements of how the range of interaction affects dynamics of spin correlations propagating through the chain, and the excellent agreement between our observations and numerical simulations indicate that at larger sizes, our experiment can meaningfully contribute to the open question of the fundamental speed limit on the transfer of information through such a spin chain. Finally, for classically intractable system sizes, it will be crucial to have multiple techniques at our disposal for validating our understanding of the exact microscopic model being implemented. We have developed and demonstrated an MRI-like spectroscopic technique for probing the energies of the many-body Hamiltonian, which serves as a new method for validating quantum simulations of the transverse Ising model. Our experiments can potentially be scaled up in the near future to study fully connected lattice spin models with several tens of spins, where classical computation begins to fail, and the results described in this thesis contribute to the effort to build experiments that can break new ground in the study of quantum many-body physics.
Many outstanding problems in quantum physics, such as high-Tc superconductivity or quark confinement, are still - after decades of research - awaiting commonly accepted explanations. One reason is that such systems are often difficult to control, show an intermingling of several effects, or are not easily accessible to measurement. To arrive at a deeper understanding of the physics at work, researchers typically derive simplified models designed to capture the most striking phenomena of the system under consideration. However, due to the exponential complexity of Hilbert space, even some of the simplest of such models pose formidable challenges to analytical and numerical calculations. In 1982, Feynman proposed to solve such quantum models with experimental simulation on a physically distinct, specifically engineered quantum system [Int. J. Theor.Phys. 21, 467]. Designed to be governed by the same underlying equations as the original model, it is hoped that direct measurements on these so called quantum simulators (QSs) will allow to gather deep insights into outstanding problems of physics and beyond. In this thesis, we identify four requirements that a useful QS has to fulfill, relevance, control, reliability, and efficiency. Focusing on these, we review the state of the art of two popular approaches, digital QSs (i.e., special purpose quantum computers) and analog QSs (devices with always-on interactions). Further, focusing on possibilities to increase control over QSs, we discuss a scheme to engineer quantum correlations between mesoscopic numbers of spinful particles in optical lattices. This technique, based on quantum polarization spectroscopy, may be useful for state preparation and quantum information protocols. Additionally, employing several analytical and numerical methods for the calculation of many-body ground states, we demonstrate the variety of condensed-matter problems that can be attacked with QSs consisting of ultracold ions or neutral atoms in optical lattices. The chosen examples, some of which have already been realized in experiment, include such diverse settings as frustrated antiferromagnetism, quantum phase transitions in exotic lattice geometries, topological insulators, non-Abelian gauge-fields, orbital order of ultracold Fermions, and systems with long-range interactions. The experimental realization of all of these models requires techniques which go beyond standard optical lattices, e.g., time-periodic driving of lattices with exotic geometry, loading ultracold atoms into higher bands, or immersing trapped ions into an optical lattice. The chosen models, motivated by important open questions of quantum physics, pose difficult problems for classical computers, but they may be amenable in the near future to quantum simulation with ultracold atoms or ions. While the experimental control over relevant models has increased dramatically in the last years, the reliability and efficiency of QSs has received considerably less attention. As a second important part of this thesis, we emphasize the need to consider these aspects under realistic experimental conditions. We discuss specific situations where terms that have typically been neglected in the description of the QS introduce systematic errors and even lead to novel physics. Further, we characterize in a generic example the influence of quenched disorder on an analog QS. Its performance for simulating universal behavior near a quantum phase transition seems satisfactory for low disorder. Moreover, our results suggest a connection between the reliability and efficiency of a QS: it works less reliable exactly in those interesting regimes where classical calculations are less efficient. If QSs fulfill all of our four requirements, they may revolutionize our approach to quantum-mechanical problems, allowing to solve the behavior of complex Hamiltonians, and to design nano-scale materials and chemical compounds from the ground up.
(English) In recent years, the evolution of quantum technologies has resulted in an unprecedented control over individual quantum particles and many-body systems. This remarkable progress has given rise to a new era, marked by the convergence of classical and quantum methodologies to investigate fundamental questions concerning the nature of quantum matter, improving our understanding of the role of entanglement in solid-state systems or the mechanisms behind high-energy physics. From analog quantum simulators to digital quantum computers, these advancements hold potential across diverse domains. This thesis explores the interplay between classical and quantum methods in understanding topological phases of matter. We concentrate on three distinct directions: non-conventional topological superconductors, interaction-induced topological phases in ultracold atom quantum simulators, and applications of variational quantum algorithms. Each trajectory relies on the combination of different techniques with the aim of understanding and characterizing topological phenomena in different settings. Exploring non-conventional topological superconductors involves extending the paradigmatic Kitaev chain model by incorporating additional terms in the Hamiltonian such as long-range interactions and quasi-periodic potentials. This investigation is relevant to better understand the impact of real-world conditions on the both the topological and localization properties of systems hosting non-local Majorana modes, which are promising candidates for topological quantum computation. In the realm of interacting systems, we explore the realization of interaction-induced topological phases in systems of ultracold atoms in optical lattices, both in one and two dimensions. The remarkable control and versatility of such platforms enable the simulation of both theoretical topological models and strongly correlated physics. Notably, the interplay between interactions and topology can give rise to intriguing phenomena, such as delocalized fractional charges and gapless topological phases,challenging existing intuition. We employ advanced numerical methods based on tensor networks to benchmark the experimental proposals that open the door to the realization and detection of novel many-body phases of matter, including topological quantum critical points and a higher-order topological Peierls insulator in Bose-Hubbard models with long-range interactions. Variational quantum algorithms, conversely, have the potential to efficiently tackle a wide range of problems, including ground state search, phase classification or accessing topological invariants. Despite current limitations in trainability and scalability, these hybrid classical-quantum algorithms provide practical insights into current quantum hardware capabilities and can inspire future architectures. We explore the application of variational quantum algorithms to shed light on topological phenomena, raising questions about their ability to discern topological phase transitions and compute topological invariants in situations where classical approaches fail. This thesis presents a comprehensive exploration of distinct approaches to topological quantum matter by leveraging quantum technologies and quantum-inspired classical algorithms. Our results not only advance our understanding of quantum systems but also pave the way for the realization and discovery of novel physics extending to quantum information processing, materials science, and beyond.