The field of quantum science and technology has seen tremendous recent progress. Despite this, building large-scale quantum devices remains daunting as fault tolerance is a distant goal in all current experimental platforms. This dissertation discusses two complementary avenues towards practically relevant quantum technologies. In the first part, we explore physically inspired quantum algorithms that run on near-term devices without quantum error correction. We investigate the robustness of adiabatic quantum algorithms, placing stringent requirements on noise induced by the environment. In addition, we construct quantum algorithms that sample from classical Gibbs distributions. These algorithms elucidate connections between computational complexity and phase transitions and provide physical insight into the origin of quantum speedup. The second part focuses on novel platforms and optical interfaces for quantum applications. We demonstrate that optical resonances in ordered arrays of atoms and atomically thin semiconductors offer a powerful tool to control and manipulate light at both the classical and single-photon level. We further study interactions between optical excitations and charge carriers in two-dimensional semiconductors, which give rise to complex quantum many-body dynamics in a largely unexplored regime.
The field of quantum science and technology has seen tremendous recent progress. Despite this, building large-scale quantum devices remains daunting as fault tolerance is a distant goal in all current experimental platforms. This dissertation discusses two complementary avenues towards practically relevant quantum technologies. In the first part, we explore physically inspired quantum algorithms that run on near-term devices without quantum error correction. We investigate the robustness of adiabatic quantum algorithms, placing stringent requirements on noise induced by the environment. In addition, we construct quantum algorithms that sample from classical Gibbs distributions. These algorithms elucidate connections between computational complexity and phase transitions and provide physical insight into the origin of quantum speedup. The second part focuses on novel platforms and optical interfaces for quantum applications. We demonstrate that optical resonances in ordered arrays of atoms and atomically thin semiconductors offer a powerful tool to control and manipulate light at both the classical and single-photon level. We further study interactions between optical excitations and charge carriers in two-dimensional semiconductors, which give rise to complex quantum many-body dynamics in a largely unexplored regime.
Over the last decade, quantum simulation and computation has progressed from a purely scientific testbed of quantum mechanics to a mature field that is starting to offer new insights into materials, quantum effects, and algorithms that are intractable with even the most state-of-the-art classical computation. Simulating certain quantum Hamiltonians that are theorized to be at the heart of high-Tc superconductivity, topological quantum systems such as the fractional quantum Hall effect or fundamental questions of thermalization quickly exceed the available memory of even the most advanced supercomputers – and in fact all memory in the world – due to the exponential growth of the Hilbert space with system size. As postulated by Feynman himself, the computational system best suited for solving quantum problems is to use a quantum system itself, as it can intrinsically represent the entanglement that is the key resource making quantum computing challenging but also promising. Apart from simulating problems in physics and chemistry, there is also tremendous excitement for quantum computers to provide speedups for general algorithms in optimization at a rate that is exponentially faster than existing classical programming. So far only a small class of algorithms has been actually proven to provide such a speedup, most prominently Shor's algorithm which can factor large prime numbers, and several other search and oracle algorithms. In the last two decades, many experiments using ultracold atoms, ions, or superconducting circuits have focused on analog quantum simulation. Here, a model Hamiltonian that is believed to capture all the relevant physics of the system of study is experimentally realized using different building blocks and interactions but replicating condensed matter effects at an increased scale. This has led to a number of bespoke experiments such as BEC/Fermigass machines, quantum gas microscopes and more exotic setups that are purpose built to study a particular effect. More recently, there has been a shift to develop more universal simulation platforms and optical tweezer arrays have emerged as a leading solution due to their high degree of reconfigurability. Through tremendous improvements in the degree of control and measurement of single qubits, error correction has become a viable route to build a true universal digital quantum computer. Even as we transition into the digital age of quantum simulation, certain classes of problems with additional physics constraints such as Fermionic statistics, gauge fields and lattice gauge theories still incur too large of an overhead to be encoded on these digital simulators. In this thesis, we use a highly degenerate twisted cavity to simulate the effect of a magnetic field on a two-dimensional system of interacting photons to enable realization of states of the quantum Hall effect. We design, build, and commission a new lens based cavity apparatus realizing a lowest Landau level for a mesoscopic number of modes. We demonstrate the integration of highly excited Rydberg atoms to mediate strong interactions and demonstrate photon blockade as well as mean field interactions. As a second application of cavities to quantum information leveraging our newfound comfort with intra-cavity optics, and experience with aberration modeling in resonators, we demonstrate a new class of small waist optical resonators enabled by lens-based cavities and then apply our understanding of optical aberrations in cavities to the development of a new class of cavity array. This Cavity Array Microscope (CAM) realizes a large number of cavities (up to currently 600) using only a fixed number of free space optics and is both scalable with constant overhead as well as compatible with Rydberg atoms. This platform provides a route to highly parallel quantum repeater operation or entanglement generation between atom arrays in the future.
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.
Quantum computation is an exciting and rapidly developing paradigm of computing, which has the potential to improve or accelerate numerous important applications ranging from cryptography to drug discovery. Inspired by these prospects, researchers and engineers across the world have, in recent years, made tremendous advances in building programmable quantum devices. Nevertheless, the size and error rates in state-of-the-art quantum computers are still several orders of magnitude away from those required to achieve computational speedups using existing quantum algorithms. These developments, along with their limitations, motivate us to consider two important questions: First, are there any useful applications in which current or near-term quantum devices can outperform classical computers? Second, can we develop efficient error-correction schemes to suppress the error rates in near-term quantum devices? In this dissertation, we present novel solutions to both of these questions. To address the first question, we identify an important class of problems in condensed-matter physics, namely the identification and characterization of quantum phases of matter, as one promising application of current and near-term quantum information processors. We develop new algorithms for using such quantum devices to solve these problems, and we demonstrate how our methods substantially outperform existing approaches. In addition, we respond to the second question by developing hardware-efficient quantum error correction protocols. By leveraging the distinctive properties and advantages of a given experimental setup to overcome its particular limitations, our proposals significantly reduce the number of quantum bits and operations required for performing quantum error correction and fault-tolerant quantum computation. Together, the works in this dissertation thus pave the way for the near-term realization of quantum computational advantages.
A frontier challenge in quantum science and technology is the construction of scalable quantum systems which can operate in regimes beyond classical simulatability. Such systems can be used as tools for simulating and exploring complex phenomena in quantum physics; they can also be used to benchmark and test quantum algorithms. Several experimental platforms, based on a variety of quantum mechanical building blocks, are currently being pursued with these goals in mind, with state-of-the-art systems capable of controlling up to around fifty particles. In this thesis, we present the development of a new platform based on individually controlled neutral atoms. In this approach, hundreds of individual atoms are trapped in an array of optical tweezers, and they are sorted in real-time into programmable geometries in one and two dimensions. After initialization of an array, atom interactions are switched on by coherent excitation to highly excited Rydberg states, resulting in a rich spin Hamiltonian. We experimentally advance several key aspects of this platform, developing new tools for controlling strongly interacting atom arrays and probing novel quantum phases and non-equilibrium dynamics. We additionally utilize Rydberg interactions to entangle atoms, demonstrating high fidelity universal quantum logic gates as well as the preparation of fully entangled Schrödinger cat states. This work highlights the prospects for scalable quantum simulation and quantum information processing beyond the limit of classical computation using neutral atom arrays.
Quantum mechanical problems are among the hardest to simulate and, in some cases, remain intractable even for the most powerful computers. Quantum computing has emerged as a new technological platform to address such challenges, with rapid advances in recent years. Yet, current quantum devices remain noisy and limited in scale. Hence, it is essential to identify classically hard problems of practical interest and tractable with existing quantum devices. Among potential applications, the real-time simulation of quantum systems is one of the most promising to deliver an early, practical quantum advantage. This doctoral thesis is therefore centered around simulating quantum dynamics on quantum devices. We first present an overview of the most relevant quantum algorithms for quantum dynamics, highlighting respective advantages and limitations. Further, we identify relevant problems within quantum dynamics that could benefit from quantum simulation in the near future. Second, we propose a method for benchmarking hardware and error mitigation algorithms that is based on well-understood theoretical results and suffers from no scaling issues. The resulting quality metric is intuitive and transferable to other applications. We successfully implement the scheme on up to 133 qubits, demonstrating coherent evolution up to a two-qubit gate depth of 28, featuring 1396 two-qubit gates, before noise becomes prevalent. Third, we propose a novel variant of probabilistic error amplification to implement open quantum dynamics, relying on characterizing and altering hardware noise to mimic the system-environment interaction under study. Lastly, we present two studies on state preparation and phase classification: first, a hybrid algorithm to prepare ground states of electron-phonon systems; second, a quantum machine learning-based approach to distinguish phases in previously prepared quantum states.
Quantum computation exploits superposition, entanglement, interference, and measurement to process information.Research has moved from theoretical algorithms to functional devices where the performance is not only limited by qubit physics, but also by the control, compilation, error mitigation, and error correction.This review considers quantum computing on various levels of abstraction, including physical qubits, quantum algorithms, system architecture, fault-tolerance, and emerging applications.Study-specific evidence regarding scale, operational quality, connectivity, control and suppression of errors is compared across the different types of superconducting circuits, trapped ions, semiconductor spin qubits, neutral atoms and photonic processors.The review of the fundamental algorithms, noisy intermediate-scale quantum computing, variational and hybrid quantum-classical approaches, quantum simulation, quantum machine learning, and security implications is also discussed.Measurable progress has been demonstrated in published experiments for logical-qubit operation, below-threshold surface-code memory, programmable photonic sampling and platformspecific scaling.However, the reported metrics are not directly interchangeable, and practical advantage remains task-and baseline-dependent.Further progress will need to be accompanied by coordinated developments in hardware reliability, error correction, classical control, estimates of algorithmic resources, and clear classical method comparisons.