Algorithms and Architectures for Quantum Simulation with Neutral-atom Arrays

Abstract

Fast and scalable quantum simulations promise to revolutionize our understanding of complex quantum systems, In this thesis, we primarily aim to develop algorithms and architectures for leveraging programmable quantum devices, to model complex physical phenomena. As quantum computers can natively capture superposition and entanglement, two key attributes which are challenging for classical computers to accurately model, this approach promises significant benefits in the long run. We focus primarily on neutral-atom arrays, an emerging experimental platform, although many of our results apply more generally as well. The work is structured into three phases, each progressively advancing the complexity and control of considered experimental hardware, and in parallel the importance and applicability of the considered quantum simulations. In the first phase (Chapters 1–3), we address the challenge of programming and controlling quantum many-body systems through analog techniques. Analog quantum simulation utilizes continuous control parameters to engineer desired quantum states and dynamics. Chapter 1 introduces novel methods for steering entanglement using quantum many-body scars, harnessing special strongly-interacting dynamics to manipulate quantum entanglement robustly. Chapter 2 advances this approach by showing how Floquet engineering can be used to systematically generate interactions, and how this enables sophisticated control over entanglement and access to novel quantum phases. Chapter 3 integrates these developments into a general framework for programming Hamiltonians into analog quantum simulators with time-reversal capabilities, illustrating the power of programmable analog strategies for simulations of lattice gauge theories. The second phase (Chapters 4–6) shifts focus to topologically ordered quantum states, known for their exotic long-range entanglement and fundamental significance in condensed matter physics and quantum computation. Chapter 4 presents strategies to enhance the experimental detection and verification of topological order using ideas from the renormalization group. The procedure we develop, order parameters dressed by local quantum error correction, significantly improve the practical observability of these delicate quantum phases. In Chapters 5 and 6, we explore novel techniques for realizing topological phases, by exploiting newly developed experimental capabilities, notably atom reconfiguration, to achieve precise digital control. In particular, we show how to engineer chiral Floquet spin liquids - exotic quantum phases exhibiting robust quantum coherence and non-Abelian excitations — as well as simulations of topological fermionic matter. These advancements not only illuminate foundational physics but also bridge towards robust quantum error correction schemes. The final phase (Chapters 7 and 8) expands the techniques developed thus far towards the simulation of increasingly complex physical systems relevant to chemistry and materials science. Chapter 7 discusses a general framework for digital quantum simulation of effective spin models, prevalent in condensed matter physics, introducing crucial techniques for engineering and characterizing these Hamiltonians. Chapter 8 extends these insights by proving that fermionic quantum systems, essential for realistic simulations of electronic structures in molecules and materials, can be efficiently encoded into qubits. This advance significantly reduces computational complexity and opens pathways for genuine quantum simulations of chemical systems. Collectively, these contributions represent substantial progress towards practical quantum simulation with neutral-atom quantum processors, laying critical foundations for future applications in physics, chemistry, and quantum information science.