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Preparation, characterization, and certification of quantum states in Rydberg atom arrays

Edison Carrera Unaucho

Published Oct 6, 2026• 0 citations
OpenAlex

Abstract

Programmable Rydberg atom arrays provide a versatile platform for generating, controlling, and measuring interacting many-body quantum states. This thesis investigates which states can be explored using global controls, whether selected states can be prepared efficiently, how robust their useful properties are to imperfections, and how these properties can be certified from finite experimental data. First, we study ensembles generated by random global pulse sequences and compare their statistical properties with those of Haar-random states within the dynamically accessible symmetry sector. Weak interactions generate correlations slowly, whereas strong Rydberg blockade confines the dynamics to a restricted set of configurations. At intermediate interaction strengths, the system develops Haar-like statistical signatures on experimentally relevant timescales, revealing a compromise between interaction-induced exploration and blockade-induced confinement. However, quantum optimal-control calculations show that highly entangled target states are systematically more difficult to prepare than weakly entangled ones, demonstrating that expressibility does not imply trainability. Second, we use gradient-based quantum optimal control to prepare spin-squeezed states. For small systems, the optimized protocols approach the finite-size lower bound of the Wineland parameter and produce substantially stronger squeezing than uncontrolled quantum-quench dynamics. Pulses optimized for N=10 can be transferred without re-optimization to larger arrays, reaching a Wineland parameter of 0.227 for N=50. The robustness analysis further shows that the states with the strongest squeezing under unitary dynamics are not necessarily the most resilient to dephasing: states with a larger mean-spin length can retain greater metrological usefulness in the presence of noise. Finally, we formulate spin-squeezing certification with finite statistics as a hypothesis-testing problem. We derive rigorous non-asymptotic bounds on the corresponding p-value, thereby controlling the probability that finite-sample fluctuations lead to a false certification of squeezing. Together, these results show that reliable quantum-state engineering requires not only broad state-space exploration, but also efficient preparation, robustness to imperfections, and statistically controlled certification.

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Programmable quantum systems provide insights into many-body quantum phenomena and enable new methods for computation and metrology. The frontier challenge for these systems is scaling up in the number of quantum particles while retaining a high degree of quantum control. In recent years arrays of neutral atoms have emerged as a scalable and powerful platform for tackling these challenges, thanks to their large number of qubits, flexible geometry, and a well-established toolbox for preparation, detection, coherent control. At the forefront of quantum science and engineering, these systems have been used for quantum simulation of various spin models and have also demonstrated building blocks of quantum computation. In this thesis I will present advances in development of large two-dimensional atom arrays, where hundreds of individual atoms are trapped, rearranged, and initialized in various defect-free arrangements in one or two dimensions. Afterwards, interactions between atoms is controlled via coherent excitation to highly excited Rydberg states, resulting in strong long-range van der Waals forces. We utilize these interaction for quantum simulation of many-body spin Hamiltonians by demonstrating preparation of several exotic phases of matter, study phase transitions, and probe non-equilibrium dynamics. Further, we study the quantum speedup in solving a hard combinatorial optimization problem via efficiently mapping the problem onto the Rydberg atom array. We also utilize Rydberg interactions to demonstrate high-fidelity two-qubit gate operations in a reconfigurable atom array architecture. Lastly I will demonstrate recent technical improvements that have enabled larger system sizes, higher fidelity rydberg excitations, and local control of individual atoms, paving the way for novel approaches for studying quantum many-body phenomena.

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Programmable Rydberg atom arrays provide a versatile platform for generating, controlling, and measuring interacting many-body quantum states. This thesis investigates which states can be explored using global controls, whether selected states can be prepared efficiently, how robust their useful properties are to imperfections, and how these properties can be certified from finite experimental data. First, we study ensembles generated by random global pulse sequences and compare their statistical properties with those of Haar-random states within the dynamically accessible symmetry sector. Weak interactions generate correlations slowly, whereas strong Rydberg blockade confines the dynamics to a restricted set of configurations. At intermediate interaction strengths, the system develops Haar-like statistical signatures on experimentally relevant timescales, revealing a compromise between interaction-induced exploration and blockade-induced confinement. However, quantum optimal-control calculations show that highly entangled target states are systematically more difficult to prepare than weakly entangled ones, demonstrating that expressibility does not imply trainability. Second, we use gradient-based quantum optimal control to prepare spin-squeezed states. For small systems, the optimized protocols approach the finite-size lower bound of the Wineland parameter and produce substantially stronger squeezing than uncontrolled quantum-quench dynamics. Pulses optimized for N=10 can be transferred without re-optimization to larger arrays, reaching a Wineland parameter of 0.227 for N=50. The robustness analysis further shows that the states with the strongest squeezing under unitary dynamics are not necessarily the most resilient to dephasing: states with a larger mean-spin length can retain greater metrological usefulness in the presence of noise. Finally, we formulate spin-squeezing certification with finite statistics as a hypothesis-testing problem. We derive rigorous non-asymptotic bounds on the corresponding p-value, thereby controlling the probability that finite-sample fluctuations lead to a false certification of squeezing. Together, these results show that reliable quantum-state engineering requires not only broad state-space exploration, but also efficient preparation, robustness to imperfections, and statistically controlled certification.
Rydberg atom arrays are powerful platforms for studying quantum many-body systems. We consider the Rydberg-Ising Hamiltonian in a ring geometry and numerically study ensembles of states generated by random global pulse sequences subject to hardware constraints and fixed evolution times. We compare the statistical properties of such states with those of Haar-random states within the relevant lattice symmetry sector. In the strong-interaction regime (short interatomic distance), the dynamics is governed by an effective blockade that restricts Hilbert-space exploration and limits entanglement growth. In this regime, level-spacing statistics of the entanglement spectrum are close to random-matrix predictions, while the distribution of measurement probabilities deviates from Porter-Thomas behavior. For weaker interactions (larger interatomic distance), the system approaches Haar-like statistics at long times, as reflected in entanglement entropy, entanglement-spectrum statistics, and the distribution of measurement probabilities. At intermediate interactions, this behavior is observed on experimentally relevant timescales. Motivated by this observation, we investigate whether individual target states can be efficiently prepared using quantum optimal control in this regime. Employing target states drawn from an ensemble with a broad entropy distribution, we observe high fidelities (infidelities between 10^-5 and 3 x 10^-2 for nine spins). Within this ensemble, the fidelity decreases with the entanglement entropy of the target state, indicating that highly entangled targets are more difficult to prepare under the considered finite-time control constraints.
We present a quantum optimal control protocol to generate highly spin-squeezed states in Rydberg atom arrays coupled via Ising-type van der Waals interactions. Using gradient-based optimization techniques, we construct time-dependent pulse sequences that steer an initial product state toward highly entangled, spin-squeezed states with predefined magnetization and squeezing axes. We focus on the Wineland parameter ${\ensuremath{\xi}}_{W}^{2}$ to measure spin squeezing, and our approach achieves near-optimal spin squeezing in one-dimensional ring arrays of up to N=8N=8N=8 spins, significantly outperforming conventional quench dynamics for all system sizes studied. Remarkably, optimized pulse sequences can be directly scaled to larger arrays without additional optimization, achieving a squeezing parameter as low as ${\ensuremath{\xi}}_{W}^{2}=0.227$ in systems containing N=50N=50N=50 spins. This work demonstrates the potential of quantum optimal control methods for preparing highly spin-squeezed states, opening pathways to enhanced quantum metrology.
Entangled many-body states are a key resource for quantum technologies. Yet their preparation through analog control of interacting quantum systems is often hindered by experimental imperfections. Here, we introduce the adiabatic echo protocol, a general approach to state preparation designed to suppress the effect of static perturbations. We provide an analytical understanding of its robustness in terms of dynamically engineered destructive interference. By applying quantum optimal control methods, we demonstrate that such a protocol emerges naturally in a variety of settings, without requiring assumptions on the form of the control fields. Examples include Greenberger-Horne-Zeilinger state preparation in Ising spin chains and two-dimensional Rydberg atom arrays, as well as the generation of quantum spin liquid states in frustrated Rydberg lattices. Our results highlight the broad applicability of this protocol, providing a practical framework for reliable many-body state preparation in present-day quantum platforms.
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension of the Hilbert space increases exponentially with the size of the system. For systems that possess a high degree of symmetry, however, classical simulation can reach much larger sizes. Here we consider an ensemble of strongly interacting atoms with permutation symmetry, enabling the computation of certain collective observables for hundreds of atoms at arbitrarily long evolution times. The system is realized by an ensemble of three-level atoms, where one of the levels corresponds to a highly excited Rydberg state. In the limit of all-to-all Rydberg blockade, the Hamiltonian is invariant under permutation of the atoms. Using techniques from representation theory, we construct a block-diagonal form of the Hamiltonian, where the size of the largest block increases only linearly with the system size. We apply this formalism to derive efficient pulse sequences to prepare arbitrary permutation-invariant quantum states. Moreover, we study the quantum dynamics following a quench, uncovering a parameter regime in which the system thermalizes slowly and exhibits pronounced revivals. Our results create opportunities for the experimental and theoretical study of large interacting and nonintegrable quantum systems. Published by the American Physical Society 2024
Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to the generation of spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.
Programmable quantum systems provide insights into many-body quantum phenomena and enable new methods for computation and metrology. The frontier challenge for these systems is scaling up in the number of quantum particles while retaining a high degree of quantum control. In recent years arrays of neutral atoms have emerged as a scalable and powerful platform for tackling these challenges, thanks to their large number of qubits, flexible geometry, and a well-established toolbox for preparation, detection, coherent control. At the forefront of quantum science and engineering, these systems have been used for quantum simulation of various spin models and have also demonstrated building blocks of quantum computation. In this thesis I will present advances in development of large two-dimensional atom arrays, where hundreds of individual atoms are trapped, rearranged, and initialized in various defect-free arrangements in one or two dimensions. Afterwards, interactions between atoms is controlled via coherent excitation to highly excited Rydberg states, resulting in strong long-range van der Waals forces. We utilize these interaction for quantum simulation of many-body spin Hamiltonians by demonstrating preparation of several exotic phases of matter, study phase transitions, and probe non-equilibrium dynamics. Further, we study the quantum speedup in solving a hard combinatorial optimization problem via efficiently mapping the problem onto the Rydberg atom array. We also utilize Rydberg interactions to demonstrate high-fidelity two-qubit gate operations in a reconfigurable atom array architecture. Lastly I will demonstrate recent technical improvements that have enabled larger system sizes, higher fidelity rydberg excitations, and local control of individual atoms, paving the way for novel approaches for studying quantum many-body phenomena.