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.
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.
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.
The emergence of randomness from unitary quantum dynamics is a central problem across diverse disciplines, ranging from the foundations of statistical mechanics to quantum algorithms and quantum computation. Physical systems are invariably subject to constraints -- from simple scalar symmetries to more complex non-Abelian ones -- that restrict the accessible regions of Hilbert space and obstruct the generation of pure random states. In this work, we show that for systems with noncommuting symmetries such as SU(2), the degree of Haar-like randomization achievable under unitary dynamics is strongly constrained by experimental limitations on state initialization, in particular low-entanglement initial states, rather than by the symmetry-constrained dynamics themselves. Specifically, we show that time-evolved states can, in principle, reproduce Haar-like behavior at the level of finite statistical moments (i.e., those accessible under realistic experimental conditions with a finite number of state copies) provided that the initial state matches the corresponding moments of the conserved operators in the Haar ensemble. However, for the unentangled initial states commonly used in programmable quantum systems, this condition cannot be satisfied. Consequently, even at asymptotically long times in strongly quantum-chaotic regimes, late-time states remain distinguishable from Haar-random states in probes such as entanglement entropy, with deviations from Haar behavior that remain finite with increasing system size. We quantify the maximal entanglement entropy achievable and identify the unentangled initial conditions that yield the most entropic late-time states. Our results show that the combination of non-Abelian symmetry structure and experimental constraints on state preparation can strongly limit the degree of Haar-like randomization achievable at late times.
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
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=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=50 spins. This work demonstrates the potential of quantum optimal control methods for preparing highly spin-squeezed states, opening pathways to enhanced quantum metrology.
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of quantum computational advantage. While statistical mechanics successfully captures the temporal averages of local observables, understanding randomness at the level of higher statistical moments remains a daunting challenge, with analytic progress largely confined to random quantum circuit models or fine-tuned systems exhibiting space-time duality. Here we study how much randomness can be dynamically generated by generic quantum-chaotic evolution under physical, non-random Hamiltonians. Combining theoretical insights with numerical simulations, we show that for broad classes of initially unentangled states, the dynamics become effectively Haar-random well before the system can ergodically explore the physically accessible Hilbert space. Both local and highly nonlocal observables, including entanglement measures, equilibrate to their Haar expectation values and fluctuations on polynomial timescales with remarkably high numerical precision, and with the fastest randomization occurring in regions of parameter space previously identified as maximally chaotic. Interestingly, this effective randomization can occur on timescales linear in system size, suggesting that the sub-ballistic growth of Renyi entropies typically observed in systems with conservation laws can be bypassed in non-random Hamiltonians with an appropriate choice of initial conditions.
The creation and coherent control of systems of many strongly-interacting quantum particles represents one of the most important challenges in quantum science and technology. Devices capable of performing such a task have applications ranging from sensing and simulation, to communications and computation. The past few decades have seen remarkable progress in the development of different platforms to address the challenges of isolating and controlling individual quantum objects and increasing the number of interacting elements. This thesis presents a novel platform using arrays of individually controlled neutral atoms in optical tweezers which enables high-fidelity control of large systems of strongly interacting particles. Using real-time imaging and feedback, we initialize the positions of hundreds of atoms in arbitrary one- and two-dimensional geometries. By coupling the internal state of the atoms to highly excited Rydberg states, we are able to introduce spatially-dependent interactions to the system. Combining the remarkable coherence properties of isolated neutral atoms with strong Rydberg interactions, we study complex spin Hamiltonians in regimes beyond classical simulability. In the context of quantum simulation, we use this platform to study the phase diagram of regular arrays, including the critical properties of some of the associated quantum phase transitions. Additionally, we report on the discovery of special slowly-thermalizing states known as quantum many-body scars, which are then used as a starting point to stabilize many-body dynamics across the Hilbert space. Through the addition of specialized local controls, we demonstrate the ability to generate large N-partite entangled states with up to 20 atoms, as well as the ability to implement quantum logic gates. We combine quantum simulation with quantum information processing by preparing states with signatures of quantum spin liquids, which may be developed as topologically protected qubits. Lastly, we explore the potential applications of this platform to classical combinatorial optimization problems by approximating the Maximum Independent Set of different graphs.