[
    {
        "title": "The Quantum Overlap Gap Property and Algorithmic Hardness for the Quantum Hypergraph Max-Cut Problem",
        "type": "thesis",
        "publication_date": "2026",
        "doi": "10.7907/tgg7-nh54",
        "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06042026-205016029",
        "abstract": "In this work, we analyze the average-case hardness of the Quantum Hypergraph Max-Cut problem using the theoretical framework of the Quantum Overlap Gap Property (QOGP). We establish two main results: a weak hardness result for a wide class of stable quantum algorithms, and a strong hardness result for a much more restricted class of local quantum algorithms. We apply these results to establish concrete conditions under which known quantum algorithms fail to produce near-optimal solutions for this problem.",
        "author_list": "Mints, Mikhail"
    },
    {
        "title": "Efficient and SPAM-Robust Ansatz-Free Lindbladian Learning",
        "type": "thesis",
        "publication_date": "2026",
        "doi": "10.7907/hprr-fq68",
        "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04142026-214248334",
        "abstract": "Describing the dynamics of open systems is essential for fault-tolerant quantum computation. Under Markovian assumptions, we can characterize dissipative dynamics via the Lindbladian. Using Bell sampling, we provide an efficient, ansatz-free Lindbladian learning algorithm with polynomial-time classical postprocessing. Motivated by the prevalence of state preparation and measurement (SPAM) noise on near-term devices, we also introduce the first efficient SPAM-robust protocol capable of learning the gauge-independent components of sparse Lindbladians to arbitrary precision in the presence of constant-order SPAM error. In doing so, we provide the first rigorous characterization of the gauge degrees of freedom in noisy Lindbladian learning, precisely identifying which components remain learnable under SPAM noise.",
        "author_list": "Sinha, Savar Dayal"
    },
    {
        "title": "Interacting Particle Systems for Sampling from Non-Gaussian Targets",
        "type": "thesis",
        "publication_date": "2026",
        "doi": "10.7907/jkfa-cc97",
        "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10202025-024638416",
        "abstract": "<p>Sampling from a target distribution is a fundamental problem in applied mathematics, arising naturally in Bayesian inference and uncertainty quantification. Classical methods such as Markov Chain Monte Carlo can converge prohibitively slowly for complex, high-dimensional targets, and typically require access to gradient information that may be unavailable when the forward model is a black-box numerical solver. The Ensemble Kalman Sampler (EKS) addresses both difficulties, as it is a gradient-free interacting particle algorithm in which particles evolve under an empirical covariance-preconditioned force, making the dynamics affine invariant and well-adapted to the geometry of the target. As the number of particles tends to infinity, the empirical distribution of the EKS converges formally to a nonlinear PDE (the mean-field limit) which can be interpreted as a gradient flow in the Kalman-Wasserstein metric. However, rigorous justification of this mean-field limit has so far been confined to Gaussian or near-Gaussian targets, a restriction that precludes the majority of practical applications.</p>\r\n\r\n<p>This thesis develops a regularized variant of the EKS mean-field PDE, obtained by replacing the potential and entropy terms with mollified counterparts parameterized by a smoothing scale. This covariance-modulated blob flow inherits the gradient flow structure of EKS while admitting a rigorous analysis for general targets. We prove existence of weak solutions via a covariance-modulated JKO variational scheme, characterize the steady states and their bias, and prove convergence of the mollified solutions to the EKS mean-field PDE as we take the limit of the smoothing scale. Numerical experiments on benchmark targets confirm that the resulting particle algorithm is competitive with EKS in practice.</p>",
        "author_list": "Teegavarapu, Ritvik S."
    }
]