Browsing by Author "Pfister, Henry"
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Item Open Access Hölder Bounds for Sensitivity Analysis in Causal Reasoning.(CoRR, 2021) Assaad, Serge; Zeng, Shuxi; Pfister, Henry; Li, Fan; Carin, LawrenceWe examine interval estimation of the effect of a treatment T on an outcome Y given the existence of an unobserved confounder U. Using H\"older's inequality, we derive a set of bounds on the confounding bias |E[Y|T=t]-E[Y|do(T=t)]| based on the degree of unmeasured confounding (i.e., the strength of the connection U->T, and the strength of U->Y). These bounds are tight either when U is independent of T or when U is independent of Y given T (when there is no unobserved confounding). We focus on a special case of this bound depending on the total variation distance between the distributions p(U) and p(U|T=t), as well as the maximum (over all possible values of U) deviation of the conditional expected outcome E[Y|U=u,T=t] from the average expected outcome E[Y|T=t]. We discuss possible calibration strategies for this bound to get interval estimates for treatment effects, and experimentally validate the bound using synthetic and semi-synthetic datasets.Item Embargo On the Left-Right Lifted Product Quantum LDPC Code(2024) Zhang, BoqingRecent advances in both theory and experiment have identified quantum Low-Density Parity-Check (LDPC) codes as a prime candidate for fault-tolerant quantum computation in the near future. This thesis addresses various challenges related to the construction and decoding of quantum LDPC (qLDPC) codes. A major contribution of this research is the creation of a unified family of qLDPC codes called left-right lifted product codes. The proposed approach not only makes the construction process simpler but also brings different qLDPC constructions together into a single framework that greatly improves both understanding and practical use.
This thesis aims to highlight the practical and theoretical advantages of the left-right lifted product construction. As part of this, we present the first finite-length distance bounds for the general lifted product code, subject to certain mild technical conditions. Moreover, we also extend the finite-length result to asymptotic lengths and provide a conjecture for a new kind of asymptotically good quantum LDPC code that holds promise for more feasible and practical applications.
From a practical standpoint, this work includes the first detailed cycle analysis, specifically focusing on dominant 8-cycles, which significantly impact decoding performance. Our findings indicate that the lifted product construction substantially reduces the number of short 8-cycles compared to the hypergraph product code. Additionally, we establish an upper bound for the girth of the left-right lifted product code, demonstrating that, unlike classical QC-LDPC codes, the presence of 8-cycles is unavoidable, regardless of how the group algebra elements are selected in the base matrices.
Lastly, leveraging newly developed mathematical tools in spectral hypergraph theory, we offer a computable lower bound for the left-expansion property of the target factor graph. We believe that this contribution can be particularly valuable for code design, as the left-expansion property was previously difficult to quantify.