Information-theoretic lower bounds for quantum sorting

We analyze the quantum query complexity of sorting under partial information. In this problem, we are given a partially ordered set $P$ and are asked to identify a linear extension of $P$ using pairwise comparisons. For the standard sorting problem, in which $P$ is empty, it is known that the quantum query complexity is not asymptotically smaller than the classical information-theoretic lower bound. We prove that this holds for a wide class of partially ordered sets, thereby improving on a result from Yao (STOC'04)

Hierarchical Entity Resolution using an Oracle

In many applications, entity references (i.e., records) and entities need to be organized to capture diverse relationships like type-subtype, is-A (mapping entities to types), and duplicate (mapping records to entities) relationships. However, automatic identification of such relationships is often inaccurate due to noise and heterogeneous representation of records across sources. Similarly, manual maintenance of these relationships is infeasible and does not scale to large datasets. In this work, we circumvent these challenges by considering weak supervision in the form of an oracle to formulate a novel hierarchical ER task. In this setting, records are clustered in a tree-like structure containing records at leaf-level and capturing record-entity (duplicate), entity-type (is-A) and subtype-supertype relationships. For effective use of supervision, we leverage triplet comparison oracle queries that take three records as input and output the most similar pair(s). We develop HierER, a querying strategy that uses record pair similarities to minimize the number of oracle queries while maximizing the identified hierarchical structure. We show theoretically and empirically that HierER is effective under different similarity noise models and demonstrate empirically that HierER can scale up to million-size datasets