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Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…
The C programming language and its cousins such as C++ stipulate the static storage of sets of structured data: Developers have to commit to one, invariant data model -- typically a structure-of-arrays (SoA) or an array-of-structs (AoS) --…
We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between…
Ordinary differential equations (ODEs) are widely used to model complex dynamics that arises in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally very difficult. In…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
Automatic evaluation for Open Domain Event Detection (ODED) is a highly challenging task, because ODED is characterized by a vast diversity of un-constrained output labels from various domains. Nearly all existing evaluation methods for…
Analytical processing on XML repositories is usually enabled by designing complex data transformations that shred the documents into a common data warehousing schema. This can be very time-consuming and costly, especially if the underlying…
We introduce a new approach to computation on encrypted data -- Encrypted Operator Computing (EOC) -- as an alternative to Fully Homomorphic Encryption (FHE). Given a plaintext vector $|{x}\rangle$, $x\in \{0,1\}^n$, and a function $F(x)$…
Quantum operations with indefinite causal order (ICO) represent a framework in quantum information processing where the relative order between two events can be indefinite. In this paper, we investigate whether sensing and computation, two…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
In classic program synthesis algorithms, such as counterexample-guided inductive synthesis (CEGIS), the algorithms alternate between a synthesis phase and an oracle (verification) phase. Many synthesis algorithms use a white-box oracle…
Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantum circuits. The class of quantum…
Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size~$N$ and margin~$\gamma$ (how well the given data are separated), the query complexity of the best-known…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
We consider the compilation of a binary neural network's decision function into tractable representations such as Ordered Binary Decision Diagrams (OBDDs) and Sentential Decision Diagrams (SDDs). Obtaining this function as an OBDD/SDD…
This paper explores artificial intelligence (AI) methods for the approximate compiling of unitaries, focusing on the use of fixed two-qubit gates and arbitrary single-qubit rotations typical in superconducting hardware. Our approach…
Encoding classical data into quantum states is a central bottleneck in quantum machine learning: many widely used encodings are circuit-inefficient, requiring deep circuits and substantial quantum resources, which limits scalability on…
We present an algorithm that decomposes any $n$-qubit Clifford operator into a circuit consisting of three subcircuits containing only CNOT or CPHASE gates with layers of one-qubit gates before and after each of these subcircuits. As with…
Differential-algebraic equations (DAEs) have been used in modeling various dynamical systems in science and engineering. Several preprocessing methods for DAEs, such as consistent initialization and index reduction, use structural…
Purpose: This study extends the structural theory of finite commutative ternary $\Gamma$-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration…