Situated as a language between computer science, quantum physics and mathematics,
tensor network theory has steadily grown in popularity and can now be found in applications …

We present an infinite number of construction schemes involving unitary error bases,
Hadamard matrices, quantum Latin squares and controlled families, many of which have not …

We introduce a pictorial approach to quantum information, called holographic software. Our
software captures both algebraic and topological aspects of quantum networks. It yields a bi …

We present a 3D topological picture-language for quantum information. Our approach
combines charged excitations carried by strings, with topological properties that arise from …

We give an efficient algorithm to evaluate a certain class of exponential sums, namely the
periodic, quadratic, multivariate half Gauss sums. We show that these exponential sums …

From Feynman diagrams to tensor networks, diagrammatic representations of computations
in quantum mechanics have catalyzed progress in physics. These diagrams represent the …

We give an overview of our philosophy of pictures in mathematics. We emphasize a
bidirectional process between picture language and mathematical concepts: abstraction and …

We give a scheme for interpreting shaded tangles as quantum programs, with the property
that isotopic tangles yield equivalent programs. We analyze many known quantum programs …

Tensor networks in physics can be traced back to a 1971 paper by Penrose (1). Such
network diagrams appear in digital circuit theory, and they form the foundations of quantum …

We give a scheme for interpreting shaded tangles as quantum circuits, with the property that
if two shaded tangles are ambient isotopic, their corresponding computational effects are …