相关论文: Well-tempered ZX and ZH Calculi

Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a…

This paper is a `spiritual child' of the 2005 lecture notes Kindergarten Quantum Mechanics, which showed how a simple, pictorial extension of Dirac notation allowed several quantum features to be easily expressed and derived, using language…

ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain…

This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning, specifically the ZX-calculus, to practical…

To approximate arbitrary unitary transformations on one or more qubits, one must perform transformations which are outside of the Clifford group. The gate most commonly considered for this purpose is the T = diag(1, exp(i \pi/4)) gate. As T…

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…

Binary decision diagram (BDD) and zero-suppressed binary decision diagram (ZDD) are data structures to represent a family of (sub)sets compactly, and it can be used as succinct indexes for a family of sets. To build BDD/ZDD representing a…

This paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information.…

Let $V_1 \otimes V_2$ be a tensor product of VOAs. Using Zhu theory we discuss the theory of representations of V (associative algebra, modules and fusion rules). We prove that this theory is more or less the same as representation theory…

These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You…

We build a symmetric monoidal and compact closed bicategory by combining spans and cospans inside a topos. This can be used as a framework in which to study open networks and diagrammatic languages. We illustrate this framework with Coecke…

Following the ideas of [AGG11] about Zt x Z2,2-cocyclic Hadamard matrices, we introduce the notion of diagram, which visually represents any set of coboundaries. Diagrams are a very useful tool for the description and the study of paths and…

The task to construct parametrices of elliptic differential operators on a manifold with edges requires a calculus of operators with a two-component principal symbolic hierarchy, consisting of (edge-degenerate) interior and…

Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…

Symbolic algebra relevant to the renormalization of gauge theories can be efficiently performed by machine using modern packages. We devise a scheme for representing and manipulating the objects involved in perturbative calculations of…

Because of the efficiency of modeling fuzziness and vagueness, Z-number plays an important role in real practice. However, Z-numbers, defined in the real number field, lack the ability to process the quantum information in quantum…

Squared tensor networks (TNs) and their extension as computational graphs--squared circuits--have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces…

We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a…

We present a smorgasbord of results on the stabiliser ZX-calculus for odd prime-dimensional qudits (i.e. qupits). We derive a simplified rule set that closely resembles the original rules of qubit ZX-calculus. Using these rules, we…

Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most…