Related papers: The ZX-calculus is complete for stabilizer quantum…
This note describes how the the scalable ZXH calculus can be used to represent in a compact way the quantum gates that are diagonal in the computational basis. This includes controlled and multi-controlled Z gates, their generalizations,…
As state-of-the-art quantum computers are capable of running increasingly complex algorithms, the need for automated methods to design and test potential applications rises. Equivalence checking of quantum circuits is an important, yet…
We present a new graphical calculus that is sound and complete for a universal family of quantum circuits, which can be seen as the natural string-diagrammatic extension of the approximately (real-valued) universal family of Hadamard+CCZ…
Recent advances in classical simulation of Clifford+T circuits make use of the ZX calculus to iteratively decompose and simplify magic states into stabiliser terms. We improve on this method by studying stabiliser decompositions of ZX…
Two circuits are considered to be equivalent under noise if the effect of faults on one circuit is no worse than the effect of faults on the other circuit. We call this relationship fault equivalence. Fault equivalence offers a way to…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
Quantum computing is an emerging computational paradigm with the potential to outperform classical computers in solving a variety of problems. To achieve this, quantum programs are typically represented as quantum circuits, which must be…
Diagrammatic techniques for reasoning about monoidal categories provide an intuitive understanding of the symmetries and connections of interacting computational processes. In the context of categorical quantum mechanics, Coecke and…
In this paper we give a complete axiomatisation of qubit ZX-calculus via elementary transformations which are basic operations in linear algebra. This formalism has two main advantages. First, all the operations of the phases are algebraic…
We introduce a new family of models for measurement-based quantum computation which are deterministic and approximately universal. The resource states which play the role of graph states are prepared via 2-qubit gates of the form…
Graphical languages are a convenient shorthand to represent computation, with rewrite rules relating one graph to another. In contrast, proof assistants rely heavily on inductive datatypes, particularly when giving semantics to embedded…
Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…
Counting the solutions to Boolean formulae defines the problem #SAT, which is complete for the complexity class #P. We use the ZH-calculus, a universal and complete graphical language for linear maps which naturally encodes counting…
We introduce a ZX-like diagrammatic language devoted to manipulating real matrices - and rebits -, with its own set of axioms. We prove the necessity of some non trivial axioms of these. We show that some restriction of the language is…
Unitary fusion categories formalise the algebraic theory of topological quantum computation. These categories come naturally enriched in a subcategory of the category of Hilbert spaces, and by looking at this subcategory, one can identify a…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
Quantum circuit cutting refers to a series of techniques that allow one to partition a quantum computation on a large quantum computer into several quantum computations on smaller devices. This usually comes at the price of a sampling…
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…
We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the…