相关论文: The decohered ZX-calculus

Classical simulation of quantum circuits is a pivotal part of the quantum computing landscape, specially within the NISQ era, where the constraints imposed by available hardware are unavoidable. The Gottesman-Knill theorem further motivates…

We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with…

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.…

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…

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…

We present an abstract model of quantum computation, the "Pauli Fusion" model, whose primitive operations correspond closely to generators of the ZX calculus (a formal graphical language for quantum computing). The fundamental operations of…

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…

Loop quantum gravity (LQG) attempts to unify general relativity with quantum physics to offer a complete description of the universe by quantising spacetime geometry, but the numerical calculations we encounter are extraordinarily…

Recent astonishing experiments with quantum computers have demonstrated unambiguously the existence of a quantum multiverse, where calculations of mind-boggling complexity are effortlessly computed in just a few minutes. Here, we…

The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection…

This article presents a novel algorithmic methodology for performing automated diagrammatic deductions over combinatorial structures, using a combination of modified equational theorem-proving techniques and the extended Wolfram model…

The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a type of tensor networks that can represent arbitrary linear maps between qubits. Using the ZX-calculus, we can intuitively reason about quantum theory, and optimise…

We give a complete presentation for the fragment, ZX&, of the ZX-calculus generated by the Z and X spiders (corresponding to copying and addition) along with the not gate and the and gate. To prove completeness, we freely add a unit and…

Categorical Quantum Mechanics, and graphical calculi in particular, has proven to be an intuitive and powerful way to reason about quantum computing. This work continues the exploration of graphical calculi, inside and outside of the…

The theory of decoherent histories is an attempt to derive classical physics from positing only quantum laws at the fundamental level without notions of a classical apparatus or collapse of the wave-function. Searching for a marked target…

Categorical quantum mechanics and the Wolfram model offer distinct but complementary approaches to studying the relationship between diagrammatic rewriting systems over combinatorial structures and the foundations of physics; the objective…

We propose a quantum programming language that generalizes the $\lambda$-calculus. The language is non-linear; duplicated variables denote, not cloning of quantum data, but sharing a qubit's state; that is, producing an entangled pair of…

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…

Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed…

Decoupling theorems have proven useful in various applications in the area of quantum information theory. This thesis builds upon preceding work by Fr\'{e}d\'{e}ric Dupuis [arXiv:1012.6044v1], where a general decoupling theorem is obtained…