Related papers: The ZX-calculus as a Language for Topological Quan…
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 introduce the first complete and approximatively universal diagrammatic language for quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by Coecke and Duncan, complete for the so-called Clifford+T quantum…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
Unitary Ribbon Fusion Categories (URFC) formalize anyonic theories. It has been widely assumed that the same category formalizes a topological quantum computing model. However, in previous work, we addressed and resolved this confusion and…
We propose an encoding for topological quantum computation utilizing quantum representations of mapping class groups. Leakage into a non-computational subspace seems to be unavoidable for universality in general. We are interested in the…
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…
Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they…
The fusion basis of Fibonacci anyons supports unitary braid representations that can be utilized for universal quantum computation. We show a mapping between the fusion basis of three Fibonacci anyons, $\{|1\rangle, |\tau\rangle\}$, and the…
In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations…
The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics.The language is sound and complete: a stabilizer ZX-diagram can be transformed into another one if and only if these two diagrams represent…
We propose and analyze a physical system capable of performing topological quantum computation with Majorana zero modes (MZM) in a one-dimensional topological superconductor (1DTS). One of the leading methods to realize quantum gates in…
Mapping fermionic systems to qubits on a quantum computer is often the first step for algorithms in quantum chemistry and condensed matter physics. However, it is difficult to reconcile the many different approaches that have been proposed,…
Diagrammatic representations of quantum algorithms and circuits offer novel approaches to their design and analysis. In this work, we describe extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
Traditional quantum circuit optimization is performed directly at the circuit level. Alternatively, a quantum circuit can be translated to a ZX-diagram which can be simplified using the rules of the ZX-calculus, after which a simplified…
We present a complete optimization procedure for hybrid quantum-classical circuits with classical parity logic. While common optimization techniques for quantum algorithms focus on rewriting solely the pure quantum segments, there is…
Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called non-Abelian anyons, and the simplest anyon model which allows…
Quantum matrices $A(R)$ are known for every $R$ matrix obeying the Quantum Yang-Baxter Equations. It is also known that these act on `vectors' given by the corresponding Zamalodchikov algebra. We develop this interpretation in detail,…
Topological quantum computing is an alternative framework for avoiding the quantum decoherence problem in quantum computation. The problem of executing a gate in this framework can be posed as the problem of braiding quasiparticles. Because…
Models for topological quantum computation are based on braiding and fusing anyons (quasiparticles of fractional statistics) in (2+1)-D. The anyons that can exist in a physical theory are determined by the symmetry group of the Hamiltonian.…