Related papers: Towards a Minimal Stabilizer ZX-calculus
Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. Using ZX calculus, we represent QECC's in a form called a ZX diagram, consisting of a tensor network. In this paper, we present…
Improving the simulation of quantum circuits on classical computers is important for understanding quantum advantage and increasing development speed. In this paper, we explore a new way to express stabilizer states and further improve the…
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…
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.…
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…
The ZX-calculus, and the variant we consider in this paper (ZXH-calculus), are formal diagrammatic languages for qubit quantum computing. We show that it can also be used to describe SU(2) representation theory. To achieve this, we first…
In a recent paper Lechner, Hauke and Zoller (LHZ) described a means to translate a Hamiltonian of $N$ spin-$\frac{1}{2}$ particles with 'all-to-all' interactions into a larger physical lattice with only on-site energies and local parity…
This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an efficient way to describe an important class of…
The ZH-calculus is a complete graphical calculus for linear maps between qubits that admits a straightforward encoding of hypergraph states and circuits arising from the Toffoli+Hadamard gate set. In this paper, we establish a…
Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…
It is known that a quantum circuit may be simulated with classical hardware via stabilizer state (T-)decomposition in $O(2^{\alpha t})$ time, given $t$ non-Clifford gates and a decomposition efficiency $\alpha$. The past years have seen a…
Quantum computers allow a near-exponential speed-up for specific applications when compared to classical computers. Despite recent advances in the hardware of quantum computers, their practical usage is still severely limited due to a…
Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…
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…
This paper presents a novel approach to quantum architecture search by integrating the techniques of ZX-calculus with Genetic Programming (GP) to optimize the structure of parameterized quantum circuits employed in Quantum Machine Learning…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
Structured reversible flowchart languages is a class of imperative reversible programming languages allowing for a simple diagrammatic representation of control flow built from a limited set of control flow structures. This class includes…
We apply the recent graphical framework of "Quantum Lego" to XP stabilizer codes where the stabilizer group is generally non-Abelian. We show that the idea of operator matching continues to hold for such codes and is sufficient for…
Contextuality is a fundamental non-classical property of quantum theory, which has recently been proven to be a key resource for achieving quantum speed-ups in some leading models of quantum computation. However, which of the forms of…
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…