Related papers: The ZX-calculus is complete for stabilizer quantum…
The ZX-calculus is a convenient formalism for expressing and reasoning about quantum circuits at a low level, whereas the recently-proposed ZH-calculus yields convenient expressions of mid-level quantum gates such as Toffoli and CCZ. In…
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…
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…
Measurement-based quantum computation (MBQC) is a universal platform to realize unitary gates, only using measurements which act on a pre-prepared entangled resource state. By deforming the measurement bases, as well as the geometry of the…
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…
We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect may be necessary, but not sufficient to make…
What resources are universal for quantum computation? In the standard model, a quantum computer consists of a sequence of unitary gates acting coherently on the qubits making up the computer. This paper shows that a very different model…
We introduce a model-checking tool intended specially for the analysis of quantum information protocols. The tool incorporates an efficient representation of a certain class of quantum circuits, namely those expressible in the so-called…
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…
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…
Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are…
A catalysis state is a quantum state that is used to make some desired operation possible or more efficient, while not being consumed in the process. Recent years have seen catalysis used in state-of-the-art protocols for implementing magic…
Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitively about interacting quantum systems. The compositional structure of this calculus was shown to be well-equipped to sufficiently express…
The ubiquity of stabilizer circuits in the design and operation of quantum computers makes techniques to verify their correctness essential. The simulation of stabilizer circuits, which aims to replicate their behavior using a classical…
The ZH calculus is a graphical language for quantum computation reasoning. The phase-free variant offers a simple set of generators that guarantee universality. ZH calculus is effective in MBQC and analysis of quantum circuits constructed…
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…
We develop a unified geometric framework for quantum circuit compilation based on quantized orbifold phases and their diagrammatic semantics. Physical qubit platforms impose heterogeneous phase resolutions, anisotropic Bloch-ball…
Stabilizer simulation can efficiently simulate an important class of quantum circuits consisting exclusively of Clifford gates. However, all existing extensions of this simulation to arbitrary quantum circuits including non-Clifford gates…
String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of…
We consider the problem of minimizing resources required for universal quantum computation using only projective measurements. The resources we focus on are observables, which describe projective measurements, and ancillary qubits. We show…