相关论文: Towards a Minimal Stabilizer ZX-calculus
We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the…
Graphical calculi are vital tools for representing and reasoning about quantum circuits and processes. Some are not only graphically intuitive but also logically complete. The best known of these is the ZX-calculus, which is an industry…
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…
This paper is a `spiritual child' of the 2005 lecture notes Kindergarten Quantum Mechanics, which showed how a simple, pictorial extension of Dirac notation allowed several quantum features to be easily expressed and derived, using language…
From Feynman diagrams to tensor networks, diagrammatic representations of computations in quantum mechanics have catalysed progress in physics. These diagrams represent the underlying mathematical operations and aid physical interpretation,…
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…
The discard ZX-calculus is known to be complete and universal for mixed-state quantum mechanics, allowing for both quantum and classical processes. However, if the quantum aspects of ZX-calculus have been explored in depth, little work has…
A quantum circuit may be strongly classically simulated with the aid of ZX-calculus by decomposing its $t$ T-gates into a sum of $2^{\alpha t}$ classically computable stabiliser terms. In this paper, we introduce a general procedure to find…
In the one-way model of measurement-based quantum computation (MBQC), computation proceeds via measurements on some standard resource state. So-called flow conditions ensure that the overall computation is deterministic in a suitable sense,…
Graphical languages, like quantum circuits or ZX-calculus, have been successfully designed to represent (memoryless) quantum computations acting on a finite number of qubits. Meanwhile, delayed traces have been used as a graphical way to…
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…
Coherent control of quantum computations can be used to improve some quantum protocols and algorithms. For instance, the complexity of implementing the permutation of some given unitary transformations can be strictly decreased by allowing…
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…
Universal quantum computation requires the implementation of a logical non-Clifford gate. In this paper, we characterize all stabilizer codes whose code subspaces are preserved under physical $T$ and $T^{-1}$ gates. For example, this could…
Quantum computing is currently strongly limited by the impact of noise, in particular introduced by the application of two-qubit gates. For this reason, reducing the number of two-qubit gates is of paramount importance on noisy…
The Scalable ZX-calculus is a compact graphical language used to reason about linear maps between quantum states. These diagrams have multiple applications, but they frequently have to be constructed in a case-by-case basis. In this work we…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
The dynamical-algebraic structure underlying all the schemes for quantum information stabilization is argued to be fully contained in the reducibility of the operator algebra describing the interaction with the environment of the coding…
Quantum computations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantum computing, where the graphical syntax…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…