相关论文: ZX-Rules for 2-qubit Clifford+T Quantum Circuits

As state-of-the-art quantum computers are capable of running increasingly complex algorithms, the need for automated methods to design and test potential applications rises. Equivalence checking of quantum circuits is an important, yet…

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…

Quantum computing is an emerging computational paradigm with the potential to outperform classical computers in solving a variety of problems. To achieve this, quantum programs are typically represented as quantum circuits, which must be…

The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical possibility of a purely graphical description of quantum…

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…

Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…

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…

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…

In this paper, we introduce a technique for contracting (i.e. numerically evaluating) ZX-diagrams whose complexity scales with their rank-width, a graph parameter that behaves nicely under ZX rewrite rules. Given a rank-decomposition of…

The real stabilizer fragment of quantum mechanics was shown to have a complete axiomatization in terms of the angle-free fragment of the ZX-calculus. This fragment of the ZX-calculus---although abstractly elegant---is stated in terms of…

Reducing the number of non-Clifford quantum gates present in a circuit is an important task for efficiently implementing quantum computations, especially in the fault-tolerant regime. We present a new method for reducing the number of…

The ZW-calculus is a graphical language capable of representing 2-dimensional quantum systems (qubit) through its diagrams, and manipulating them through its equational theory. We extend the formalism to accommodate finite dimensional…

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…

In the noisy intermediate-scale quantum (NISQ) era, two-qubit gates in quantum circuits are more susceptible to noise than single-qubit gates. Therefore, reducing the number of two-qubit gates is crucial for improving circuit efficiency and…

Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We show here how, by considering certain non-stabiliser…

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…

The ZX calculus is a mathematical tool to represent and analyse quantum operations by manipulating diagrams which in effect represent tensor networks. Two families of nodes of these networks are ones which commute with either Z rotations or…

Two circuits are considered to be equivalent under noise if the effect of faults on one circuit is no worse than the effect of faults on the other circuit. We call this relationship fault equivalence. Fault equivalence offers a way to…

We introduce here a new axiomatisation of the rational fragment of the ZX-calculus, a diagrammatic language for quantum mechanics. Compared to the previous axiomatisation introduced in [8], our axiomatisation does not use any metarule , but…

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…