相关论文: The ZX&-calculus: A complete graphical calculus fo…
Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum…
We show the problem of counting homomorphisms from the fundamental group of a homology $3$-sphere $M$ to a finite, non-abelian simple group $G$ is #P-complete, in the case that $G$ is fixed and $M$ is the computational input. Similarly,…
The ZX-calculus is a graphical language for quantum processes with built-in rewrite rules. The rewrite rules allow equalities to be derived entirely graphically, leading to the question of completeness: can any equality that is derivable…
We modularly build increasingly larger fragments of the ZX-calculus by modularly adding new generators and relations, at each point, giving some concrete semantics in terms of some category of spans. This is performed using Lack's technique…
We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations…
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…
Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations…
Categorical Quantum Mechanics, and graphical calculi in particular, has proven to be an intuitive and powerful way to reason about quantum computing. This work continues the exploration of graphical calculi, inside and outside of the…
The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear…
The ZX-calculus is a graphical calculus for reasoning about pure state qubit quantum mechanics. It is complete for pure qubit stabilizer quantum mechanics, meaning any equality involving only stabilizer operations that can be derived using…
We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that…
Finite-dimensional quantum theory serves as the theoretical foundation for quantum information and computation. Mathematically, it is formalized in the category FHilb, comprising all finite-dimensional Hilbert spaces and linear maps between…
The relevance of shallow-depth quantum circuits has recently increased, mainly due to their applicability to near-term devices. In this context, one of the main goals of quantum circuit complexity is to find problems that can be solved by…
This is the second in a series of "graphical grokking" papers in which we study how stabiliser codes can be understood using the ZX-calculus. In this paper we show that certain complex rules involving ZX-diagrams, called spider nest…
The controlled-SWAP and controlled-controlled-NOT gates are at the heart of the original proposal of reversible classical computation by Fredkin and Toffoli. Their widespread use in quantum computation, both in the implementation of…
We give a sound and complete equational theory for 3-qubit quantum circuits over the Toffoli-Hadamard gate set { X, CX, CCX, H }. That is, we introduce a collection of true equations among Toffoli-Hadamard circuits on three qubits that is…
The ZX-calculus is a graphical language for suitably represented tensor networks, called ZX-diagrams. Calculations are performed by transforming ZX-diagrams with rewrite rules. The ZX-calculus has found applications in reasoning about…
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…
We present two new constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T =…
All-to-all interactions arise naturally in many areas of theoretical physics and across diverse experimental quantum platforms, motivating a systematic study of their information-processing power. Assuming each pair of qubits interacts with…