相关论文: Completeness of Graphical Languages for Mixed Stat…

We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…

In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…

Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra, programming language semantics, representation theory,…

Convergent rewriting systems are well-known tools in the study of the word-rewriting problem. In particular, a presentation of a monoid by a finite convergent rewriting system gives an algorithm to decide the word problem for this monoid.…

Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…

We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for…

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…

Despite significant advances in quantum computing across various domains, research on applying quantum approaches to language compositionality - such as modeling linguistic structures and interactions - remains limited. This gap extends to…

The quantum programming language Quipper supports circuit operations such as reversing and controlling certain quantum circuits. Additionally, Quipper provides a function called with-computed, which can be used to program circuits of the…

Magic refers to the degree of "quantumness" in a system that cannot be fully described by stabilizer states and Clifford operations alone. In quantum computing, stabilizer states and Clifford operations can be efficiently simulated on a…

We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…

This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.

We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…

Since masking of quantum information was introduced by Modi et al. in [PRL 120, 230501 (2018)], many discussions on this topic have been published. In this paper, we consider relationship between quantum multipartite maskers (QMMs) and…

We develop a symmetric monoidal closed category of games, incorporating sums and products, to model quantum computation at higher types. This model is expressive, capable of representing all unitary operators at base types. It is compatible…

Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…

We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology invariants naturally give rise to diagonal logical gates. We…

A class of unital qubit maps displaying diagonal unitary and orthogonal symmetries is analyzed. Such maps already found a lot applications in quantum information theory. We provide a complete characterization of this class of maps showing…

Recently, we gave a complete axiomatisation of the ZX-calculus for the overall pure qubit quantum mechanics. Based on this result, here we also obtain a complete axiomatisation of the ZX-calculus for the Clifford+T quantum mechanics by…

A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so called crossbar…