Related papers: LOv-Calculus: A Graphical Language for Linear Opti…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of…
In this paper we study the subset of generalized quantum measurements on finite dimensional systems known as local operations and classical communication (LOCC). While LOCC emerges as the natural class of operations in many important…
One of the main advantages of an optical approach to quantum computing is the fact that optical fibers can be used to connect the logic and memory devices to form useful circuits, in analogy with the wires of a conventional computer. Here…
We propose and analyze a nanomechanical architecture where light is used to perform linear quantum operations on a set of many vibrational modes. Suitable amplitude modulation of a single laser beam is shown to generate squeezing,…
ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose a token-machine-based asynchronous model of both pure…
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics. A simulator for quantum algorithms must be capable of performing heavy mathematical matrix transforms. The design of the simulator…
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 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…
This paper describes a quantum algorithm for proof search in sequent calculus of a subset of Linear Logic using the Grover Search Algorithm. We briefly overview the Grover Search Algorithm and Linear Logic, show the detailed steps of the…
Quantum assembly languages are machine-independent languages that traditionally describe quantum computation in the circuit model. Open quantum assembly language (OpenQASM 2) was proposed as an imperative programming language for quantum…
Computability logic (CoL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
A fully optical method to perform any quantum computation with optical waveguide modes is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum…
Replicating In-Context Learning (ICL) in computer vision remains challenging due to task heterogeneity. We propose \textbf{VIRAL}, a framework that elicits visual reasoning from a pre-trained image editing model by formulating ICL as…
We describe a graphical calculus for completely positive maps and in doing so review the theory of open quantum systems and other fundamental primitives of quantum information theory using the language of tensor networks. In particular we…
Visual question answering (VQA) in medical imaging aims to support clinical diagnosis by automatically interpreting complex imaging data in response to natural language queries. Existing studies typically rely on distinct visual and textual…
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…
This paper explores the integration of neural networks with logic programming, addressing the longstanding challenges of combining the generalization and learning capabilities of neural networks with the precision of symbolic logic.…
In this paper, we give a universal completion of the ZX-calculus for the whole of pure qubit quantum mechanics. This proof is based on the completeness of another graphical language: the ZW-calculus, with direct translations between these…