相关论文: Beyond Penrose tensor diagrams with the ZX calculu…

The spin of particles on a non-commutative geometry is investigated within the framework of the representation theory of the q-deformed Poincare algebra. An overview of the q-Lorentz algebra is given, including its representation theory…

The ability to perform high-precision one- and two-qubit operations is sufficient for universal quantum computation. For the Loss-DiVincenzo proposal to use single electron spins confned to quantum dots as qubits, it is therefore sufficient…

We present a fully extrinsic, parametrization-free variant of tensor calculus on embedded, possibly evolving, submanifolds with boundary in arbitrary dimension and codimension. The proposed approach is component-free and, for general rank…

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…

We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…

Numerical computations and methods have become increasingly crucial in the study of spin foam models across various regimes. This paper adds to this field by introducing new algorithms based on tensor network methods for computing…

Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…

A flexible unified framework for both classical and quantum Schubert calculus is proposed. It is based on a natural combinatorial approach relying on the Hasse-Schmidt extension of a certain family of pairwise commuting endomorphisms of an…

A new link between tetrahedra and the group SU(2) is pointed out: by associating to each face of a tetrahedron an irreducible unitary SU(2) representation and by imposing that the faces close, the concept of quantum tetrahedron is seen to…

The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…

The study of three dimensional CFT correlators in twistor space has recently garnered a significant interest. Conformal symmetry acts linearly in the twistor space, which streamlines the analysis. Moreover, twistors provide a connection to…

We present a quantum compilation algorithm that maps Clifford encoders, encoding maps for stabilizer quantum codes, to a unique graphical representation in the ZX calculus. Specifically, we develop a canonical form in the ZX calculus and…

These notes are based on my lectures given at $\text{ST}^4$ 2025 held at IISER Bhopal. We study the application of spinor and twistor methods to three dimensional conformal field theories in these notes. They are divided into three parts…

We introduce the PBS-calculus to represent and reason on quantum computations involving coherent control of quantum operations. Coherent control, and in particular indefinite causal order, is known to enable multiple computational and…

We consider the scalar-tensor theories of gravity extended by the pseudoscalar couplings to matter and gauge fields and derive constraints on the CP-odd combinations of scalar and pseudoscalar couplings from laboratory spin precession…

The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the…

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…

Neural network quantum states (NQS) have been widely applied to spin-1/2 systems where they have proven to be highly effective. The application to systems with larger on-site dimension, such as spin-1 or bosonic systems, has been explored…

The three-dimensional universal complex Clifford algebra is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the…

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…