Related papers: Generalizing Pauli Spin Matrices Using Cubic Latti…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
The Pauli matrices are a set of three 2x2 complex Hermitian, unitary matrices. In this article, we investigate the relationships between certain roots of the Pauli matrices and how gates implementing those roots are used in quantum…
Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is,…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
We present an operator-algebraic approach to the quantization and reduction of lattice field theories. Our approach uses groupoid C*-algebras to describe the observables and exploits Rieffel induction to implement the quantum gauge…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
Quantum systems can be prepared in an infinite continuum of states, but only some of them can be used as resources for quantum technologies. Discerning whether a specific quantum state falls into this class, is often a challenging task. We…
We investigate a lattice model for Euclidean quantum gravity based on discretization of the Palatini formulation of General Relativity. Using Monte Carlo simulation we show that while a naive approach fails to lead to a vacuum state…
For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises…
We provide new examples of pure entangled systems related to cluster state quantum computation that can be efficiently simulated classically. In cluster state quantum computation input qubits are initialised in the `equator' of the Bloch…
In order to use quantum devices for computations, it is necessary to understand the intricacies of the theoretical description. To this end, we provide several novel constructions useful for the comprehension of quantum mechanics from the…
We present a new treatment for the spin of a massive relativistic particle in the context of quantum information based on a physical interpretation of the Wigner rotations, obtaining different results in relation to the previous works. We…
The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…
Just as any state of a single qubit or 2-level system can be obtained from any other state by a rotation operator parametrized by three real Euler angles, we show how any state of an n-qubit or 2^n-level system can be obtained from any…
Recent development in quantum information sciences and technologies, especially building programmable quantum computers, provide us new opportunities to study fundamental aspects of quantum mechanics. We propose qubit models to emulate the…
We propose an experimental design for universal continuous-variable quantum computation that incorporates recent innovations in linear-optics-based continuous-variable cluster state generation and cubic-phase gate teleportation. The first…
We present generalized and improved constructions for simulating quantum computers with a polynomial slowdown on lattices composed of qubits on which certain global versions of one- and two-qubit operations can be performed.
The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss…
We propose an orbifold lattice formulation of QCD suitable for quantum simulations. We show explicitly how to encode gauge degrees of freedom into qubits using noncompact variables, and how to write down a simple truncated Hamiltonian in…