Related papers: Geometry of Quantum Logic Gates
We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are considered. The construction of the Hamilton operator for a…
We present a new graphical calculus that is sound and complete for a universal family of quantum circuits, which can be seen as the natural string-diagrammatic extension of the approximately (real-valued) universal family of Hadamard+CCZ…
We construct a Heisenberg-like algebra for the one dimensional infinite square-well potential in quantum mechanics. The ladder operators are realized in terms of physical operators of the system as in the harmonic oscillator algebra. These…
Topological insulators have been studied intensively over the last decades. Earlier research focused on Hermitian Hamiltonians, but recently, peculiar and interesting properties were found by introducing non-Hermiticity. In this work, we…
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…
Tunneling processes offer a promising path for finding signatures of quantum gravity. While tunneling of geometry has long been recognized in the literature, few detailed analyses in covariant Loop Quantum Gravity have been carried out. We…
The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
The challenge of quantum computing is to combine error resilience with universal computation. Diagonal gates such as the transversal $T$ gate play an important role in implementing a universal set of quantum operations. This paper…
Quantum dot-based spin qubit realization is one of the most promising quantum computing systems owing to its integrability with classical computation hardware and its versatility in realizing qubits and quantum gates. In this work, we…
Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…
High-precision, robust quantum gates are essential components in quantum computation and information processing. In this study, we present an alternative perspective, exploring the potential applicability of quantum gates that exhibit…
We study two-level q-deformed angular momentum states and us- ing q-deformed harmonic oscillators, we provide a framework for con- structing qubits and quantum gates. We also present the construction of some basic quantum gates including…
In this work, we solve the quantum absorption refrigerator analytically in the space of holomorphic functions with Gaussian measure . Our approach simplifies the calculations since for a given quantum system the coordinate representation of…
The chiral algebra of tetrahedral molecules, derived from Fischer projections, is discussed in the framework of quantum mechanics. A quantum chiral algebra is obtained whose operators, acting as rotations or inversions, commute with the…
There is developed a current algebra representation scheme for reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space and its application to quantum Hamiltonian and symmetry operators in…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…