相关论文: Quantum Simulation of Klein Gordon Equation and Ob…
In light of the significance of non-commutative quaternionic algebra in modern physics, the current study proposes the existence of the Klein paradox in the quaternionic (3+1)-dimensional space-time structure. By introducing the…
The year 2025 marked the centennial of quantum mechanics, inaugurated by Heisenberg's matrix formulation and the foundational contributions of Pauli, Schrodinger, and Dirac. Concurrently, 2026 marks the centennial of the Klein - Gordon…
Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…
A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the…
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…
Expository paper providing a historical survey of the gradual transformation of the "philosophical discussions" between Bohr, Einstein and Schr\"odinger on foundational issues in quantum mechanics into a quantitative prediction of a new…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
Simulation of time dynamical physical problems has been a challenge for classical computers due to their time-complexity. To demonstrate the dominance of quantum computers over classical computers in this regime, here we simulate a…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to…
Major technological advances of the past century are rooted in our understanding of quantum physics in the non-interacting limit. A central challenge today is to understand the behavior of complex quantum many-body systems, where…
In spite of its problems with interactions, the first-quantized Klein-Gordon equation is a satisfactory theory of free spinless particles. Moreover, the usual theory may be extended to describe Lorentz-violating behavior, of the same types…
A classical computer simulating Schrodinger dynamics of a quantum system requires resources which scale exponentially with the size of the system, and is regarded as inefficient for such purposes. However, a quantum computer made up of a…
Last years witnessed a remarkable interest in application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, even first proof-of-principle experimental realizations…
We present a resolution of the Klein paradox within the framework of one-particle relativistic quantum mechanics. Not only reflection becomes total but the vacuum remains neutral as well. This is accomplished by replacing the pair…
Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum…
The existence of minimal length scale has motivated the proposal of generalized uncertainty principle, which provides a potential routine to probe quantum gravitational effects in low-energy quantum mechanics experiment. Hitherto, the…
When speaking of the unification of quantum mechanics and relativity, one normally refers to special relativity (SR) or to Einstein general relativity (GR). The Dirac and Klein-Gordon wave equations are an example of unification of quantum…
The Schrodinger equation, Klein-Gordon equation (KGE), and Dirac equation are believed to be the fundamental equations of quantum mechanics. Schrodinger's equation has a defect in that there are no negative kinetic energy (NKE) solutions.…