Related papers: Some Remarks on Quantum Brachistochrone
In this paper a quantum mechanics is built by means of a non-Hermitian momentum operator. We have shown that it is possible to construct two Hermitian and two non-Hermitian type of Hamiltonians using this momentum operator. We can construct…
In this paper, we suggest an alternative interpretation for the quantum state vector, which, by considering temporal parts for physical objects, aims to give an intelligible account of measurement problem in quantum mechanics. We examine…
It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one…
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…
The author discusses a different kind of Hermitian quantum mechanics, called $J$-Hermitian quantum mechanics. He shows that $PT$-symmetric quantum mechanics is indeed $J$-Hermitian quantum mechanics, and that time evolution (in the Krein…
Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as…
Bohmian mechanics is an alternative interpretation of quantum mechanics. We outline the main characteristics of its non-relativistic formulation. Most notably it does provide a simple solution to the infamous measurement problem of quantum…
Based on the notion of time translation, we develop a formalism to deal with the logic of quantum properties at different times. In our formalism it is possible to enlarge the usual notion of context to include composed properties involving…
We provide several schemes to construct the continuous-variable SWAP gate and present a Hermitian generalized many-body continuous controlled^n-NOT gate. We introduce and study the hybrid controlled-NOT gate and controlled-SWAP gate, and…
In this paper, the problem of synthesizing a general Hermitian quantum gate into a set of primary quantum gates is addressed. To this end, an extended version of the Jacobi approach for calculating the eigenvalues of Hermitian matrices in…
Parameterized complexity theory was developed in the 1990s to enrich the complexity-theoretic analysis of problems that depend on a range of parameters. In this paper we establish a quantum equivalent of classical parameterized complexity…
Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
Topological quantum computing is an alternative framework for avoiding the quantum decoherence problem in quantum computation. The problem of executing a gate in this framework can be posed as the problem of braiding quasiparticles. Because…
Non-hermitian quantum graphs possessing real (i.e., in principle, observable) spectra are studied via their discretization. The discretized Hamiltonians are assigned, constructively, an elementary pseudometric and/or a more complicated…
I discuss computational challenges in the relativistic few-nucleon problem and the resolution of some of these challenges. I also discuss the outlook for the future.
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a…