Related papers: Comments on "Quantum Control by Decompositions of …

Two typos in the published paper are pointed out. Both are just typos and the calculations in that paper are based on the correct formulism.

In this paper we provide an explicit parameterization of arbitrary unitary transformation acting on n qubits, in terms of one and two qubit quantum gates. The construction is based on successive Cartan decompositions of the semi-simple Lie…

A central question in Quantum Computing is how matrices in $SU(2)$ can be approximated by products over a small set of generators. A topology will be defined on $SU(2)$ so as to introduce the notion of a covering exponent which compares the…

A minimal practical formal structure for a fundamental theory is suggested. A mechanism that produces such a structure is reviewed. The proposed mechanism has possibilities of producing non-canonical phenomena in SU(2) and SU(3) quantum…

Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…

We comment on the Reply of G. Su and M. Suzuki [cond-mat/9808011] to our Comment [cond-mat/9807402] about the papers of G. Su [Phys. Rev. B 54, 8291 (1996)] and G. Su and M. Suzuki [Phys. Rev. B 57, 13367 (1998)]. The algebraic mistake…

We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that every minimal non-degenerate critical…

In this note the authors have raised the question regarding the validity of the main result in [1] by setting an example.

We study how to generate in minimum time special unitary transformations for a two-level quantum system under the assumptions that: (i) the system is subject to a constant drift, (ii) its dynamics can be affected by three independent,…

In this paper, for continuous, linearly-controllable quadratic control systems with a single input, an explicit, constructive method is proposed for studying their Brunovsky forms, initially studied in [W. Kang and A. J. Krener, Extended…

Maximally supersymmetric SO(10) and SU(6) unified theories are constructed on the orbifold T^2/(Z_2 x Z'_2), with one length scale R_5 taken much larger than the other, R_6. The effective theory below 1/R_6 is found to be the highly…

This paper examines the controllability for quantum control systems with SU(1,1) dynamical symmetry, namely, the ability to use some electromagnetic field to redirect the quantum system toward a desired evolution. The problem is formalized…

This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…

It is demonstrated that remarks and criticism in work [1] (arXiv:1005.2436 nucl-th) have resulted from inattentive reading of work [2] (Phys. Rev.C 81, 035501 (2010)) or just some misunderstanding and do not influence conclusions of work…

The question raised by [Bastin and Martin 2003 J. Phys. B: At. Mol. Opt. Phys. 36, 4201] is examined and used to explain in more detail a key point of our calculations. They have sought to rebut criticisms raised by us of certain techniques…

Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.

We present an outline of a technique to associate certain methods from time optimal quantum control with various transforms on SU(3). Unitary operators are taken from certain time dependent Hamiltonians and transformation laws are derived.…

In this paper, we test and extend a proposal of Gu, Pei, and Zhang for an application of decomposition to three-dimensional theories with one-form symmetries and to quantum K theory. The theories themselves do not decompose, but, OPEs of…

We revisit the reduction of type II supergravity on SU(3) structure manifolds, conjectured to lead to gauged N=2 supergravity in 4 dimensions. The reduction proceeds by expanding the invariant 2- and 3-forms of the SU(3) structure as well…

I discuss the scope and naturalness of the proton mass decomposition (or sum rule) published in PRL74, 1071 (1995) and answer a few criticisms that appeared recently in the literature, focusing particularly on its interpretation and the…