Synthesis of Novel 6-Substituted and 5-Substituted Pyrrolo[2,3-D] Pyrimidine Antifolates as Targeted Anticancer Therapies

The dissertation will give an introduction, background and current research progress in the areas of antifolates and chemotherapy of anticancer. The design and synthesis of classical 6- substituted pyrrolo[2,3-d]pyrimidines and 5-substituted pyrrolo[2,3-d]pyrimidines as potential antifolates have been described. The design variations include: methylated thiophene regioisomers, fluorinated phenyl regioisomers, thionyl regioisomers on the side chain of pyrrolo[2,3-d]pyrimidines. As a part of this study, a series of new compounds have been synthesized and characterized. Of these, ten final compounds were submitted for biological evaluation

An entanglement measure for n-qubits

Recently, Coffman, Kundu, and Wootters introduced the residual entanglement for three qubits to quantify the three-qubit entanglement in Phys. Rev. A 61, 052306 (2000). In Phys. Rev. A 65, 032304 (2007), we defined the residual entanglement for $n$ qubits, whose values are between 0 and 1. In this paper, we want to show that the residual entanglement for $n$ qubits is a natural measure of entanglement by demonstrating the following properties. (1). It is SL-invariant, especially LU-invariant. (2). It is an entanglement monotone. (3). It is invariant under permutations of the qubits. (4). It vanishes or is multiplicative for product states.Comment: 16 pages, no figure

SLOCC invariant and semi-invariants for SLOCC classification of four-qubits

We show there are at least 28 distinct true SLOCC entanglement classes for four-qubits by means of SLOCC invariant and semi-invariants and derive the number of the degenerated SLOCC classes for n-qubits.Comment: 22 pages, no figures, 9 tables, submit the paper to a journa

A More General Quantum Searching Algorithm And the Precise Formula of the Amplitude and the Non-symmetric Effects of Different Rotating Angles

This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm being optimal among the algorithms with arbitrary phase rotations was given in this paper. This first reported the non-symmetric effects of different rotating angles, and gave the first-order approximate phase condition when rotating angles are different.Comment: 13 pages, misusing tex formatting commands in title, shorted the titles, corrected typos, added the justifications to the section

Fixed-point Quantum Search for Different Phase Shifts

Grover recently presented the fixed-point search algorithm. In this letter, we study the fixed-point search algorithm obtained by replacing equal phase shifts of $\pi /3$ by different phase shifts.Comment: 8 page

No-cloning of nonorthogonal states does not require inner product preserving

The no-cloning theorem says there is no quantum copy machine which can copy any one-qubit state. Inner product preserving was always used to prove the no-cloning of nonorthogonal states. In this paper we show that the no-cloning of nonorthogonal states does not require inner product preserving and discuss the minimal properties which a linear operator possesses to copy two different states at the same device. In this paper, we obtain the following necessary and sufficient condition. For any two different states ∣ψ〉 = a∣0〉+b∣1〉∣ψ〉=a∣0〉+b∣1〉 and ∣ϕ〉 = c∣0〉+d∣1〉∣ϕ〉=c∣0〉+d∣1〉, assume that a linear operator LL can copy them, that is, L(∣ψ,0〉) = ∣ψ,ψ〉L(∣ψ,0〉)=∣ψ,ψ〉 and L(∣ϕ,0〉) = ∣ϕ,ϕ〉L(∣ϕ,0〉)=∣ϕ,ϕ〉. Then the two states are orthogonal if and only if L(∣0,0〉)L(∣0,0〉) and L(∣1,0〉)L(∣1,0〉) are unit length states. Thus we only need linearity and that L(∣0,0〉)L(∣0,0〉) and L(∣1,0〉)L(∣1,0〉) are unit length states to prove the no-cloning of nonorthogonal states. It implies that inner product preserving is not necessary for the no-cloning of nonorthogonal states.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87751/2/082102_1.pd