Maximum deflection of symmetric wall-frame buildings

The system of governing differential equations of lateral deflection of symmetric multi-storey buildings subjected to uniformly distributed horizontal load is presented. It is shown that the “standard” equivalent column approach (when the stiffnesses of the bracing units are added up) is only applicable to the deflection analysis in the rare case when the system only consists of shear walls and a single framework. When the bracing system contains more frameworks, then a more sophisticated approach is needed where the full interaction between the vertical elements in bending and shear may need to be taken into account. Two new methods are developed for the determination of the maximum deflection of mixed bracing systems consisting of frameworks and shear walls: one is very simple while the other one is more accurate. The accuracy of both procedures is demonstrated using the results of over 200 bracing systems. The error range of the more accurate method is -4% to +4% when the buildings contain frameworks and shear walls/cores. A worked example and step-by-step instructions are presented to aid practical application

Comment on "Probabilistic Quantum Memories"

This is a comment on two wrong Phys. Rev. Letters papers by C.A. Trugenberger. Trugenberger claimed that quantum registers could be used as exponentially large "associative" memories. We show that his scheme is no better than one where the quantum register is replaced with a classical one of equal size. We also point out that the Holevo bound and more recent bounds on "quantum random access codes" pretty much rule out powerful memories (for classical information) based on quantum states.Comment: REVTeX4, 1 page, published versio

Thresholds for Linear Optics Quantum Computing with Photon Loss at the Detectors

We calculate the error threshold for the linear optics quantum computing proposal by Knill, Laflamme and Milburn [Nature 409, pp. 46--52 (2001)] under an error model where photon detectors have efficiency <100% but all other components -- such as single photon sources, beam splitters and phase shifters -- are perfect and introduce no errors. We make use of the fact that the error model induced by the lossy hardware is that of an erasure channel, i.e., the error locations are always known. Using a method based on a Markov chain description of the error correction procedure, our calculations show that, with the 7 qubit CSS quantum code, the gate error threshold for fault tolerant quantum computation is bounded below by a value between 1.78% and 11.5% depending on the construction of the entangling gates.Comment: 7 pages, 6 figure

Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation

We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schroedinger equation, on a discrete grid. We start with a classically obtained eigenvector for a problem discretized on a coarse grid, and we efficiently construct, quantum mechanically, an approximation of the same eigenvector on a fine grid. We use this approximation as the initial state for the eigenvalue estimation algorithm, and show the relationship between its success probability and the size of the coarse grid.Comment: 4 page

Polynomial-Time Simulation of Pairing Models on a Quantum Computer

We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between ground and first excited states, and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultra-small metallic grains.Comment: 5 pages, RevTeX, Latest, modified version to appear in Phys. Rev. Let

Quantum complexities of ordered searching, sorting, and element distinctness

We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list, we prove a lower bound of \frac{1}{\pi}(\ln(N)-1) accesses to the list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary comparisons for element distinctness. The previously best known lower bounds are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}), respectively. Our proofs are based on a weighted all-pairs inner product argument. In addition to our lower bound results, we give a quantum algorithm for ordered searching using roughly 0.631 \log_2(N) oracle accesses. Our algorithm uses a quantum routine for traversing through a binary search tree faster than classically, and it is of a nature very different from a faster algorithm due to Farhi, Goldstone, Gutmann, and Sipser.Comment: This new version contains new results. To appear at ICALP '01. Some of the results have previously been presented at QIP '01. This paper subsumes the papers quant-ph/0009091 and quant-ph/000903