Quantum Fourier transform revisited

The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank-1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix-2 QFT decomposition to a radix-d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view

Cellular automaton models for time-correlated random walks: derivation and analysis.

Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is "data-driven". Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.The authors thank the Centre for Information Services and High Performance Computing (ZIH) at TU Dresden for providing an excellent infrastructure. The authors acknowledge support by the German Research Foundation and the Open Access Publication Funds of the TU Dresden.The authors would like to thank Anja Voß-Böhme, Lutz Brusch, Fabian Rost, Osvaldo Chara, Simon Syga, and Oleksandr Ostrenko for their helpful comments and fruitful discussions. Andreas Deutsch is grateful to the Deutsche Krebshilfe for support. Andreas Deutsch is supported by the German Research Foundation (Deutsche Forschungsgemeinschaft) within the projects SFB-TR 79 “Materials for tissue regeneration within systemically altered bones” and Research Cluster of Excellence “Center for Advancing Electronics Dresden” (cfaed). Haralampos Hatzikirou would like to acknowledge the SYSMIFTA ERACoSysMed grant (031L0085B) for the financial support of this work and the German Federal Ministry of Education and Research within the Measures for the Establishment of Systems Medicine, project SYSIMIT (BMBF eMed project SYSIMIT, FKZ: 01ZX1308D). Josué Manik Nava-Sedeño is supported by the joint scolarship program DAAD-CONACYT-Regierungsstipendien (50017046) by the German Academic Exchange Service and the National Council on Science and Technology of Mexico

The Uncertainty Principle in the Presence of Quantum Memory

The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, a device which is likely to soon be available, it is possible to predict the outcomes for both measurement choices precisely. In this work we strengthen the uncertainty principle to incorporate this case, providing a lower bound on the uncertainties which depends on the amount of entanglement between the particle and the quantum memory. We detail the application of our result to witnessing entanglement and to quantum key distribution.Comment: 5 pages plus 12 of supplementary information. Updated to match the journal versio

Bell Correlations and the Common Future

Reichenbach's principle states that in a causal structure, correlations of classical information can stem from a common cause in the common past or a direct influence from one of the events in correlation to the other. The difficulty of explaining Bell correlations through a mechanism in that spirit can be read as questioning either the principle or even its basis: causality. In the former case, the principle can be replaced by its quantum version, accepting as a common cause an entangled state, leaving the phenomenon as mysterious as ever on the classical level (on which, after all, it occurs). If, more radically, the causal structure is questioned in principle, closed space-time curves may become possible that, as is argued in the present note, can give rise to non-local correlations if to-be-correlated pieces of classical information meet in the common future --- which they need to if the correlation is to be detected in the first place. The result is a view resembling Brassard and Raymond-Robichaud's parallel-lives variant of Hermann's and Everett's relative-state formalism, avoiding "multiple realities."Comment: 8 pages, 5 figure

Quantum Computation with Coherent Spin States and the Close Hadamard Problem

We study a model of quantum computation based on the continuously-parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close Hadamard problem. We prove that the close Hadamard problem can be solved in the spin system model with arbitrarily small error probability in a constant number of oracle queries. We conclude that this model of quantum computation is suitable for solving certain types of problems. The model is effective for problems where symmetries between the structure of the information associated with the problem and the structure of the unitary operators employed in the quantum algorithm can be exploited.Comment: RevTeX4, 13 pages with 8 figures. Accepted for publication in Quantum Information Processing. Article number: s11128-015-1229-

High efficacy and low toxicity of weekly docetaxel given as first-line treatment for metastatic breast cancer

Background: Docetaxel is one of the most effective antitumor agents currently available for the treatment of metastatic breast cancer (MBC). This phase II multicenter study prospectively analyzed the efficacy and toxicity of docetaxel given on a weekly schedule as first-line treatment of metastatic breast cancer. Patients and Methods: All patients received docetaxel, 35 mg/m(2) weekly for 6 weeks, followed by 2 weeks of rest. Subsequent cycles ( 3 weeks of treatment, 2 weeks of rest) were given until a maximum of 5 cycles or disease progression. Premedication consisted of 8 mg dexamethasone intravenously 30 min prior to the infusion of docetaxel. Results: Fifty-four patients at a median age of 58 years with previously untreated MBC were included in the study. A median of 10 doses ( median cumulative dose 339 mg/m(2)) was administered ( range: 2 - 18). The overall response rate was 48.1% ( 95% CI: 34 - 61%, intent-to-treat). Median survival was 15.8 months and median time to progression was 5.9 months ( intent-to-treat). Hematological toxicity was mild with absence of neutropenia-related complications. Grade 3 neutropenia was observed in 3.7% of patients and grade 3 and 4 anemia was observed in 5.6 and 1.9% of patients, respectively. Conclusion: The weekly administration of docetaxel is highly efficient and safe as first-line treatment for MBC and may serve as an important treatment option specifically in elderly patients and patients with a reduced performance status. Copyright (C) 2005 S. Karger AG, Basel

Intraoperative radiotherapy (IORT) is an option for patients with localized breast recurrences after previous external-beam radiotherapy

<p>Abstract</p> <p>Background</p> <p>For patients suffering of recurrent breast cancer within the irradiated breast, generally mastectomy is recommended. The normal tissue tolerance does not permit a second full-dose course of radiotherapy to the entire breast after a second breast-conserving surgery (BCS). A novel option is to treat these patients with partial breast irradiation (PBI). This approach is based on the hypothesis that re-irradiation of a limited volume will be effective and result in an acceptable frequency of side effects. The following report presents a single center experience with intraoperative radiotherapy (IORT) during excision of recurrent breast cancer in the previously irradiated breast.</p> <p>Methods</p> <p>Between 4/02 and 11/06, 15 patients were treated for in-breast recurrences at a median of 10 years (3–25) after previous EBRT (10 recurrences in the initial tumor bed, 3 elsewhere in-breast failures, 2 invasive recurrences after previous DCIS). Additional 2 patients were selected for IORT with new primary breast cancer after previous partial breast EBRT for treatment of Hodgkin's disease. IORT with a single dose of 14.7 – 20 Gy 50 kV X-rays at the applicator surface was delivered with the Intrabeam™-device (Carl Zeiss, Oberkochen, Germany).</p> <p>Results</p> <p>After a median follow-up of 26 months (1–60), no local recurrence occurred. 14 out of 17 patients are alive and free of disease progression. Two patients are alive with distant metastases. One patient died 26 months after BCS/IORT due to pulmonary metastases diagnosed 19 months after BCS/IORT. Acute toxicity after IORT was mild with no Grade 3/4 toxicities and cosmetic outcome showed excellent/good/fair results in 7/7/3 cases.</p> <p>Conclusion</p> <p>IORT for recurrent breast cancer using low energy X-rays is a valuable option for patients with recurrent breast cancer after previous radiotherapy.</p

An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards

A central question of dynamics, largely open in the quantum case, is to what extent it erases a system's memory of its initial properties. Here we present a simple statistically solvable quantum model describing this memory loss across an integrability-chaos transition under a perturbation obeying no selection rules. From the perspective of quantum localization-delocalization on the lattice of quantum numbers, we are dealing with a situation where every lattice site is coupled to every other site with the same strength, on average. The model also rigorously justifies a similar set of relationships recently proposed in the context of two short-range-interacting ultracold atoms in a harmonic waveguide. Application of our model to an ensemble of uncorrelated impurities on a rectangular lattice gives good agreement with ab initio numerics.Comment: 29 pages, 5 figure

Many-body localization in a quantum simulator with programmable random disorder

When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. Exceptions to quantum thermalization have been predicted and observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize in spite of strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. Here we experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium. We observe the essential signatures of MBL: memory retention of the initial state, a Poissonian distribution of energy level spacings, and entanglement growth in the system at long times. Our platform can be scaled to higher numbers of spins, where detailed modeling of MBL becomes impossible due to the complexity of representing such entangled quantum states. Moreover, the high degree of control in our experiment may guide the use of MBL states as potential quantum memories in naturally disordered quantum systems.Comment: 9 pages, 9 figure