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Cesar Miquel

Publications and source records attributed to Cesar Miquel.

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Intelligent Arxiv: Sort daily papers by learning users topics preference

Current daily paper releases are becoming increasingly large and areas of research are growing in diversity. This makes it harder for scientists to keep up to date with current state of the art and identify relevant work within their lines of interest. The goal of this article is to address this problem using Machine Learning techniques. We model a scientific paper to be built as a combination of different scientific knowledge from diverse topics into a new problem. In light of this, we implement the unsupervised Machine Learning technique of Latent Dirichlet Allocation (LDA) on the corpus of papers in a given field to: i) define and extract underlying topics in the corpus; ii) get the topics weight vector for each paper in the corpus; and iii) get the topics weight vector for new papers. By registering papers preferred by a user, we build a user vector of weights using the information of the vectors of the selected papers. Hence, by performing an inner product between the user vector and each paper in the daily Arxiv release, we can sort the papers according to the user preference on the underlying topics. We have created the website IArxiv.org where users can read sorted daily Arxiv releases (and more) while the algorithm learns each users preference, yielding a more accurate sorting every day. Current IArxiv.org version runs on Arxiv categories astro-ph, gr-qc, hep-ph and hep-th and we plan to extend to others. We propose several new useful and relevant implementations to be additionally developed as well as new Machine Learning techniques beyond LDA to further improve the accuracy of this new tool.

cs.LG

Quantum computers in phase space

We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier Transform and Grover's search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to directly measure the Wigner function in a given phase space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm.

quant-ph

Tomography and spectroscopy as quantum computations

Determining the state of a system and measuring properties of its evolution are two of the most important tasks a physicist faces. For the first purpose one can use tomography, a method that after subjecting the system to a number of experiments determines all independent elements of the density matrix. For the second task, one can resort to spectroscopy, a set of techniques used to determine the spectrum of eigenvalues of the evolution operator. In this letter, we show that tomography and spectroscopy can be naturally interpreted as dual forms of quantum computation. We show how to adapt the simplest case of the well-known phase estimation quantum algorithm to perform both tasks, giving it a natural interpretation as a simulated scattering experiment. We show how this algorithm can be used to implement an interesting form of tomography by performing a direct measurement of the Wigner function of a quantum system. We present results of such measurements performed on a system of three qubits using liquid state NMR quantum computation techniques in a sample of trichloroethylene. Remarkable analogies with other experiments are discussed.

quant-ph

Discrete Wigner functions and the phase space representation of quantum computers

We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is defined in a phase space grid of $2N\times 2N$ points. We compute such Wigner function for states which are relevant for quantum computation. Finally, we discuss properties of quantum algorithms in phase space and present the phase space representation of Grover's quantum search algorithm.

quant-ph

Quantum computation with phase drift errors

We present results of numerical simulations of the evolution of an ion trap quantum computer made out of 18 ions which are subject to a sequence of nearly 15000 laser pulses in order to find the prime factors of N=15. We analyze the effect of random and systematic phase drift errors arising from inaccuracies in the laser pulses which induce over (under) rotation of the quantum state. Simple analytic estimates of the tolerance for the quality of driving pulses are presented. We examine the use of watchdog stabilization to partially correct phase drift errors concluding that, in the regime investigated, it is rather inefficient.

quant-ph

Perfect Quantum Error Correction Code

We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. The circuit can be converted into a decoding one by simply running it backward. Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. The original state of the encoded qubit can then be restored by a simple unitary transformation.

quant-ph

Factoring in a Dissipative Quantum Computer

We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders, etc) which are described in terms of elementary Toffoli gates. We present a simple analysis of the impact of losses and decoherence on the performance of this quantum factoring circuit. For that purpose, we simulate a quantum computer which is running the program to factor N = 15 while interacting with a dissipative environment. As a consequence of this interaction randomly selected qubits may spontaneously decay. Using the results of our numerical simulations we analyze the efficiency of some simple error correction techniques.

quant-ph