Experimental realisation of Shor's quantum factoring algorithm using qubit recycling

Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations. Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol. Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N=21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures.Comment: 7 pages, 3 figure

Identification of backgrounds in the EDELWEISS-I dark matter search experiment

This paper presents our interpretation and understanding of the different backgrounds in the EDELWEISS-I data sets. We analyze in detail the several populations observed, which include gammas, alphas, neutrons, thermal sensor events and surface events, and try to combine all data sets to provide a coherent picture of the nature and localisation of the background sources. In light of this interpretation, we draw conclusions regarding the background suppression scheme for the EDELWEISS-II phase

Measurement of the response of heat-and-ionization germanium detectors to nuclear recoils

The heat quenching factor Q' (the ratio of the heat signals produced by nuclear and electron recoils of equal energy) of the heat-and-ionization germanium bolometers used by the EDELWEISS collaboration has been measured. It is explained how this factor affects the energy scale and the effective quenching factor observed in calibrations with neutron sources. This effective quenching effect is found to be equal to Q/Q', where Q is the quenching factor of the ionization yield. To measure Q', a precise EDELWEISS measurement of Q/Q' is combined with values of Q obtained from a review of all available measurements of this quantity in tagged neutron beam experiments. The systematic uncertainties associated with this method to evaluate Q' are discussed in detail. For recoil energies between 20 and 100 keV, the resulting heat quenching factor is Q' = 0.91+-0.03+-0.04, where the two errors are the contributions from the Q and Q/Q' measurements, respectively. The present compilation of Q values and evaluation of Q' represent one of the most precise determinations of the absolute energy scale for any detector used in direct searches for dark matter.Comment: 28 pages, 7 figures. Submitted to Phys. Rev.

Event categories in the EDELWEISS WIMP search experiment

Four categories of events have been identified in the EDELWEISS-I dark matter experiment using germanium cryogenic detectors measuring simultaneously charge and heat signals. These categories of events are interpreted as electron and nuclear interactions occurring in the volume of the detector, and electron and nuclear interactions occurring close to the surface of the detectors(10-20 mu-m of the surface). We discuss the hypothesis that low energy surface nuclear recoils,which seem to have been unnoticed by previous WIMP searches, may provide an interpretation of the anomalous events recorded by the UKDMC and Saclay NaI experiments. The present analysis points to the necessity of taking into account surface nuclear and electron recoil interactions for a reliable estimate of background rejection factors.Comment: 11 pages, submitted to Phys. Lett.

Background discrimination capabilities of a heat and ionization germanium cryogenic detector

The discrimination capabilities of a 70 g heat and ionization Ge bolometer are studied. This first prototype has been used by the EDELWEISS Dark Matter experiment, installed in the Laboratoire Souterrain de Modane, for direct detection of WIMPs. Gamma and neutron calibrations demonstrate that this type of detector is able to reject more than 99.6% of the background while retaining 95% of the signal, provided that the background events distribution is not biased towards the surface of the Ge crystal. However, the 1.17 kg.day of data taken in a relatively important radioactive environment show an extra population slightly overlapping the signal. This background is likely due to interactions of low energy photons or electrons near the surface of the crystal, and is somewhat reduced by applying a higher charge-collecting inverse bias voltage (-6 V instead of -2 V) to the Ge diode. Despite this contamination, more than 98% of the background can be rejected while retaining 50% of the signal. This yields a conservative upper limit of 0.7 event.day^{-1}.kg^{-1}.keV^{-1}_{recoil} at 90% confidence level in the 15-45 keV recoil energy interval; the present sensitivity appears to be limited by the fast ambient neutrons. Upgrades in progress on the installation are summarized.Comment: Submitted to Astroparticle Physics, 14 page

First Results of the EDELWEISS WIMP Search using a 320 g Heat-and-Ionization Ge Detector

The EDELWEISS collaboration has performed a direct search for WIMP dark matter using a 320 g heat-and-ionization cryogenic Ge detector operated in a low-background environment in the Laboratoire Souterrain de Modane. No nuclear recoils are observed in the fiducial volume in the 30-200 keV energy range during an effective exposure of 4.53 kg.days. Limits for the cross-section for the spin-independent interaction of WIMPs and nucleons are set in the framework of the Minimal Supersymmetric Standard Model (MSSM). The central value of the signal reported by the experiment DAMA is excluded at 90% CL.Comment: 14 pages, Latex, 4 figures. Submitted to Phys. Lett.

Approximate Quantum Cloning with Nuclear Magnetic Resonance

Here we describe a Nuclear Magnetic Resonance (NMR) experiment that uses a three qubit NMR device to implement the one to two approximate quantum cloning network of Buzek et al.Comment: 4 pages RevTeX4 including 5 postscript figures. Submitted to PR

On the Quantum Complexity of the Continuous Hidden Subgroup Problem

The Hidden Subgroup Problem (HSP) aims at capturing all problems that are susceptible to be solvable in quantum polynomial time following the blueprints of Shor's celebrated algorithm. Successful solutions to this problems over various commutative groups allow to efficiently perform number-theoretic tasks such as factoring or finding discrete logarithms. The latest successful generalization (Eisentrager et al. STOC 2014) considers the problem of finding a full-rank lattice as the hidden subgroup of the continuous vector space Rm , even for large dimensions m . It unlocked new cryptanalytic algorithms (Biasse-Song SODA 2016, Cramer et al. EUROCRYPT 2016 and 2017), in particular to find mildly short vectors in ideal lattices. The cryptanalytic relevance of such a problem raises the question of a more refined and quantitative complexity analysis. In the light of the increasing physical difficulty of maintaining a large entanglement of qubits, the degree of concern may be different whether the above algorithm requires only linearly many qubits or a much larger polynomial amount of qubits. This is the question we start addressing with this work. We propose a detailed analysis of (a variation of) the aforementioned HSP algorithm, and conclude on its complexity as a function of all the relevant parameters. Incidentally, our work clarifies certain claims from the extended abstract of Eisentrager et al

Bridging topological and functional information in protein interaction networks by short loops profiling

Protein-protein interaction networks (PPINs) have been employed to identify potential novel interconnections between proteins as well as crucial cellular functions. In this study we identify fundamental principles of PPIN topologies by analysing network motifs of short loops, which are small cyclic interactions of between 3 and 6 proteins. We compared 30 PPINs with corresponding randomised null models and examined the occurrence of common biological functions in loops extracted from a cross-validated high-confidence dataset of 622 human protein complexes. We demonstrate that loops are an intrinsic feature of PPINs and that specific cell functions are predominantly performed by loops of different lengths. Topologically, we find that loops are strongly related to the accuracy of PPINs and define a core of interactions with high resilience. The identification of this core and the analysis of loop composition are promising tools to assess PPIN quality and to uncover possible biases from experimental detection methods. More than 96% of loops share at least one biological function, with enrichment of cellular functions related to mRNA metabolic processing and the cell cycle. Our analyses suggest that these motifs can be used in the design of targeted experiments for functional phenotype detection.This research was supported by the Biotechnology and Biological Sciences Research Council (BB/H018409/1 to AP, ACCC and FF, and BB/J016284/1 to NSBT) and by the Leukaemia & Lymphoma Research (to NSBT and FF). SSC is funded by a Leukaemia & Lymphoma Research Gordon Piller PhD Studentship

Status of the EDELWEISS Experiment

The status of the EDELWEISS experiment (underground dark matter search with heat-ionisation bolometers) is reviewed. Auspicious results achieved with a prototype 70 g Ge heat-ionisation detector under a 2 V reverse bias tension are discussed. Based on gamma and neutron calibrations, a best-case rejection factor, over the 15-45 keV range, of 99.7 % for gammas, with an acceptance of 94 % for neutrons, is presented first. Some operational results of physical interest obtained under poor low radioactivity conditions follow. They include a raw event rate of around 30 events/day/kg/keV over the same energy range, and, after rejection of part of the background, lead to a conservative upper limit on the signal of approximately 1.6 events/day/kg/keV at a 90 % confidence level. Performance degrading surface effects of the detector are speculated upon; and planned upgrades are summarized.Comment: 5 pages, 4 eps figures, LaTeX requires espcrc2.sty; Proceedings of TAUP97, Gran Sasso, Italy, September 7-11, 199