scholarly journals The Efficient Preparation of Normal Distributions in Quantum Registers

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 609
Author(s):  
Arthur G. Rattew ◽  
Yue Sun ◽  
Pierre Minssen ◽  
Marco Pistoia
Keyword(s):  
Quantum Algorithm ◽  
Normal Distributions ◽  
State Preparation ◽  
System Models ◽  
Bounded Number ◽  
Wide Range ◽  
Empirical Demonstration ◽  
Bit Flip

The efficient preparation of input distributions is an important problem in obtaining quantum advantage in a wide range of domains. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in quantum registers. To the best of our knowledge, our work is the first to leverage the power of Mid-Circuit Measurement and Reuse (MCMR), in a way that is broadly applicable to a range of state-preparation problems. Specifically, our algorithm employs a repeat-until-success scheme, and only requires a constant-bounded number of repetitions in expectation. In the experiments presented, the use of MCMR enables up to a 862.6x reduction in required qubits. Furthermore, the algorithm is provably resistant to both phase-flip and bit-flip errors, leading to a first-of-its-kind empirical demonstration on real quantum hardware, the MCMR-enabled Honeywell System Models H0 and H1-2.

scholarly journals Agentic Misfit: An Empirical Demonstration of Non-Matching Human Agency amid Complexity

2020 ◽  
pp. 017084062094455 ◽  
Author(s):  
Konstantinos Poulis ◽  
Efthimios Poulis ◽  
Paul Jackson
Keyword(s):  
Corporate Governance ◽  
Human Agency ◽  
Organizational Decline ◽  
Requisite Variety ◽  
Wide Range ◽  
Law Of Requisite Variety ◽  
The Law ◽  
Novel Concept ◽  
Empirical Demonstration ◽  
Do So

Alignment of organizations with external imperatives is seen as a sine qua non of proper organizing and strategizing by many fit and complexity scholars. Any deviation from this management mantra engenders organizational decline and, ultimately, mortality. We put this axiomatic principle under empirical scrutiny and use the law of requisite variety as our organizing principle to do so. The law is an iconic cornerstone of this matching contingency logic and it has served to legitimize a wide range of fit decisions in, e.g., leadership, organizational learning and corporate governance. Inspired by organizational vignettes inhabiting antithetical complexity regimes, we introduce a novel concept, which we label ‘agentic misfit’. In this way, we deconstruct deterministic assumptions related to environmental fittingness, we challenge teleological orientations in the fit literature, and we flesh out the viability of non-matching human agency amid complexity.

scholarly journals Improved Hamiltonian simulation via a truncated Taylor series and corrections

2017 ◽  
Vol 17 (7&8) ◽  
pp. 623-635
Author(s):  
Leonardo Novo ◽  
Dominic Berry
Keyword(s):  
Quantum Chemistry ◽  
Taylor Series ◽  
Evolution Operator ◽  
Quantum Algorithm ◽  
Simulation Method ◽  
Quantum Simulation ◽  
Wide Range ◽  
Simulation Based ◽  
Extra Step ◽  
Hamiltonian Simulation

We describe an improved version of the quantum algorithm for Hamiltonian simulation based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an operator that corrects the weightings of the Taylor series. This way, the desired accuracy is achieved with an improvement in the overall complexity of the algorithm. This quantum simulation method is applicable to a wide range of Hamiltonians of interest, including to quantum chemistry problems.

scholarly journals Next generation framework for aquatic modeling of the Earth System

2009 ◽  
Vol 2 (1) ◽  
pp. 279-307 ◽  
Author(s):  
B. M. Fekete ◽  
W. M. Wollheim ◽  
D. Wisser ◽  
C. J. Vörösmarty
Keyword(s):  
Model Development ◽  
Learning Curves ◽  
Earth System ◽  
Next Generation ◽  
Model Calculations ◽  
System Models ◽  
The Earth ◽  
Wide Range ◽  
Spatial Domains ◽  
Earth System Models

Abstract. Earth System model development is becoming an increasingly complex task. As scientists attempt to represent the physical and bio-geochemical processes and various feedback mechanisms in unprecedented detail, the models themselves are becoming increasingly complex. At the same time, the complexity of the surrounding IT infrastructure is growing as well. Earth System models must manage a vast amount of data in heterogeneous computing environments. Numerous development efforts are on the way to ease that burden and offer model development platforms that reduce IT challenges and allow scientists to focus on their science. While these new modeling frameworks (e.g. FMS, ESMF, CCA, OpenMI) do provide solutions to many IT challenges (performing input/output, managing space and time, establishing model coupling, etc.), they are still considerably complex and often have steep learning curves. The Next generation Framework for Aquatic Modeling of the Earth System (NextFrAMES, a revised version of FrAMES) have numerous similarities to those developed by other teams, but represents a novel model development paradigm. NextFrAMES is built around a modeling XML that lets modelers to express the overall model structure and provides an API for dynamically linked plugins to represent the processes. The model XML is executed by the NextFrAMES run-time engine that parses the model definition, loads the module plugins, performs the model I/O and executes the model calculations. NextFrAMES has a minimalistic view representing spatial domains and treats every domain (regardless of its layout such as grid, network tree, individual points, polygons, etc.) as vector of objects. NextFrAMES performs computations on multiple domains and interactions between different spatial domains are carried out through couplers. NextFrAMES allows processes to operate at different frequencies by providing rudimentary aggregation and disaggregation facilities. NextFrAMES was designed primarily for hydrological modeling purposes, but many of its functionality should be applicable for a wide range of land surface models. In its present capabilities NextFrAMES is probably inadequate to implement fully coupled Earth System models, but future versions with the guidance from Earth System developers might someday eliminate its limitations. Our intent with NextFrAMES is to initiate a dialog about new ways of expressing models that is less tied to the actual implementation and allow scientist to develop models at a more abstract level.

scholarly journals OMEN-SED 0.9: A novel, numerically efficient organic matter sediment diagenesis module for coupling to Earth system models

2018 ◽  
Author(s):  
Dominik Hülse ◽  
Sandra Arndt ◽  
Stuart Daines ◽  
Pierre Regnier ◽  
Andy Ridgwell
Keyword(s):  
Organic Matter ◽  
Marine Sediments ◽  
Earth System Model ◽  
System Model ◽  
Earth System ◽  
Model Framework ◽  
System Models ◽  
Wide Range ◽  
Earth System Models ◽  
Sediment Model

Abstract. We present the first version of OMEN-SED (Organic Matter ENabled SEDiment model), a new, one-dimensional analytical early diagenetic model resolving organic matter cycling and associated biogeochemical dynamics in marine sediments designed to be coupled to Earth system models. OMEN-SED explicitly describes organic matter (OM) cycling as well as associated dynamics of the most important terminal electron acceptors (i.e. O2, NO3, SO4) and methane (CH4), related reduced substances (NH4, H2S), macronutrients (PO4) and associated pore water quantities (ALK, DIC). Its reaction network accounts for the most important primary and secondary redox reactions, equilibrium reactions, mineral dissolution and precipitation, as well as adsorption and desorption processes associated with OM dynamics that affect the dissolved and solid species explicitly resolved in the model. To represent a redox-dependent sedimentary P cycle we also include a representation of the formation and burial of Fe-bound P and authigenic Ca-P minerals. Thus, OMEN-SED is able to capture the main features of diagenetic dynamics in marine sediments and, therefore, offers similar predictive abilities than a complex, numerical diagenetic model. Yet, its computational efficiency allows its coupling to global Earth system models and therefore the investigation of coupled global biogeochemical dynamics over a wide range of climate relevant timescales. This paper provides a detailed description of the new sediment model, an extensive sensitivity analysis, as well as an evaluation of OMEN-SED's performance through comprehensive comparisons with observations and results from a more complex numerical model. We find solid phase and dissolved pore water profiles for different ocean depths are reproduced with good accuracy and simulated terminal electron acceptor fluxes fall well within the range of globally observed fluxes. Finally, we illustrate its application in an Earth system model framework by coupling OMEN-SED to the Earth system model cGENIE and tune the OM degradation rate constants to optimise the fit of simulated benthic OM contents to global observations. We find simulated sediment characteristics of the coupled model framework, such as OM degradation rates, oxygen penetration depths and sediment-water interface fluxes are generally in good agreement with observations and in line with what one would expect on a global scale. Coupled to an Earth system model, OMEN-SED is thus a powerful tool that will not only help elucidate the role of benthic-pelagic exchange processes in the evolution and, in particular, the termination of a wide range of climate events, but will also allow a direct comparison of model output with the sedimentary record – the most important climate archive on Earth.

Algorithms Based on Amplitude Amplification

2006 ◽  
Author(s):  
Phillip Kaye ◽  
Raymond Laflamme ◽  
Michele Mosca
Keyword(s):  
Search Algorithm ◽  
Quantum Algorithm ◽  
Mathematical Structure ◽  
Large Integer ◽  
Problem Instance ◽  
Wide Range ◽  
Naive Algorithm ◽  
Long Time ◽  
Speed Up ◽  
Amplitude Amplification

In this section, we discuss a broadly applicable quantum algorithm that provides a polynomial speed-up over the best-known classical algorithms for a wide class of important problems. The quantum search algorithm performs a generic search for a solution to a very wide range of problems. Consider any problem where one can efficiently recognize a good solution and wishes to search through a list of potential solutions in order to find a good one. For example, given a large integer N, one can efficiently recognize whether an integer p is a non-trivial factor of N, and thus one naive strategy for finding non-trivial factors of N is to simply search through the set {2, 3, 4, . . . , ⌊√N⌋} until a factor is found. The factoring algorithm we described in Chapter 7 is not such a naive algorithm, as it makes profound use of the structure of the problem. However, for many interesting problems, there are no known techniques that make much use of the structure of the problem, and the best-known algorithm for solving these problems is to naively search through the potential solutions until one is found. Typically the number of potential solutions is exponential in the size of the problem instance, and so the naive algorithm is not efficient. Often the best-known classical search makes some very limited use of the structure of the problem, perhaps to rule out some obviously impossible candidates, or to prioritize some more likely candidates, but the overall complexity of the search is still exponential. Quantum searching is a tool for speeding up these sorts of generic searches through a space of potential solutions. It is worth noting that having a means of recognizing a solution to a problem, and knowing the set of possible solutions, means that in some sense one ‘knows’ the solution. However, one cannot necessarily efficiently produce the solution. For example, it is easy to recognize the factors of a number, but finding those factors can take a long time. We give this problem a more general mathematical structure as follows.

scholarly journals Developing the next-generation climate system models: challenges and achievements

2008 ◽  
Vol 367 (1890) ◽  
pp. 815-831 ◽  
Author(s):  
Julia Slingo ◽  
Kevin Bates ◽  
Nikos Nikiforakis ◽  
Matthew Piggott ◽  
Malcolm Roberts ◽  
...  
Keyword(s):  
Adaptive Mesh Refinement ◽  
Climate Models ◽  
Spatial Scales ◽  
Climate System ◽  
System Modelling ◽  
Earth System ◽  
System Models ◽  
Wide Range ◽  
Petascale Computing ◽  
Climate System Models

Although climate models have been improving in accuracy and efficiency over the past few decades, it now seems that these incremental improvements may be slowing. As tera/petascale computing becomes massively parallel, our legacy codes are less suitable, and even with the increased resolution that we are now beginning to use, these models cannot represent the multiscale nature of the climate system. This paper argues that it may be time to reconsider the use of adaptive mesh refinement for weather and climate forecasting in order to achieve good scaling and representation of the wide range of spatial scales in the atmosphere and ocean. Furthermore, the challenge of introducing living organisms and human responses into climate system models is only just beginning to be tackled. We do not yet have a clear framework in which to approach the problem, but it is likely to cover such a huge number of different scales and processes that radically different methods may have to be considered. The challenges of multiscale modelling and petascale computing provide an opportunity to consider a fresh approach to numerical modelling of the climate (or Earth) system, which takes advantage of the computational fluid dynamics developments in other fields and brings new perspectives on how to incorporate Earth system processes. This paper reviews some of the current issues in climate (and, by implication, Earth) system modelling, and asks the question whether a new generation of models is needed to tackle these problems.

scholarly journals Lineage Functional Types (LFTs): Characterizing functional diversity to enhance the representation of ecological behavior in Earth System Models

2020 ◽  
Author(s):  
Daniel M. Griffith ◽  
Colin Osborne ◽  
Erika J. Edwards ◽  
Seton Bachle ◽  
David J. Beerling ◽  
...  
Keyword(s):  
Functional Diversity ◽  
Species Level ◽  
Earth System ◽  
Trait Variation ◽  
System Models ◽  
Biogeographic History ◽  
Functional Types ◽  
Wide Range ◽  
Vegetation Models ◽  
Earth System Models

SummaryProcess-based vegetation models attempt to represent the wide range of trait variation in biomes by grouping ecologically similar species into plant functional types (PFTs). This approach has been successful in representing many aspects of plant physiology and biophysics, but struggles to capture biogeographic history and ecological dynamics that determine biome boundaries and plant distributions. Grass dominated ecosystems are broadly distributed across all vegetated continents and harbor large functional diversity, yet most Earth System Models (ESMs) summarize grasses into two generic PFTs based primarily on differences between temperate C3 grasses and (sub)tropical C4 grasses. Incorporation of species-level trait variation is an active area of research to enhance the ecological realism of PFTs, which form the basis for vegetation processes and dynamics in ESMs. Using reported measurements, we developed grass functional trait values (physiological, structural, biochemical, anatomical, phenological, and disturbance-related) of dominant lineages to improve ESM representations. Our method is fundamentally different from previous efforts, as it uses phylogenetic relatedness to create lineage-based functional types (LFTs), situated between species-level trait data and PFT-level abstractions, thus providing a realistic representation of functional diversity and opening the door to the development of new vegetation models.

scholarly journals Detailed Account of Complexity for Implementation of Circuit-Based Quantum Algorithms

2021 ◽  
Vol 9 ◽  
Author(s):  
Fernando R. Cardoso ◽  
Daniel Yoshio Akamatsu ◽  
Vivaldo Leiria Campo Junior ◽  
Eduardo I. Duzzioni ◽  
Alfredo Jaramillo ◽  
...  
Keyword(s):  
Detailed Analysis ◽  
Quantum System ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Review Article ◽  
Detailed Account ◽  
Final States ◽  
Superposition State ◽  
Final State ◽  
State Preparation

In this review article, we are interested in the detailed analysis of complexity aspects of both time and space that arises from the implementation of a quantum algorithm on a quantum based hardware. In particular, some steps of the implementation, as the preparation of an arbitrary superposition state and readout of the final state, in most of the cases can surpass the complexity aspects of the algorithm itself. We present the complexity involved in the full implementation of circuit-based quantum algorithms, from state preparation to the number of measurements needed to obtain good statistics from the final states of the quantum system, in order to assess the overall space and time costs of the processes.

scholarly journals Evaluation of biospheric components in Earth system models using modern and palaeo observations: the state-of-the-art

2013 ◽  
Vol 10 (7) ◽  
pp. 10937-10995 ◽  
Author(s):  
A. M. Foley ◽  
D. Dalmonech ◽  
A. D. Friend ◽  
F. Aires ◽  
A. Archibald ◽  
...  
Keyword(s):  
Carbon Cycle ◽  
Model Evaluation ◽  
State Of The Art ◽  
The State ◽  
System Level ◽  
Earth System ◽  
Evaluation Methodologies ◽  
System Models ◽  
Wide Range ◽  
Earth System Models

Abstract. Earth system models are increasing in complexity and incorporating more processes than their predecessors, making them important tools for studying the global carbon cycle. However, their coupled behaviour has only recently been examined in any detail, and has yielded a very wide range of outcomes, with coupled climate-carbon cycle models that represent land-use change simulating total land carbon stores by 2100 that vary by as much as 600 Pg C given the same emissions scenario. This large uncertainty is associated with differences in how key processes are simulated in different models, and illustrates the necessity of determining which models are most realistic using rigorous model evaluation methodologies. Here we assess the state-of-the-art with respect to evaluation of Earth system models, with a particular emphasis on the simulation of the carbon cycle and associated biospheric processes. We examine some of the new advances and remaining uncertainties relating to (i) modern and palaeo data and (ii) metrics for evaluation, and discuss a range of strategies, such as the inclusion of pre-calibration, combined process- and system-level evaluation, and the use of emergent constraints, that can contribute towards the development of more robust evaluation schemes. An increasingly data-rich environment offers more opportunities for model evaluation, but it is also a challenge, as more knowledge about data uncertainties is required in order to determine robust evaluation methodologies that move the field of ESM evaluation from "beauty contest" toward the development of useful constraints on model behaviour.

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