Quantum Algorithms for Scientific Computing and Approximate Optimization

Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we study the application of quantum computers to computational problems in science and engineering, and to combinatorial optimization problems. We outline the results below. Algorithms for scientific computing require modules, i.e., building blocks, implementing elementary numerical functions that have well-controlled numerical error, are uniformly scalable and reversible, and that can be implemented efficiently. We derive quantum algorithms and circuits for computing square roots, logarithms, and arbitrary fractional powers, and derive worst-case error and cost bounds. We describe a modular approach to quantum algorithm design as a first step towards numerical standards and mathematical libraries for quantum scientific computing. A fundamental but computationally hard problem in physics is to solve the time-independent Schrödinger equation. This is accomplished by computing the eigenvalues of the corresponding Hamiltonian operator. The eigenvalues describe the different energy levels of a system. The cost of classical deterministic algorithms computing these eigenvalues grows exponentially with the number of system degrees of freedom. The number of degrees of freedom is typically proportional to the number of particles in a physical system. We show an efficient quantum algorithm for approximating a constant number of low-order eigenvalues of a Hamiltonian using a perturbation approach. We apply this algorithm to a special case of the Schrödinger equation and show that our algorithm succeeds with high probability, and has cost that scales polynomially with the number of degrees of freedom and the reciprocal of the desired accuracy. This improves and extends earlier results on quantum algorithms for estimating the ground state energy. We consider the simulation of quantum mechanical systems on a quantum computer. We show a novel divide and conquer approach for Hamiltonian simulation. Using the Hamiltonian structure, we can obtain faster simulation algorithms. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under mild assumptions. We turn to combinatorial optimization problems. An important open question is whether quantum computers provide advantages for the approximation of classically hard combinatorial problems. A promising recently proposed approach of Farhi et al. is the Quantum Approximate Optimization Algorithm (QAOA). We study the application of QAOA to the Maximum Cut problem, and derive analytic performance bounds for the lowest circuit-depth realization, for both general and special classes of graphs. Along the way, we develop a general procedure for analyzing the performance of QAOA for other problems, and show an example demonstrating the difficulty of obtaining similar results for greater depth. We show a generalization of QAOA and its application to wider classes of combinatorial optimization problems, in particular, problems with feasibility constraints. We introduce the Quantum Alternating Operator Ansatz, which utilizes more general unitary operators than the original QAOA proposal. Our framework facilitates low-resource implementations for many applications which may be particularly suitable for early quantum computers. We specify design criteria, and develop a set of results and tools for mapping diverse problems to explicit quantum circuits. We derive constructions for several important prototypical problems including Maximum Independent Set, Graph Coloring, and the Traveling Salesman problem, and show appealing resource cost estimates for their implementations

Divide and conquer approach to quantum Hamiltonian simulation

We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions

Managing AI Risks in an Era of Rapid Progress

In this short consensus paper, we outline risks from upcoming, advanced AI systems. We examine large-scale social harms and malicious uses, as well as an irreversible loss of human control over autonomous AI systems. In light of rapid and continuing AI progress, we propose urgent priorities for AI R&D and governance

Managing extreme AI risks amid rapid progress

Preparation requires technical research and development, as well as adaptive, proactive governance

The SOLAS air-sea gas exchange experiment (SAGE) 2004

Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part II: Topical Studies in Oceanography 58 (2011): 753-763, doi:10.1016/j.dsr2.2010.10.015.The SOLAS air-sea gas exchange experiment (SAGE) was a multiple-objective study investigating gas-transfer processes and the influence of iron fertilisation on biologically driven gas exchange in high-nitrate low-silicic acid low-chlorophyll (HNLSiLC) Sub-Antarctic waters characteristic of the expansive Subpolar Zone of the southern oceans. This paper provides a general introduction and summary of the main experimental findings. The release site was selected from a pre-voyage desktop study of environmental parameters to be in the south-west Bounty Trough (46.5°S 172.5°E) to the south-east of New Zealand and the experiment conducted between mid-March and mid-April 2004. In common with other mesoscale iron addition experiments (FeAX’s), SAGE was designed as a Lagrangian study quantifying key biological and physical drivers influencing the air-sea gas exchange processes of CO2, DMS and other biogenic gases associated with an iron-induced phytoplankton bloom. A dual tracer SF6/3He release enabled quantification of both the lateral evolution of a labelled volume (patch) of ocean and the air-sea tracer exchange at the 10’s of km’s scale, in conjunction with the iron fertilisation. Estimates from the dual-tracer experiment found a quadratic dependency of the gas exchange coefficient on windspeed that is widely applicable and describes air-sea gas exchange in strong wind regimes. Within the patch, local and micrometeorological gas exchange process studies (100 m scale) and physical variables such as near-surface turbulence, temperature microstructure at the interface, wave properties, and wind speed were quantified to further assist the development of gas exchange models for high-wind environments. There was a significant increase in the photosynthetic competence (Fv/Fm) of resident phytoplankton within the first day following iron addition, but in contrast to other FeAX’s, rates of net primary production and column-integrated chlorophyll a concentrations had only doubled relative to the unfertilised surrounding waters by the end of the experiment. After 15 days and four iron additions totalling 1.1 tonne Fe2+, this was a very modest response compared to the other mesoscale iron enrichment experiments. An investigation of the factors limiting bloom development considered co- limitation by light and other nutrients, the phytoplankton seed-stock and grazing regulation. Whilst incident light levels and the initial Si:N ratio were the lowest recorded in all FeAX’s to date, there was only a small seed-stock of diatoms (less than 1% of biomass) and the main response to iron addition was by the picophytoplankton. A high rate of dilution of the fertilised patch relative to phytoplankton growth rate, the greater than expected depth of the surface mixed layer and microzooplankton grazing were all considered as factors that prevented significant biomass accumulation. In line with the limited response, the enhanced biological draw-down of pCO2 was small and masked by a general increase in pCO2 due to mixing with higher pCO2 waters. The DMS precursor DMSP was kept in check through grazing activity and in contrast to most FeAX’s dissolved dimethylsulfide (DMS) concentration declined through the experiment. SAGE is an important low-end member in the range of responses to iron addition in FeAX’s. In the context of iron fertilisation as a geoengineering tool for atmospheric CO2 removal, SAGE has clearly demonstrated that a significant proportion of the low iron ocean may not produce a phytoplankton bloom in response to iron addition.SAGE was jointly funded through the New Zealand Foundation for Research, Science and Technology (FRST) programs (C01X0204) "Drivers and Mitigation of Global Change" and (C01X0223) "Ocean Ecosystems: Their Contribution to NZ Marine Productivity." Funding was also provided for specific collaborations by the US National Science Foundation from grants OCE-0326814 (Ward), OCE-0327779 (Ho), and OCE 0327188 OCE-0326814 (Minnett) and the UK Natural Environment Research Council NER/B/S/2003/00282 (Archer). The New Zealand International Science and Technology (ISAT) linkages fund provided additional funding (Archer and Ziolkowski), and the many collaborator institutions also provided valuable support

Effect of a Perioperative, Cardiac Output-Guided Hemodynamic Therapy Algorithm on Outcomes Following Major Gastrointestinal Surgery A Randomized Clinical Trial and Systematic Review

Importance: small trials suggest that postoperative outcomes may be improved by the use of cardiac output monitoring to guide administration of intravenous fluid and inotropic drugs as part of a hemodynamic therapy algorithm.Objective: to evaluate the clinical effectiveness of a perioperative, cardiac output–guided hemodynamic therapy algorithm.Design, setting, and participants: OPTIMISE was a pragmatic, multicenter, randomized, observer-blinded trial of 734 high-risk patients aged 50 years or older undergoing major gastrointestinal surgery at 17 acute care hospitals in the United Kingdom. An updated systematic review and meta-analysis were also conducted including randomized trials published from 1966 to February 2014.Interventions: patients were randomly assigned to a cardiac output–guided hemodynamic therapy algorithm for intravenous fluid and inotrope (dopexamine) infusion during and 6 hours following surgery (n=368) or to usual care (n=366).Main outcomes and measures: the primary outcome was a composite of predefined 30-day moderate or major complications and mortality. Secondary outcomes were morbidity on day 7; infection, critical care–free days, and all-cause mortality at 30 days; all-cause mortality at 180 days; and length of hospital stay.Results: baseline patient characteristics, clinical care, and volumes of intravenous fluid were similar between groups. Care was nonadherent to the allocated treatment for less than 10% of patients in each group. The primary outcome occurred in 36.6% of intervention and 43.4% of usual care participants (relative risk [RR], 0.84 [95% CI, 0.71-1.01]; absolute risk reduction, 6.8% [95% CI, ?0.3% to 13.9%]; P?=?.07). There was no significant difference between groups for any secondary outcomes. Five intervention patients (1.4%) experienced cardiovascular serious adverse events within 24 hours compared with none in the usual care group. Findings of the meta-analysis of 38 trials, including data from this study, suggest that the intervention is associated with fewer complications (intervention, 488/1548 [31.5%] vs control, 614/1476 [41.6%]; RR, 0.77 [95% CI, 0.71-0.83]) and a nonsignificant reduction in hospital, 28-day, or 30-day mortality (intervention, 159/3215 deaths [4.9%] vs control, 206/3160 deaths [6.5%]; RR, 0.82 [95% CI, 0.67-1.01]) and mortality at longest follow-up (intervention, 267/3215 deaths [8.3%] vs control, 327/3160 deaths [10.3%]; RR, 0.86 [95% CI, 0.74-1.00]).Conclusions and relevance: in a randomized trial of high-risk patients undergoing major gastrointestinal surgery, use of a cardiac output–guided hemodynamic therapy algorithm compared with usual care did not reduce a composite outcome of complications and 30-day mortality. However, inclusion of these data in an updated meta-analysis indicates that the intervention was associated with a reduction in complication rate

Hyperoxemia and excess oxygen use in early acute respiratory distress syndrome : Insights from the LUNG SAFE study

Publisher Copyright: © 2020 The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.Background: Concerns exist regarding the prevalence and impact of unnecessary oxygen use in patients with acute respiratory distress syndrome (ARDS). We examined this issue in patients with ARDS enrolled in the Large observational study to UNderstand the Global impact of Severe Acute respiratory FailurE (LUNG SAFE) study. Methods: In this secondary analysis of the LUNG SAFE study, we wished to determine the prevalence and the outcomes associated with hyperoxemia on day 1, sustained hyperoxemia, and excessive oxygen use in patients with early ARDS. Patients who fulfilled criteria of ARDS on day 1 and day 2 of acute hypoxemic respiratory failure were categorized based on the presence of hyperoxemia (PaO2 > 100 mmHg) on day 1, sustained (i.e., present on day 1 and day 2) hyperoxemia, or excessive oxygen use (FIO2 ≥ 0.60 during hyperoxemia). Results: Of 2005 patients that met the inclusion criteria, 131 (6.5%) were hypoxemic (PaO2 < 55 mmHg), 607 (30%) had hyperoxemia on day 1, and 250 (12%) had sustained hyperoxemia. Excess FIO2 use occurred in 400 (66%) out of 607 patients with hyperoxemia. Excess FIO2 use decreased from day 1 to day 2 of ARDS, with most hyperoxemic patients on day 2 receiving relatively low FIO2. Multivariate analyses found no independent relationship between day 1 hyperoxemia, sustained hyperoxemia, or excess FIO2 use and adverse clinical outcomes. Mortality was 42% in patients with excess FIO2 use, compared to 39% in a propensity-matched sample of normoxemic (PaO2 55-100 mmHg) patients (P = 0.47). Conclusions: Hyperoxemia and excess oxygen use are both prevalent in early ARDS but are most often non-sustained. No relationship was found between hyperoxemia or excessive oxygen use and patient outcome in this cohort. Trial registration: LUNG-SAFE is registered with ClinicalTrials.gov, NCT02010073publishersversionPeer reviewe

Addressing the climate challenge

In 2021, colleagues from across the University of Birmingham community were invited to write articles about topics relevant to the COP26 climate change summit. In this series of articles, experts from across many different disciplines provide new insight and evidence on how we might all understand and tackle climate change