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One-dimensional model

For a simplified 1D model we consider only a martensitic phase which is assumed to exist in two different variants. Hence the microstructure consists of a line of grains of these variants, as depicted in the inset of Fig.1a. To be explicit, we assume that both variants have a stress free strain (eigenstrain), which leads to a shear deformation relative to the austenitic mother phase, and denote these variants by state variables (s_i=pm 1). As in the end we will map the description to a one-dimensional Ising model, we also use here the terminology of spins with two possible alignments in the spirit of a magnetic model. As each of the variants leads to a shearing of the cell, we get an overall stress free deformation of this line (compared to the shear strain free austenite), depending on the spin configuration. We assume that all grains have the same height (d), the same elastic constants, and opposite shear eigenstrain (pm varepsilon _0). As one can readily see from the inset of Fig.1a, the stress free equilibrium position of the top grain (x_0) depends only on the number of variants (N_+) with orientation (s_i=+1) and (N_-) with (s_i=-1), but not on the individual arrangement, which is a particularity of the simplified 1D model and the chosen eigenstrain. Hence, for a fixed number (N=N_++N_-) spins in a row, the macroscopic stress free strain is (bar{varepsilon } = (N_+ - N_-)varepsilon _0/N), which leads to (x_0 = N d bar{varepsilon }). If an external deformation is enforced, i.e.(xne x_0) the elastic energy is (F_{el}=mu _text{eff} (x-x_0)^2) with an effective shear modulus (mu _text{eff}). Obviously, the elastic energy is minimized if the spin configuration is such that (x=x_0), which implies ((N_+-N_-)_text{min} = x/varepsilon _0 d), up to the point of saturation, where all spins are aligned. This expression serves as reference for the comparison with the numerical minimization approaches below. We note that we neglected at this stage the discrete nature of the variants, which means that the integer value (N_+-N_-) should be as close as possible to the continuum value ((N_+-N_-)_text{min}) above. Although the energy in the simple 1D model does not depend on the arrangement of the variants but only on the total numbers (N_+) and (N_-=N-N_+), we formulate the model here on the level of the individual spins (s_i) for the later extension towards higher dimensions and the use of the quantum annealer. Hence we get (N_+ - N_- = sum _i s_i). Inserting this into the elastic energy expression yields (F_text{el} = mu _text{eff} varepsilon _0^2d ^2 sum _{i,j} s_i s_j - 2mu _text{eff} x varepsilon _0 d sum _i s_i +mu _text{eff} x^2), where the summations run over all spins. For the implementation on a quantum annealer, we need to bring this to the Ising form of a Hamiltonian H with

$$begin{aligned} H =sum _ih_is_i + sum _{i

(1)

where the first term corresponds to the interaction with an external magnetic field (h_i) and the second term to a spin-spin interaction, which favors ferromagnetic (antiferromagnetic) ordering in case that the coupling constant (J_{ij}) is negative (positive). The last, spin-independent term (H_0) is only an irrelevant additive constant. From the comparison of the two above expressions we identify (h_i = - 2mu _text{eff} x varepsilon _0 d) and (J_{ij} = 2 mu _text{eff} varepsilon _0^2 d ^2). First, we note that the external deformation is here analogous to the magnetic field in the Ising description. Second, the spin-spin interaction term (J_{ij}) is positive, hence favoring antiferromagnetic ordering. Also, this term is independent of the spin numbers i,j, which means that this interaction does not depend on the distance between the grains. In other words, the elastic interaction depends only on the averaged magnetization (N_+-N_-), which implies a mean field interaction.

The goal of the formulation is to minimize the elastic energy and to find the optimal spin or variant configuration ({s_i}). To this end, we use three different numerical approaches (see methods section), and the results are compared to the analytical solution above: First, a brute force approach iterates over all spin configurations to find the energetic minimum exactly, second we use simulated annealing as probabilistic ground state finder, and finally the quantum annealing approach. Fig.1a shows the resulting magnetization ((N_+-N_-)/N), i.e.the average variant orientation, as function of applied displacement (x/d Nvarepsilon _0), which corresponds to the magnetic field in the Ising model.

Results of the one-dimensional model comparing different numerical and analytical methods. (a) Mean variant orientation ((N_+-N_-) / N) as function of the displacement (x / d N varepsilon _0). Comparison between the results obtained by numerical minimization (solid lines) versus the analytical theory for an infinite and continuous system (dashed line). For large displacement, all spins are aligned and therefore the magnetization saturates. The inset shows a sketch of the one-dimensional arrangement of martensite variants (s_i=+1) (red) and (s_i=-1) (green). The bottom row is fixed to position (x=0), whereas the top grain has a mean position (x_0) in the stress free state. If an additional external stress or strain is applied, the top layer is moved to position x, and the entire microstructure is sheared to the dashed configuration. (b) Elapsed computation time as a function of the number of grains. Different methods and algorithms are compared. Dashed parts of the QA curve belong to the regime of chain breaks. For large system sizes, only the hybrid quantum annealing approach remains feasible, showing an almost constant computing time need for less than 1000 spin variables (inset).

As expected, the results agree with the analytical theory up to the aforementioned discretization effect, which becomes less pronounced for large grain numbers. For high displacements saturation sets in when all variants are de-twinned, which means that all spins are either in the state (+1) or (-1). We note that for the investigated number of spins all used algorithms lead to the same energy minimum, which confirms that also the probabilistic approaches indeed find the global minimum states.

Fig.1b shows the required computation time for the different methods and algorithms as a function of the number of grains N. All conventional algorithm implementations are based on single core computations without parallelization and are mainly shown for a qualitative comparison, as the focus of the investigations is on the quantum annealing approach. For the latter, we use quantum processing unit (QPU) implementations up to the highest possible number of spins (typically (Napprox 170) for the Pegasus architecture34 of a D-Wave machine). The brute force approach, where iterations over all spin configurations are run, has the highest computation time. Even at small spin systems of around (Napprox 40) the elapsed user time was too large for practical applications due to the simulation time scaling (sim {{mathcal {O}}}(2^N)). The pure quantum annealing method produces the fastest results and ends up with an almost constant elapsed QPU access time. Overall, the computations for (Napprox 150) are roughly three orders of magnitude faster than for the other classical approaches. Beyond around (Napprox 50) spins, so called chain breaks35 occur occasionally. They result from the need to encode strongly coupled spins as a single logical spin. Ideally, these spins should represent the same state as the individual spins, but in practise this identity can be violated. To avoid this issue and to simulate even larger systems, which are essential for higher dimensional modeling in the following sections, hybrid classical and quantum annealing approaches can be used, which combine pure QA with conventional minimization approaches36. The numerical results in Fig.1b show an increase of the computation time of the hybrid solver compared to the pure QA, but the relative acceleration compared to the classical algorithms becomes even more striking. For the hybrid solver, the elapsed computation time is essentially independent of the number of spin variables and increases only beyond (10^3) grains to several seconds. Altogether, the hybrid QA is clearly the fastest approach for large grain numbers and is therefore used in the following two-dimensional simulations.

For the determination of the linear elastic energy beyond one dimension, we consider coherent precipitates of different variants which form inside the matrix. In this way, the entire material can be considered to consist of small entities (in the following denoted as grains), which can be in one of the different martensitic states. The simplest possible (cartesian) discretization is to use small cuboidal grains with edge length a. All grains are assumed to be coherent (the elastic displacements and tractions are continuous at the interfaces between the grains), and we use homogeneous elasticity, i.e.we ignore differences in the elastic constants between the different phases or variants. This has the consequence that the elastic energy reduces to combinations of pairwise interactions between all grains37.

For demonstrational purposes we perform here two-dimensional simulations in a plane strain setup, but a transfer to three dimensions is straightforward. In particular, the annealer part does not depend on the dimensionality of the description. The qualitatively new aspect beyond 1D is the appearance of distance and orientation dependent spin-spin interactions, which decay only slowly with the distance between the grains, and therefore leads to fully populated matrices (J_{ij}). As it turns out that an accurate determination of the elastic interaction energy is essential for a precise prediction of the equilibrium microstructure, we use Fourier transformation approaches with periodic boundary conditions as outlined in the methods section. As boundary conditions, we use either vanishing average stress in the periodic volume V, (langle sigma _{ij} rangle = frac{1}{V} int sigma _{ij}(textbf{r}),dtextbf{r} = 0), or, similarly to the 1D description, a given average strain (langle varepsilon _{ij} rangle). We employ in the following for simplicity isotropic elasticity, which is e.g.described by the Lam coefficient (lambda) and the shear modulus (mu), i.e.the stress-strain relationship reads (sigma _{ij} = 2mu (varepsilon _{ij}-varepsilon _{ij}^{(0)}) + lambda delta _{ij} (varepsilon _{kk}-varepsilon _{kk}^{(0)})), where implicit summation over repeated indices is used. The position dependent eigenstrain (varepsilon _{ij}^{(0)}(textbf{r})) is known for a given microstructure with fixed phase dependent stress free strains (relative to the austenitic mother phase), (varepsilon _{ij}^{(0)}(textbf{r}) = theta (textbf{r}) varepsilon _{ij}^0), where the indicator function (theta) is zero in the austenite and either (+1) or (-1) in the two considered martensite variants. For a given microstructure, the elastic energy can then be computed in reciprocal space, as shown in the methods section. For the formulation as Ising model we discretize our microstructure using small non-overlapping cuboidal grains as discussed above and assign a spin (s_i) to each of them like before, such that the indicator field becomes a superposition (theta (textbf{r}) = sum _i s_i theta _i(textbf{r})), where (theta _i) equals one inside the corresponding square and is zero outside. Therefore, the elastic energy decomposes into pairwise interactions (for (ine j)) and self-energy terms (for (i=j))

$$begin{aligned} E_{i,j} = s_i s_j frac{1}{2V} int dtextbf{r} int dmathbf {r'} B(textbf{r}-mathbf {r'}) theta _i(textbf{r}) theta _j(mathbf {r'}), end{aligned}$$

(2)

where the integral kernel (B(textbf{r})) is defined through the inverse of the elastic Greens function. Hence, it is sufficient to perform the Fourier transform energy calculations for all pairs of the same martensite variant (s_i=s_j=1) on the discrete lattice sites in the volume V; for periodic boundary conditions and identical grain shapes, it is sufficient to calculate the elastic interaction energy between a reference grain and all the other grains, due to translation invariance. In case of fixed average strain boundary conditions, an additional homogeneous term appears (see methods section), contributing both to the spin-spin interaction (J_{ij}) as well as to the magnetic field term (h_i), which is absent for zero average stress boundary conditions. The resulting fully populated matrix of coupling constants with both positive and negative entries has similarities to spin glass systems with random couplings, which have been investigated in the literature with conventional approaches, see e.g.38.

For the simplest case that the eigenstrain is purely dilatational and isotropic the Bitter-Crum theorem applies and the total energy depends only on the volume fraction of the martensite variant, where no interaction between the grains is present and only a self energy term remains39.

For a nontrivial elastic interaction and the link to the previous 1D description, we consider a shear transformation strain with (varepsilon _{xy}^0=varepsilon _{yx}^0=varepsilon _0), where all other components vanish. In this case, we obtain a distance and orientation dependent interaction as depicted in Fig.2a, which is computed here for the case of vanishing average stress, (langle sigma _{ik}rangle =0). Here and in the following parts the Poisson ratio is chosen as (nu =1/4) (i.e.(lambda =mu)).

Interaction energies of two grains of equal variant type ((mathbf {s_i=s_j})). Interaction energies in the case of (a) shear eigenstrain and vanishing average stress and (b) tetragonal eigenstrain. The interaction energy per length is given in units of (lambda a^3 varepsilon _0^2), and the computations were done using a system size of (L_x/a=L_y/a=50), where a is the edge length of the grains. At distance (r/a=0) the grains touch each other. The symbols on the continuous curves indicate the information for the interaction at discrete lattice sites, which is actually used in the annealer simulations.

The interaction energy is obtained by subtracting the elastic self energies (E_text{self}) for each of the two (isolated) martensite grains inside the austenitic matrix from the total elastic energy (E_text{el}) of the two-grain arrangement, i.e.(E_text{int}=E_text{el}-2E_text{self}), to normalize the interaction energy such that it decays to zero for large grain separations. For short distances, a transition between attraction and repulsion is found for the (langle 100rangle) direction, whereas a purely repulsive interaction results for the diagonal (langle 110rangle) directions. Due to the periodic boundary conditions, the result depends on the system size (V=L_xtimes L_y), as the grains also interact with their periodic images, hence (rll L_x, L_y) is required to observe the decay of the interaction.

We note that in two dimensions the interaction energy decays asymptotically as (r^{-2}), whereas in three dimensions it scales as (r^{-3}) in large systems, which follows from the elastic Greens function40. For the quantum annealer implementation, the interaction energies are needed only for the discrete lattice points (symbols on the curves). Although the decay of the elastic interaction may suggest to cut it off beyond a certain distance in real space, it turns out that such an approach is inappropriate, as it leads in the end to invalid equilibrium microstructures, and it is therefore essential to keep all interaction terms (J_{ij}) with high precision to avoid spurious effects. We note that the formulation on the quantum annealer does not depend on the dimensionality, therefore the scaling plot in Fig.1b applies here as well.

Based on the calculation of the elastic interactions, we obtain from the Ising model implementation on the quantum annealer with hybrid solver stripe patterns in (langle 100rangle) direction as equilibrium structures. These patterns are irregular in the sense that the widths of the stripes are not uniform. This is in analogy to the 1D model, which was discussed above, where we found that the arrangement of the two variants is not determined. This coincidence, which is physically expected, is nontrivial from the model formulation, as (i) in the 1D model we had a distance independent interaction in the discretized model, where here the interaction is significantly more complex, but adds up to the same effective descriptions for the periodic arrangement; (ii) a rotation of the pattern by 90 degree is possible and sometimes obtained from the optimal configuration due to the discrete rotational symmetry; (iii) the fixing of the average stress compared to the given average strain in the 1D formulation can lead to unequal distributions of the different variants. In particular, for the presently considered absence of an external strain (implying a vanishing magnetic field in the Ising terminology), there is no constraint of the sort (langle s_irangle = 0) for the average spin alignment. All stripe configurations are energetically equivalent, which includes the possibility of a single variant configuration. These results therefore confirm simultaneously the accuracy of the elastic interaction calculation with the pairwise decomposition as well as the ability of the quantum annealer to identify the true ground state configurations.

As next example, we use a tetragonal eigenstrain with the only nonvanishing components (varepsilon _{xx}^0=-varepsilon _{yy}^0=varepsilon _{zz}^0=varepsilon _0). First, we consider again the situation with vanishing average stress, (langle sigma _{ij}rangle = 0). The corresponding interaction energy is shown in Fig.2b for (nu =1/4). In this case, the equilibrium microstructure is trivial and consists of a single variant, as in this case the elastic energy is zero for the periodic system. Therefore, the situation differs from the previous shear transformation, where also lamellar arrangements with both variants lead to stress free situations. The reason is that any interface between two variants leads to a mismatch between adjacent variants for the tetragonal transformation, and therefore such a situation is energetically unfavorable here. A change of boundary conditions to vanishing average strain, (langle varepsilon _{ij}rangle =0), alters the situation, since then arrangements with equal amounts of both variants are preferred, as this lowers the volumic part of the elastic energy. In this case, we find regular inclined stripes as equilibrium pattern, as shown in Fig.3a.

Resulting stripe patterns for tetragonal eigenstrain. (a) Equilibrium structure with three stripe pairs (counted along the horizontal axis) in a system consisting of (50times 50) cuboidal grains. A vanishing mean strain, (langle varepsilon _{ij}rangle =0), is imposed. The width of the stripes is uniform, consisting of grains with configuration (s_i=+1) (red) and (s_i=-1) (green). (b) Elastic energy of stripe patterns with different inclination angles (phi .) The solid curves correspond to smooth stripes (the grain size (a/L_x, a/L_yll 1) is negligible) and show a pronounced stationary point for inclinations for which the pattern repeats periodically without kinks at the boundaries. The squares correspond to situations with the same number of stripes, where the system is discretized by (50times 50) quadratic grains, leading to pronounced aliasing effects, and the resulting elastic energy is higher than for the smooth stripes. This shifts the energetic minimum for 6 stripe pairs at (phi approx 40^circ) to a lower angle (phi approx 33^circ) with 3 stripe pairs. The infinite system size limit for smooth stripes is depicted as black dotted curve.

Again, the solution is not unique; in particular, due to translation invariance, the annealer returns also configurations where the stripes are shifted. Also, a switch of the sign of the inclination angle (phi) (see definition in the figure) leads to energetically equivalent solutions. However, we do not find ground state configurations which lead to different (absolute) inclination angles or strip widths or even irregular variations of the latter, contrary to the shear transformation case before.

The reason for the observed ground state morphologies is a combination of continuum elasticity effects, the granular structure of the material and constraints induced by periodic boundary conditions. Figure3b shows the computed elastic energy for different numbers of regular arrangements of stripes in the periodic system as function of the inclination angle (phi). Here we see a pronounced influence of the grain size, as the elastic energy of configurations with regular stripe pairs with a discretization by (50times 50) grains (squares in the figure) is higher than for corresponding cases with very fine grains, where discretization effects do not play a role anymore (smooth curves). The oscillating nature is due to the periodic boundary conditions, as improper choices of the inclination angle lead to discontinuities of the stripe patterns at the boundaries, which is energetically unfavorable. Therefore, continuous patterns correspond to the stationary points of the curves. For specific angles, the curves for three and six stripe pairs meet at local minima, which is a consequence of the scale invariance of linear elasticity. From the smooth, continuum limit curves one would conclude that an angle of about (phi approx 40^circ) should lead to the energetically lowest configuration (absolute minimum of the smooth red curve). Moreover, in the limit of infinite systems, where periodic boundary conditions do not play a role anymore, an analytical treatment is possible, leading to the energy expression (E_text{el}^infty = V B(n)/2) for equal volume fraction of the two variants with

$$B(n) = frac{{4mu }}{{lambda + 2mu }}varepsilon _{0}^{2} {text{ }}left[ {(3lambda + 2mu ) - 2(3lambda + 2mu )n^{2} + 4(lambda + mu )n^{4} } right]$$

with (n=cos phi). Energy minimization gives the optimal angle (phi =cos ^{-1}sqrt{5/8}approx 37.8^circ), see Fig.3b (minimum of the black dotted curve).

However, these predictions disagree with the finding from the quantum annealer, which favors a configuration with three stripe pairs at a lower angle of (phi approx 33^circ). This observation can be understood by consideration of the granular structure of the patterns investigated here, as the microstructure in the annealer simulations consists of (50times 50) square grains. First, the explicit appearance of the length scale a breaks the scale invariance of the periodic pattern, and therefore the minima of the energy curves belonging to the discrete microstructures (squares in Fig.3b) do not coincide anymore at the local minima. Additionally, with increasing inclination antialiasing effects of the patterns become more relevant, and therefore the energy curves show an increasing disagreement with the continuum limit curves. As a result, the energetic minimum in the discrete microstructure indeed shifts toward a configuration with three stripe pairs at (phi approx 33^circ) (absolute minimum of the blue squares in Fig.3b), which is in agreement with the prediction of the quantum annealer. Consequently, details of the granular structure can change the energetics compared to a full continuum approximation, especially since many local minima of the elastic energy are located close to each other.

The approach presented above is not limited to mutually interacting cuboidal grains, but can also be applied to realistic microstructures. To illustrate the procedures, we have generated a microstructure consisting of (N=400) grains using a Voronoi tesselation41. Each grain is allowed to take one out of two martensite variants with the tetragonal eigenstrain tensor, and we pre-compute all mutual elastic interactions between them. We note that contrary to the case with the cuboidal grains in a periodic array here we cannot exploit translational invarince due to the different shapes of the grains, and hence these elastic interaction energy calculations scale here as ({{mathcal {O}}}(N^2)) instead of ({{mathcal {O}}}(N)) before, although we still use periodic boundary conditions. Additionally, we consider now arbitrary given external strains (langle varepsilon _{ij}rangle), which leads to the appearance of a magnetic term like in the one dimensional description. With that, we can predict the equilibrium variant distribution within the microstructure using the hybrid quantum annealer, and this step is typically executed within a few seconds of runtime.

Examples for the equilibrium microstructures are shown in Fig.4 as function of the externally applied strain (langle varepsilon _{xx}rangle), whereas the other average strain components vanish.

Resulting equilibrium variant distribution with uniform grain orientation. The microstructures consist of 400 grains and tensile strain is applied in horizontal (x) direction. Red (green) grains correspond to variant (s_i=+1) ((s_i=-1)). The tensile strain is (a) (langle varepsilon _{xx}rangle /varepsilon _0 = 0), (b) (langle varepsilon _{xx}rangle /varepsilon _0 = 0.1), (c) (langle varepsilon _{xx}rangle /varepsilon _0 = 0.5), (d) (langle varepsilon _{xx}rangle /varepsilon _0 = 0.9), (e) (langle varepsilon _{xx}rangle /varepsilon _0 = 1.1) and (f) (langle varepsilon _{xx}rangle /varepsilon _0 = 1.3).

The observed microstructures are indeed similar to what we have found before using the square discretization, although here the band widths and orientation deviate from the previous case due to microstructural details and the smaller number of grains, and these effects can be explained using an analysis similar to the one done for Fig.3b. We note that in these microstructures all grains have the same orientation, and therefore the application of a tensile strain strongly favors the selection of the grain variant (s_i=+1) (for a compressive situation we observe the opposite behavior), and we find a full alignment of all variants in the last snapshot.

Additionally, we have performed the same analysis for grains with uniformly distributed random orientation, which implies a rotation of the local transformation strain tensor, see Fig.5 for the grain orientations and for the variant selection.

Resulting equilibrium variant distribution with random grain orientation. (a) Grain orientation map corresponding to the microstructures. In the color bar the grain rotation angle is given in radian (modulo (pi) due to symmetry). The rotation axis is along the [001] direction. The microstructures consist of 400 grains and tensile strain is applied in horizontal (x) direction. The grains have a random orientation, which is the same for all cases, based on a uniform distribution. The tensile strain in horizontal direction is (b) (langle varepsilon _{xx}rangle /varepsilon _0 = 0) and (c) (langle varepsilon _{xx}rangle /varepsilon _0 = 2.1). Red (green) grains correspond to variant (s_i=+1) ((s_i=-1)).

Here, also the equilibrated spatial distribution of the variants appears to be irregular. Application of a tensile strain again favors the alignment of the variant, but this time even for high strains not all grains select the same variant, which is due to the local rotation. In fact, a grain, which is rotated by (90^circ) with respect to the straining direction has a preference to be in variant state (s_i=-1), as then the direction of expansion is aligned with the external tensile strain. This can be clearly seen e.g.in Fig.5(c) for the highest tensile strain in x direction, where the remaining patches with spin (s_i=-1) correspond to the grains with orientation close to (pi /2) (or (3pi /2)). We emphasize that for a given microstructure (shapes of all grains) the mutual elastic grain-grain interactions have to be computed only once. As mentioned before, this step has to be done with high precision, and consequently this is the step which demands the highest amount of computing time. After that, all changes of the external boundary conditions affect only the (k=0) mode contributing to the interactions (J_{ij}) and (h_i), and these terms can be calculated analytically (see methods section). As each hybrid quantum annealing calculation typically requires only a few seconds, the entire microstructural change during mechanical loading can be calculated extremely fast.

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A new global IBM (NYSE: IBM) Institute for Business Value (IBV) study, " The ESG ultimatum: Profit or perish ," of executives and consumers reveals that while an increased focus on environmental sustainability remains a top priority for consumers and business executives, inadequate data is a key challenge for both groups when it comes to achieving personal and corporate Environmental, Social and Governance (ESG) goals.

The study* reveals that surveyed executives point to inadequate data (41%) as the biggest obstacle to their ESG progress, followed by regulatory barriers (39%), inconsistent standards (37%) and inadequate skills (36%). Without the ability to access, analyze and understand ESG data, companies struggle to deliver greater transparency to the consumer a key stakeholder and meet consumer expectations.

Seventy-four percent of surveyed executives believe that stakeholders understand their organizations' ESG objectives and performance, yet only about 4 in 10 surveyed consumers feel they have enough data to make environmentally sustainable purchasing (41%) or employment (37%) decisions.

"Consumer commitment to environmental sustainability and social responsibility has intensified with consumers voting with their wallets," said Jonathan Wright , Global Managing Partner Sustainability Services and Global Business Transformation, IBM Consulting. "As a majority of consumers choose to buy from and work for ESG leaders, businesses must prioritize transparency and break down barriers to ESG data."

Other study findings include:

Companies are investing in ESG and see it as good for business

Consumer commitment to sustainability has intensified, but consumers don't feel they have sufficient information to make informed choices

Executives admit their companies haven't made significant progress toward ESG goals, indicating data challenges impact their ability to measure progress and meet consumer demands

The study highlights ESG leaders, a sub-set of respondents with greater maturity in operationalizing ESG, who are seeing higher revenue, improved profitability, deeper customer engagement by approaching ESG as a transparency play that creates strategic business opportunities. These role models provide a roadmap for organizations looking to overcome data-related challenges and create sustainable change that includes: automating ESG processes and reporting capabilities to keep data current; tapping AI for enhanced insights into performance, forward looking analysis, and scenario development; aligning with ecosystem partners on ESG metric definitions and standards; and proactively establishing ESG data governance principles with stakeholders.

"Data is the lifeblood of ESG. Now is the time for enterprises to act. By operationalizing ESG plans, enterprises are putting information in the hands of operators who can make informed business decisions that can improve their ESG impact on a daily basis," said Wright. "Organizations looking to increase stakeholder support and meet ESG reporting requirements should implement a sustainability roadmap that is inclusive of technologies, services and ecosystem partners that can position them for greater business success and help them address regulatory compliance," said Wright.

To view the full study, visit: https://ibm.co/esg-ultimatum

*Study Methodology

The IBM Institute for Business Value (IBV) surveyed 2,500 executives from across 22 industries and34 countries, delving into their organizations' ESG strategy, approach, and operationalization; what benefits they expect from ESG initiatives; and how they weigh ESG against other business objectives. The IBV also surveyed more than 20,000 consumers across 34 countries about their attitudes toward sustainability and social responsibility, and how these beliefs influence shopping, investing, and career decisions.

About the IBM Institute for Business Value

The IBM Institute for Business Value, IBM's thought leadership think tank, combines global research and performance data with expertise from industry thinkers and leading academics to deliver insights that make business leaders smarter. For more world-class thought leadership, visit: http://www.ibm.com/ibv .

Media Contact: Jamee Nelson IBM External Relations jamee.nelson@ibm.com

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New IBM Study Reveals Inadequate Data Hinders Progress Against Environmental, Social and Governance Goals - Investing News Network

HAMBURG, Germany, April 17, 2023 ISC 2023 attendees can look forward to captivating talks for the events Tuesday and Wednesday conference keynotes. The Tuesday, May 23 keynote will be delivered by Google Principal Engineer Dr. Valentina Salapura, who will sketch out the emerging dynamic between the hyperscaler and HPC ecosystems. On Wednesday, May 24, Professor Dr. Thomas Sterling of Indiana University, and Professor Dr. Estela Suarez, of the Jlich Supercomputing Centre will recap the past year in HPC and offer predictions about its future.

Tuesdays keynote by Dr. Salapura will bring her perspective on how the escalating demand for enormous amounts of cloud-based compute power is bringing supercomputing technologies into hyperscale data centers. AI, as well as other commercial workloads requiring large amounts of data and compute power, are the main drivers of this demand, having a profound effect on the technologies employed by big cloud providers.

Heterogeneous computing, accelerators, and GPUs, which until recently were technologies mainly confined to HPC, are now being employed at scale by major tech companies. These same companies are pursuing their own custom chips and systems along the same lines and are developing software that can tap into all this powerful new hardware. In the process, both the hyperscale cloud and HPC domains are transformed.

Salapuras expertise on these topics stems from her work at Google, AMD, and IBM. At Google, where she is currently employed, she focuses on system architecture for cloud and edge computing. Before that, she worked on distributed computing and supercomputing at AMD Research. Before joining AMD, Dr. Salapura was a system architect and IBM master inventor focusing on cloud computing resiliency for several IBM cloud offerings. Her IBM Research stint also included working as a Blue Gene programs computer architect.

Wednesdays keynote will feature Professor Thomas Sterlings perennial talk highlighting the most crucial HPC-related news and events since last years conference. The 2023 rundown, though, will offer a couple of new twists: To begin with, this year, Sterling will be joined by Professor Estela Suarez, a research group leader at the Jlich Supercomputing Centre, who will be a co-presenter for the talk. Also, in addition to delivering a retrospective of the year just past, Sterling and Suarez will offer a peek into the future of HPC.

Some of this future has already been foreshadowed. With Moores Law fading and artificial intelligence workloads coming to the fore, HPC engineers and practitioners are increasingly adopting more exotic hardware, especially heterogeneous ones that use tensor accelerators, AI accelerators, ASIC-based processors, and even neuromorphic devices. As noted in Tuesdays keynote, some of this technology is being developed and commercialized by big cloud providers, who now require such HPC-capable hardware for AI and other demanding workloads. At the same time, cloud computing is becoming a more common delivery system for HPC.

Thomas Sterling is uniquely equipped to bring such wide-ranging topics into focus. Since receiving his Ph.D. from MIT as a Hertz Fellow in 1984, he has engaged in applied research in parallel computing system structures, semantics, and operation in industry, government labs, and academia. He is best known as the father of Beowulf for his pioneering research in commodity/Linux cluster computing, for which he shared the Gordon Bell Prize in 1997. He has also co-authored the introductory textbook, High Performance Computing, published by Morgan-Kaufmann in 2018. He is currently a Full Professor of Intelligent Systems Engineering at Indiana University (IU), serving as Director of the AI Computing Systems Laboratory at IUs Luddy School of Informatics, Computing, and Engineering.

Estela Suarez brings a contemporary perspective to the field, focusing on HPC system architectures and codesign. As the European DEEP project series leader, she has driven the development of the Modular Supercomputing Architecture, including hardware, software, and application implementation and validation. Additionally, she leads the codesign and validation efforts within the European Processor Initiative. Her current position is Research Group Leader at the Jlich Supercomputing Centre, which she joined in 2010. She is also a Professor of High Performance Computing at the University of Bonn. Suarez holds a Ph.D. in Physics from the University of Geneva and a Masters in Astrophysics from the University Complutense of Madrid.

As announced previously, Professor Dr. Dan Reed will kick off the conference with his opening keynote on the post-Moore environment and the technical and financial challenges the HPC industry faces, ending his talk by sharing ideas on how the HPC industry can overcome these difficulties.

Early-Bird Registration

Attendees who register by April 19 qualify for the early-bird rates, which provide considerable savings. ISC 2023 will be held in person, offering rich on-demand content to attendees who will join the event remotely.

Join ISC High Performance 2023 and Imagine Tomorrow

ISC 2023 will be held at the Congress Center Hamburg from May 21 25. Join the HPC community of attendees, speakers, and exhibitors. The exhibition will showcase the latest advancements in HPC, encompassing all the key developments in system design, applications, programming models, machine learning, quantum computing, and emerging technologies.

First held in 1986, ISC High Performance distinguishes itself as the worlds oldest and Europes most significant forum for the HPC and related domains.

Source: ISC

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ISC 2023: Google's Valentina Salapura and Leading HPC Experts ... - HPCwire

April 13, 2023• Physics 16, s53

Researchers propose a way to relieve the material requirements needed to realize topological quantum computers.

Todays quantum computers are delicate devicessensitive to disruption by environmental noise. Physicists are thus pursuing alternatives called topological quantum computers, which harness quasiparticlesMajorana fermionspredicted to be resilient to noise (see Viewpoint: A Roadmap for a Scalable Topological Quantum Computer). Now Kristian Mland and Asle Sudb at the Norwegian University of Science and Technology in Trondheim propose a way to generate Majorana fermions without the superconducting materials that were previously thought to be required for such fermions to emerge [1]. By expanding the material choice, the approach could bring topological quantum computers a step closer to realization.

Majorana fermions are hallmarks of an exotic state called a topological superconductor. To date, most proposals for generating such a state involve structures combining a superconductor and a material with strong spin-orbit coupling. Under an applied magnetic field, a topological superconductor should form at the interface between the materials.

In the model proposed by Mland and Sudb, a one-atom-thick layer of a magnetic material is sandwiched between a normal metal and a heavy metal with strong spin-orbit coupling. This coupling causes the magnetic layer to adopt a skyrmion crystal configuration, in which skyrmionstwists in the spin textureare arranged on a lattice. By scattering electrons, spin fluctuations in this skyrmion crystal produce an electronelectron interaction in the normal metal that creates a topological superconducting state at its boundary.

Besides removing the need for superconductors, the design would have another advantage over other proposed systems, say the researchers. By controlling the skyrmions, the device could manipulate the Majorana fermions, which are located at the centers of the skyrmions, to realize logical operations.

Marric Stephens

Marric Stephens is a Corresponding Editor forPhysics Magazine based in Bristol, UK.

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Physics - Topological Superconductivity without Superconductors - Physics

Quantum 101

Quantum computers harness the laws of physics at the tiniest scales. Classical computers encode information in bits, usually represented as either a 0 or a 1. But quantum computers use quantum bits, or qubits, which can exist in a superposition of states a combination of both 0 and 1 simultaneously. This translates to more computational power.

Quantum information processors are still nascent and fragile, requiring careful setup and controls in specialized labs. To scale up quantum computers so that they can solve big problems, researchers need to advance technologies to support larger numbers of qubits for longer periods of time.

Quantum computers could someday perform certain calculations faster than classical computers, with applications in science, medicine, security, finance, and beyond but first, researchers need to improve the underlying science and technology. Since its launch in 2020, the Quantum Systems Accelerator (QSA) has already made major advances in both hardware and programming, improving the quantum tools that researchers hope will help solve some of humanitys biggest questions.

QSA is one of the Department of Energys five national quantum information science research centers with a focus on all three major technologies for quantum computing: superconducting circuits, trapped-ion systems, and neutral atoms.

We believe there are synergies between these three big technologies and that each one may have unique abilities and applications for solving different kinds of problems, said Rick Muller, the director of QSA and a senior manager at Sandia National Laboratories. By looking at all three of them together, we can more easily find their strengths, apply innovations across technologies, and design a path forward to a universal quantum computer.

Led by Lawrence Berkeley National Laboratory (Berkeley Lab), QSA brings together more than 250 experts from 14 other institutions: Sandia National Laboratories, University of Colorado Boulder, MIT Lincoln Laboratory, Caltech, Duke University, Harvard University, Massachusetts Institute of Technology, Tufts University, UC Berkeley, University of Maryland, University of New Mexico, University of Southern California, University of Texas at Austin, and Canadas Universit de Sherbrooke.

Together, QSA researchers are developing ways to better control qubits (the building blocks of quantum computers), finding algorithms and applications for current and emerging quantum information systems, and speeding their transfer to industry. QSA is also preparing the next generation of quantum scientists through activities, including peer mentoring programs, career fairs, and training for high school students and teachers.

Were catalyzing national leadership in quantum information through co-design of quantum devices, algorithms, and engineering solutions, with the goal of delivering quantum advantage, said Bert de Jong, the deputy director of QSA and a senior scientist at Berkeley Lab. Were advancing imperfect quantum technologies and figuring out how we in academia and the national laboratories working with our partners in industry can start using them today. At the same time, were preparing scientists to use them to solve big science questions.

In March, the Quantum Systems Accelerator issued a full impact report on advances made since the center launched in 2020. Here are five highlights achieved by QSA scientists and partners so far:

QSA researchers from Harvard University and MIT used a special quantum device to observe several exotic states of matter for the first time and studied magnetism at the quantum level. Their findings help explain the physics underlying materials properties and could be used to engineer exotic materials of the future. Their research was performed using a programmable quantum simulator similar to a quantum computer. The team at Harvard built the simulator using hundreds of laser beams known as optical tweezers, arranging 256 ultra-cold rubidium atoms that acted as qubits. By some measures, that makes it the largest programmable quantum processor demonstrated to date. By moving the atoms into shapes such as squares, honeycombs, and triangles, QSA scientists manipulated how the qubits would interact with one another and made important measurements of quantum phases of matter and quantum spin liquids.

One way to build a useful quantum computer is by connecting qubits with superconducting circuits, which can conduct electricity without energy loss when extremely cold. But with every qubit added, engineering the connections and electronics becomes more difficult. You can imagine a group of qubits spread out like a grid on a piece of paper; trying to snake connections to the innermost qubits causes crowding that can degrade the qubits or signals. To address the challenge, scientists at MIT and MIT Lincoln Laboratory are taking inspiration from commercial electronics and investigating qubits with layers. These stacks of electronic chips reroute the connections to attach vertically, as though perpendicular to our grid a kind of 3D integration. The change allows researchers to potentially connect, control, and read larger numbers of qubits. Through funding from QSA and other partners, theyve already built and tested a 2-stack qubit chip (with two layers), and QSA researchers are working on further enhanced versions. This milestone is an important step toward more densely packed qubits that can perform more complex calculations.

This illustration of the quantum sensor shows trapped beryllium ions (red dots) arranged into a 2D crystal. (Credit: S. Burrows/JILA/UC Boulder)

Any study that uses electronics is limited by random variations or noise that can hide the information researchers are searching for. Quantum systems, such as arrays of ultracold atoms, can be used to make extremely precise measurements that are better at picking the signal from the noise. Led by the University of Colorado Boulder, QSA researchers built a quantum sensor from 150 beryllium ions (atoms with an electric charge) arranged in a flat crystal. By using entangled particles, where a change in one immediately impacts the other, the quantum sensor measured electric fields with more than 10 times the sensitivity of any previously demonstrated atomic sensor. Picking up incredibly tiny changes makes such a sensor a powerful tool that could potentially enhance gravitational wave detectors or look for dark matter, one of the biggest mysteries in modern physics.

To improve quantum computers, researchers need a way to find and correct errors, such as a qubit randomly flipping between 0 and 1. Methods such as continuous quantum error correction (CQEC) keep an eye on qubits and look for telltale signs of problems but they too are subject to noise that can hide issues. QSA researchers at UC Berkeley designed a machine learning algorithm that can process the CQEC signals and find errors more accurately than current real-time methods. Because the new algorithm is flexible, learns on the job, and requires small amounts of computing power, it could improve continuous error correction systems and support larger and more stable quantum computers.

Our everyday computers use circuits with logic gates (such as AND, OR, and NOT) to perform operations. Quantum circuits can also use gates as their building blocks but instead of devices like transistors, their gates are made of qubits and interactions between qubits. While one or two entangled qubits can be used for basic operations, linking together many qubits can speed up computations, simplify quantum circuits, and make computers more powerful. QSA researchers led by Duke University developed a new, one-step method of creating these more versatile gates with multiple entangled qubits. Their technique expands logic operations for quantum computers, and includes a particular kind of gate (known as an N-Toffoli gate) that experts predict will be important in quantum adders, multipliers, and other algorithms including ones with applications in cryptography.

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Founded in 1931 on the belief that the biggest scientific challenges are best addressed by teams, Lawrence Berkeley National Laboratory and its scientists have been recognized with 16 Nobel Prizes. Today, Berkeley Lab researchers develop sustainable energy and environmental solutions, create useful new materials, advance the frontiers of computing, and probe the mysteries of life, matter, and the universe. Scientists from around the world rely on the Labs facilities for their own discovery science. Berkeley Lab is a multiprogram national laboratory, managed by the University of California for the U.S. Department of Energys Office of Science.

DOEs Office of Science is the single largest supporter of basic research in the physical sciences in the United States, and is working to address some of the most pressing challenges of our time. For more information, please visit energy.gov/science.

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Five Ways QSA is Advancing Quantum Computing Berkeley Lab ... - Lawrence Berkeley National Laboratory (.gov)