Papers by Dr. Nike Dattani
arXiv (Cornell University), Jan 22, 2019
We group all known quadratizations of cubic and quartic terms in binary optimization problems int... more We group all known quadratizations of cubic and quartic terms in binary optimization problems into five and six unique graphs respectively. We then perform a minor embedding of these graphs onto the well-known Chimera graph, and the brand new Pegasus graph. We conclude with recommendations for which gadgets are best to use when aiming to reduce the total number of qubits required to embed a problem.
arXiv (Cornell University), Aug 28, 2015
Quantum annealing has recently been used to determine the Ramsey numbers R(m, 2) for 4 ≤ m ≤ 8 an... more Quantum annealing has recently been used to determine the Ramsey numbers R(m, 2) for 4 ≤ m ≤ 8 and R(3, 3) [Bian et al. (2013) PRL 111, 130505]. This was greatly celebrated as the largest experimental implementation of an adiabatic evolution algorithm to that date. However, in that computation, more than 66% of the qubits used were auxiliary qubits, so the sizes of the Ramsey number Hamiltonians used were tremendously smaller than the full 128-qubit capacity of the device used. The reason these auxiliary qubits were needed was because the best quantum annealing devices at the time (and still now) cannot implement multi-qubit interactions beyond 2-qubit interactions, and they are also limited in their capacity for 2-qubit interactions. We present a method which allows the full qubit capacity of a quantum annealing device to be used, by reducing multi-qubit and 2-qubit interactions. With our method, the device used in the 2013 Ramsey number quantum computation could have determined R(16, 2) and R(4, 3) with under 10 minutes of runtime.
arXiv (Cornell University), Aug 10, 2014
The recent advent of chirped-pulse FTMW technology has created a plethora of pure rotational spec... more The recent advent of chirped-pulse FTMW technology has created a plethora of pure rotational spectra for molecules for which no vibrational information is known. The growing number of such spectra demands a way to build empirical potential energy surfaces for molecules, without relying on any vibrational measurements. Using ZnO as an example, we demonstrate a powerful technique for efficiently accomplishing this. We first measure eight new ultra-high precision (±2 kHz) pure rotational transitions in the X-state of ZnO. Combining them with previous high-precision (±50 kHz) pure rotational measurements of different transitions in the same system, we have data that spans the bottom 10% of the well. Despite not using any vibrational information, our empirical potentials are able to determine the size of the vibrational spacings and bond lengths, with precisions that are more than three and two orders of magnitude greater, respectively, than the most precise empirical values previously known, and the most accurate ab initio calculations in today's reach. By calculating the C6, C8, and C10 long-range constants and using them to anchor the top of the well, our potential is globally in excellent agreement with ab initio calculations, without the need for vibrational spectra and without the need for any data in the top 90% of the well.
Database of <em>ab initio</em> energies.
<p>This code creates CGR images, compares them using DSSIM, and maps the distance matrix on... more <p>This code creates CGR images, compares them using DSSIM, and maps the distance matrix onto a 2- or 3-dimensional figure using MDS.</p
ArXiv, 2019
Pegasus is a graph which offers substantially increased connectivity between the qubits of quantu... more Pegasus is a graph which offers substantially increased connectivity between the qubits of quantum annealing hardware compared to the graph Chimera. It is the first fundamental change in the connectivity graph of quantum annealers built by D-Wave since Chimera was introduced in 2009 and then used in 2011 for D-Wave's first commercial quantum annealer. In this article we describe an algorithm which defines the connectivity of Pegasus and we provide what we believe to be the best way to graphically visualize Pegasus in order to see which qubits couple to each other. As supplemental material, we provide a wide variety of different visualizations of Pegasus which expose different properties of the graph in different ways. We provide an open source code for generating the many depictions of Pegasus that we show.
Proceedings of the 73rd International Symposium on Molecular Spectroscopy, 2018
One has to calculate thousands or millions of ab initio points for potential energy surfaces even... more One has to calculate thousands or millions of ab initio points for potential energy surfaces even for molecules with only a few atoms. For diatomics, the MLR (Morse/long-range) bc model has been very successful, making it possible to represent the entire curve accurately with just a few ab initio points, or a few spectral lines. With the MLR model it is also possible to extrapolate and interpolate in a way that allows successful predictions of energy level locations several thousand cm −1 away from the data region d. However no analogous model has existed yet for the intramolecular potentials of polyatomic molecules. A simple model is presented which accurately describes some small molecules with far fewer parameters than previous models, and can be extended to larger molecules too. The benefit of having a good model function is orders of magnitude greater for polyatomics than for diatomics since the amount of data needed for an accurate potential is reduced in each dimension. For example if the calculation of 100 ab initio points is reduced to 10 in a diatomic molecule, we may estimate that this factor of 10 reduction in cost becomes at least 10 10 for a molecule whose potential depends on 10 radial coordinates. As an example, an analytic potential for CO 2 is built, which requires fewer parameters than the previous state-of-theart analytic potential, and obeys the theoretical long-range behavior more closely than all previous potentials, including inclusion of the Axelrod-Teller three-body interaction. The model is based on accurate diatomic potentials representing all atom-atom pairwise interactions, and for CO 2 , a three-body correction representing the rest of the energy. This emphasizes the value of accurate molecular spectroscopy for simple diatomics, which is sometimes considered to be less interesting than research involving large molecules. Diatomic potentials are valuable as building blocks for large-molecule potentials. An open-source computer program for building PolyMLR potentials for polyatomic molecules is introduced.
Bulletin of the American Physical Society, 2017
and for controlling properties of the Hamiltonian such as the spectral gap, spectral width, numbe... more and for controlling properties of the Hamiltonian such as the spectral gap, spectral width, number of local minima in a particular state, and strength of couplings between/among qubits (https://arxiv.org/abs/1510.07420). We combine these methods with established methods for reducing multi-qubit terms in worse cases where auxiliary qubits are needed, into a general purpose "compiler" that reads in a general Hamiltonian, and attempts to output a 2-local Hamiltonian with **as few extra qubits as possible** and **as large a spectral gap as possible** and **as small a spectral width as possible** and **coupling strengths that are as small as possible**. We show results on several types of AQC Hamiltonians: neural network Hamiltonians, computer vision problems, Ramsey number determination, integer factorization, and quantum chemistry.
Proceedings of the 73rd International Symposium on Molecular Spectroscopy, 2018
The energy at the empirical bond length of Li 2 (1 3 Σ + u) of 4.1700Å b was obtained at all-elec... more The energy at the empirical bond length of Li 2 (1 3 Σ + u) of 4.1700Å b was obtained at all-electron FCI level with an augcc-pCV5Z-NR basis set, all-electron CCSDT(Q) with aug-cc-pCV7Z-NR, and all-electron CCSD(T) with aug-cc-pCV8Z-NR; along with corrections due to special relativity converged with respect to electron correlation and basis set size using the spin-free Dirac-Coulomb Hamiltonian, and further such corrections at the Hartree-Fock level using the Breit and Gaunt Hamiltonians. Corrections to the point-size nucleus approximation were calculated but found to be negligible. The result was compared to the lowest energy of the best empirical potentials b with the empirical Born-Oppenheimer breakdown corrections removed, making it essentially an infinite-mass to infinite-mass comparison. The discrepancy between the energy obtained from laboratory spectroscopy and the energy obtained completely by the computer was only 0.06 cm −1 , which is of the same order of magnitude as the uncertainty on the empirical value, which is ±0.007 cm −1 before including the added uncertainty coming from the Born-Oppenheimer breakdown parameter u 0 which itself has an uncertainty of 0.01 cm −1. It is discussed what is necessary for the computer spectrometer to outperform the laboratory spectrometer. The ionization energy of the carbon atom was calculated at all-electron FCI level with aug-cc-pCV8Z-NR and aug-cc-pCV7Z-NR basis sets (the latter only for basis set extrapolation); along with corrections due to special relativity converged with respect to electron correlation and basis set size using the 1e − X2C Hamiltonian, further corrections using stateaveraged Dirac-Fock for the contribution from the Breit Hamiltonian and some QED contributions; along with DBOC corrections to the clamped nucleus approximation converged with respect to electron correlation and basis set size. Again, corrections to the point-size nucleus approximation were calcualted but found to be negligible. The final energy was compared to the very recent experimental value published by NIST c with the experimental spin-orbit lowering of 12.672508 cm −1 removed. The discrepancy was 0.994 cm −1 compared to the ±0.009 cm −1 uncertainty in the laboratory value.
In this article we describe the OpenMolcas environment and invite the computational chemistry com... more In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimizati...
The Journal of Chemical Physics, 2019
We report that a recent active space model of the nitrogenase FeMo cofactor, proposed in the cont... more We report that a recent active space model of the nitrogenase FeMo cofactor, proposed in the context of simulations on quantum computers, is not representative of the electronic structure of the FeMo cofactor ground-state. A more representative model does not affect much certain resource estimates for a quantum computer such as the cost of a Trotter step, while strongly affecting others such as the cost of adiabatic state preparation. Thus, conclusions should not be drawn from the complexity of quantum or classical simulations of the electronic structure of this system in this active space. We provide a different model active space for the FeMo cofactor that contains the basic open-shell qualitative character, which may be useful as a benchmark system for making resource estimates for classical and quantum computers.
Applied Physics Letters, 2016
We propose an implementation of quantum neural networks using an array of quantum dots with dipol... more We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations which are based on SQUID-based systems operating at temperatures in the mK range.
EPJ Web of Conferences, 2016
We present the results of the simulation of a quantum neural network based on quantum dots using ... more We present the results of the simulation of a quantum neural network based on quantum dots using numerical method of path integral calculation. In the proposed implementation of the quantum neural network using an array of single-electron quantum dots with dipole-dipole interaction, the coherence is shown to survive up to 0.1 nanosecond in time and up to the liquid nitrogen temperature of 77K. We study the quantum correlations between the quantum dots by means of calculation of the entanglement of formation in a pair of quantum dots on the GaAs based substrate with dot size of 10 0 ÷ 10 1 nanometer and interdot distance of 10 1 ÷ 10 2 nanometers order.
Journal of Chemical Theory and Computation, 2015
We develop and present an improvement to the conventional technique for solving the Hierarchical ... more We develop and present an improvement to the conventional technique for solving the Hierarchical Equations of Motion which reduces the memory cost by more than 75% while retaining the same convergence rate and accuracy. This allows for a full calculation of the population dynamics of the 24-site FMO trimer for long timescales with very little effort, and we present the first fully converged, exact results for the 7-site subsystem of the monomer, and for the full 24-site trimer. Owing to this new approach, our numerically exact 24-site, 2-exponential results are the most demanding HEOM calculations performed to date, surpassing the 50-site, 1-exponential results of Strumpfer and Schulten [2012, J. Chem. Thy. & Comp., 8, 2808]. We then show where our exact 7-site results deviate from the approximation of Ishizaki and Fleming [2009, Proc. Natl. Acad. Sci. USA, 106, 17255]. Our exact results are then compared to calculations using the incoherent Förster theory, and it is found that the energy transfer from the antenna to the reaction centre occurs more than 50 times faster than the fluorescence lifetime of the excitation, whether or not coherence is considered. This means that coherence is not likely to improve the efficiency of the photosynthesis. In fact, the incoherent theory often tends to over-predict the rates of energy transfer, suggesting that in some cases electronic coherence may actually slow down the photosynthetic process.
A new method for determining whether or not a mitrochondrial DNA (mtDNA) sequence belongs to a ve... more A new method for determining whether or not a mitrochondrial DNA (mtDNA) sequence belongs to a vertebrate is described and tested. This method only needs the mtDNA sequence of the organism in question, and unlike alignment based methods, it does not require it to be compared with anything else. The method is tested on all 1877 mtDNA sequences that were on NCBI's nucleotide database on August 12, 2009, and works in 94.57% of the cases. Furthermore, all organisms on which this method failed are closely related phylogenetically in comparison to all other organisms included in the study. A list of potential extensions to this method and open problems that emerge out of this study is presented at the end.
We propose a novel combination of methods that (i) portrays quantitative characteristics of a DNA... more We propose a novel combination of methods that (i) portrays quantitative characteristics of a DNA sequence as an image, (ii) computes distances between these images, and (iii) uses these distances to output a map wherein each sequence is a point in a common Euclidean space. In the resulting Molecular Distance Map each point signifies a DNA sequence, and the geometric distance between any two points reflects the degree of relatedness between the corresponding sequences and species. Molecular Distance Maps present compelling visual representations of relationships between species and could be used for taxonomic clarifications, for species identification, placement of species in existing taxonomic categories, as well as for studies of evolutionary history. One of the advantages of this method is its general applicability since, as sequence alignment is not required, the DNA sequences chosen for comparison can be completely different regions in different genomes. In fact, this method can be used to compare any two DNA sequences. For example, in our dataset of 3,176 mitochondrial DNA sequences, it correctly finds the mtDNA sequences most closely related to that of the anatomically modern human
Journal of Molecular Spectroscopy, 2015
BeH is one of the most important benchmark systems for ab initio methods and for studying Born-Op... more BeH is one of the most important benchmark systems for ab initio methods and for studying Born-Oppenheimer breakdown. However the best empirical potential and best ab initio potential for the ground electronic state to date give drastically different predictions in the long-range region beyond which measurements have been made, which is about ∼ 1000 cm −1 for 9 BeH, ∼ 3000 cm −1 for 9 BeD, and ∼ 13000 cm −1 for 9 BeT. Improved empirical potentials and Born-Oppenheimer breakdown corrections have now been built for the ground electronic states X(1 2 Σ +) of all three isotopologues. The predicted dissociation energy for 9 BeH from the new empirical potential is now closer to the current best ab initio prediction by more than 66% of the discrepancy between the latter and the previous best empirical potential. The previous best empirical potential predicted the existence of unobserved vibrational levels for all three isotopologues, and the current best ab initio study also predicted the existence of all of these levels, and four more. The present empirical potential agrees with the ab initio prediction of all of these extra levels not predicted by the earlier empirical potential. With one exception, all energy spacings between vibrational energy levels for which measurements have been made, are predicted with an agreement of better than 1 cm −1 between the new empirical potential and the current best ab initio potential, but some predictions for unobserved levels are still in great disagreement, and the equilibrium bond lengths are different by orders of magnitude.
Uploads
Papers by Dr. Nike Dattani