arXiv subjects

Nikesh S. Dattani

Publications and source records attributed to Nikesh S. Dattani.

At least 19 recordsLinked to original sources

arXiv2018

The electronic complexity of the ground-state of the FeMo cofactor of nitrogenase as relevant to quantum simulations

We report that a recent active space model of the nitrogenase FeMo cofactor, proposed in the context of quantum simulations, is not representative of the electronic structure of the FeMo cofactor ground-state. Although quantum resource estimates, outside of the cost of adiabatic state preparation, will not be much affected, conclusions should not be drawn from the complexity of 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 classical and quantum resource estimates.

physics.chem-ph↗

arXiv2017

High-fidelity adiabatic quantum computation using the intrinsic Hamiltonian of a spin system: Application to the experimental factorization of 291311

In previous implementations of adiabatic quantum algorithms using spin systems, the average Hamiltonian method with Trotter's formula was conventionally adopted to generate an effective instantaneous Hamiltonian that simulates an adiabatic passage. However, this approach had issues with the precision of the effective Hamiltonian and with the adiabaticity of the evolution. In order to address these, we here propose and experimentally demonstrate a novel scheme for adiabatic quantum computation by using the intrinsic Hamiltonian of a realistic spin system to represent the problem Hamiltonian while adiabatically driving the system by an extrinsic Hamiltonian directly induced by electromagnetic pulses. In comparison to the conventional method, we observed two advantages of our approach: improved ease of implementation and higher fidelity. As a showcase example of our approach, we experimentally factor 291311, which is larger than any other quantum factorization known.

quant-ph↗

arXiv2017

Entanglement in a quantum neural network based on quantum dots

We studied the quantum correlations between the nodes in a quantum neural network built of an array of quantum dots with dipole-dipole interaction. By means of the quasiadiabatic path integral simulation of the density matrix evolution in a presence of the common phonon bath we have shown the coherence in such system can survive up to the liquid nitrogen temperature of 77K and above. The quantum correlations between quantum dots are studied by means of calculation of the entanglement of formation in a pair of quantum dots with the typical dot size of a few nanometers and the interdot distance of the same order. We have shown that the proposed quantum neural network can keep the mixture of entangled states of QD pairs up to the above mentioned high temperatures.

quant-ph↗

arXiv2016

Towards a feasible implementation of quantum neural networks using quantum dots

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.

quant-ph↗

arXiv2015

Crushing runtimes in adiabatic quantum computation with Energy Landscape Manipulation (ELM): Application to Quantum Factoring

We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states. Our methods are even more general. They can be used to shift a Hamiltonian's density of states away from the ground state, so that fewer states occupy the low-lying energies near the minimum, hence allowing for faster adiabatic passages to find the ground state with less risk of getting caught in an undesired low-lying excited state during the passage. Even more generally, our methods can be used to transform a discrete optimization problem into a new one whose unique minimum still encodes the desired answer, but with the objective function's values forming a different landscape. Aspects of the landscape such as the objective function's range, or the values of certain coefficients, or how many different inputs lead to a given output value, can be decreased *or* increased. One of the many examples for which these methods are useful is in finding the ground state of a Hamiltonian using NMR: If it is difficult to find a molecule such that the distances between the spins match the interactions in the Hamiltonian, the interactions in the Hamiltonian can be changed without at all changing the ground state. We apply our methods to an AQC algorithm for integer factorization, and the first method reduces the maximum runtime in our example by up to 754%, and the second method reduces the maximum runtime of another example by up to 250%. These two methods may also be combined.

quant-ph↗

arXiv2015

Analytic potentials and vibrational energies for Li$_{2}$ states dissociating to $\mbox{Li}\left(2S\right)+\mbox{Li}\left(3P\right)$. Part 1: The $^{2S+1}Π_{u/g}$ states

Analytic potentials are built for all four $^{2S+1}Π_{u/g}$ states of Li$_{2}$ dissociating to Li$(2S)$ + Li$(3P)$: $3b(3^{3}Π_{u})$, $3B(3^{1}Π_{u})$, $3C(3^{1}Π_{g}),$ and $3d(3^{3}Π_{g})$. These potentials include the effect of spin-orbit coupling for large internuclear distances, and include state of the art long-range constants. This is the first successful demonstration of fully analytic diatomic potentials that capture features that are usually considered too difficult to capture without a point-wise potential, such as multiple minima, and shelves. Vibrational energies for each potential are presented for the isotopologues $^{6,6}$Li$_{2}$, $^{6,7}$Li$_{2}$, $^{7,7}$Li$_{2}$, and the elusive `halo nucleonic molecule' $^{11,11}$Li$_{2}$. These energies are claimed to be accurate enough for new high-precision experimental setups such as the one presented in {[}Sebastian \emph{et al.} Phys. Rev. A, \textbf{90}, 033417 (2014){]} to measure and assign energy levels of these electronic states, all of which have not yet been explored in the long-range region. Measuring energies in the long-range region of these electronic states may be significant for studying the \emph{ab initio} vs experiment discrepancy discussed in {[}Tang \emph{et al.} Phys. Rev. A, \textbf{84}, 052502 (2014){]} for the $C_{3}$ long-range constant of Lithium, which has significance for improving the SI definition of the second.

physics.chem-ph↗

arXiv2015

State of the art for ab initio vs empirical potentials for predicting 6e$^{-}$ excited state molecular energies: Application to Li$_{2}\left(b,1^{3}Π_{u}\right)$

We build the first analytic empirical potential for the most deeply bound $\mbox{Li}_{2}$ state: $b\left(1^{3}Π_{u}\right)$. Our potential is based on experimental energy transitions covering $v=0-34$, and very high precision theoretical long-range constants. It provides high accuracy predictions up to $v=100$ which pave the way for high-precision long-range measurements, and hopefully an eventual resolution of the age old discrepancy between experiment and theory for the $\mbox{Li}\left(2^{2}S\right)+\mbox{Li}\left(2^{2}P\right)$ $C_{3}$ value. State of the art ab initio calculations predict vibrational energy spacings that are all in at most 0.8 cm$^{-1}$ disagreement with the empirical potential.

physics.chem-ph↗

arXiv2015

Reducing multi-qubit interactions in adiabatic quantum computation without adding auxiliary qubits. Part 2: The "split-reduc" method and its application to quantum determination of Ramsey numbers

Quantum annealing has recently been used to determine the Ramsey numbers R(m,2) for 3 < m < 9 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.

quant-ph↗

arXiv2014

Quantum factorization of 56153 with only 4 qubits

The largest number factored on a quantum device reported until now was 143. That quantum computation, which used only 4 qubits at 300K, actually also factored much larger numbers such as 3599, 11663, and 56153, without the awareness of the authors of that work. Furthermore, unlike the implementations of Shor's algorithm performed thus far, these 4-qubit factorizations do not need to use prior knowledge of the answer. However, because they only use 4 qubits, these factorizations can also be performed trivially on classical computers. We discover a class of numbers for which the power of quantum information actually comes into play. We then demonstrate a 3-qubit factorization of 175, which would be the first quantum factorization of a triprime.

quant-ph↗

arXiv2014

Why quantum coherence is not important in the Fenna-Matthews-Olsen Complex

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 Forster theory, and it is found that the energy transfer from the antenna to the reaction center 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.

physics.chem-ph↗

arXiv2014

On the empirical dipole polarizability of He from spectroscopy of HeH$^{+}$

Using a long-range polarization potential for HeH$^{+}$, we can obtain an empirical value for the Boltzmann constant $k_{B}$ with an order of magnitude greater precision than the previous best experimental value based on the dipole polarizability of $^{4}$He. We find that relativistic and QED effects of order $α_{\rm FS}^{3}$ in the fine structure constant are crucial in the quadrupole polarizability in order to fit the dipole polarizbility with this precision using the polarization potential. By calculating finite-mass corrections for $^{3}$He, we also present theoretical values for the dipole and quadrupole polarizabilities of $^{3}$He with 9 and 7 digits of precision respectively.

physics.atom-ph↗

arXiv2014

Mapping the Space of Genomic Signatures

We propose a computational method to measure and visualize interrelationships among any number of DNA sequences allowing, for example, the examination of hundreds or thousands of complete mitochondrial genomes. An "image distance" is computed for each pair of graphical representations of DNA sequences, and the distances are visualized as a Molecular Distance Map: Each point on the map represents a DNA sequence, and the spatial proximity between any two points reflects the degree of structural similarity between the corresponding sequences. The graphical representation of DNA sequences utilized, Chaos Game Representation (CGR), is genome- and species-specific and can thus act as a genomic signature. Consequently, Molecular Distance Maps could inform species identification, taxonomic classifications and, to a certain extent, evolutionary history. The image distance employed, Structural Dissimilarity Index (DSSIM), implicitly compares the occurrences of oligomers of length up to $k$ (herein $k=9$) in DNA sequences. We computed DSSIM distances for more than 5 million pairs of complete mitochondrial genomes, and used Multi-Dimensional Scaling (MDS) to obtain Molecular Distance Maps that visually display the sequence relatedness in various subsets, at different taxonomic levels. This general-purpose method does not require DNA sequence homology and can thus be used to compare similar or vastly different DNA sequences, genomic or computer-generated, of the same or different lengths. We illustrate potential uses of this approach by applying it to several taxonomic subsets: phylum Vertebrata, (super)kingdom Protista, classes Amphibia-Insecta-Mammalia, class Amphibia, and order Primates. This analysis of an extensive dataset confirms that the oligomer composition of full mtDNA sequences can be a source of taxonomic information.

q-bio.GN↗

arXiv2014

Beryllium monohydride (BeH): Where we are now, after 86 years of spectroscopy

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 \sim1000 cm^{-1} for ^{9} BeH, \sim3000 cm^{-1} for ^{9} BeD, and \sim13000 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.

physics.chem-ph↗

arXiv2014

Global empirical potentials from purely rotational measurements

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 ($\pm2$ kHz) pure rotational transitions in the $X$-state of ZnO. Combining them with previous high-precision ($\pm50$ 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 \emph{ab initio} calculations in today's reach. By calculating the $C_{6},$ $C_{8},$ and $C_{10}$ long-range constants and using them to anchor the top of the well, our potential is \emph{globally} in excellent agreement with \emph{ab initio} calculations, without the need for vibrational spectra and without the need for \emph{any} data in the top 90\% of the well.

physics.chem-ph↗

arXiv2013

High resolution photoassociation spectroscopy of the $^{6}$Li$_2$ $1^{3}Σ_{g}^{+}$ state

We present experimental observations of seven vibrational levels $v'=20-26$ of the $1^{3}Σ_{g}^{+}$ excited state of Li$_2$ molecules by the photoassociation (PA) of a degenerate Fermi gas of $^6$Li atoms. For each vibrational level, we resolve the rotational structure using a Feshbach resonance to enhance the PA rates from p-wave collisions. We also, for the first time, determine the spin-spin and spin-rotation interaction constants for this state. The absolute uncertainty of our measurements is $\pm 0.00002$ cm$^{-1}$ ($\pm 600$ kHz). We use these new data to further refine an analytic potential for this state.

physics.atom-ph↗

arXiv2013

High resolution photoassociation spectroscopy of the $^{6}$Li$_2$ $A(1^1Σ_u^+)$ state

We present spectroscopic measurements of seven vibrational levels $v=29-35$ of the $A(1^1Σ_u^+)$ excited state of Li$_2$ molecules by the photoassociation of a degenerate Fermi gas of $^6$Li atoms. The absolute uncertainty of our measurements is $\pm 0.00002$ cm$^{-1}$ ($\pm 600$ kHz) and we use these new data to further refine an analytic potential for this state. This work provides high accuracy photo-association resonance locations essential for the eventual high resolution mapping of the $X(1^1Σ_g^+)$ state enabling further improvements to the s-wave scattering length determination of Li and enabling the eventual creation of ultra-cold ground state $^6$Li$_2$ molecules.

physics.atom-ph↗

arXiv2013

Map of Life: Measuring and Visualizing Species' Relatedness with "Molecular Distance Maps"

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, and 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 (the Neanderthal, the Denisovan, and the chimp), and it finds that the sequence most different from it belongs to a cucumber. Furthermore, our method can be used to compare real sequences to artificial, computer-generated, DNA sequences. For example, it is used to determine that the distances between a Homo sapiens sapiens mtDNA and artificial sequences of the same length and same trinucleotide frequencies can be larger than the distance between the same human mtDNA and the mtDNA of a fruit-fly. We demonstrate this method's promising potential for taxonomical clarifications by applying it to a diverse variety of cases that have been historically controversial, such as the genus Polypterus, the family Tarsiidae, and the vast (super)kingdom Protista.

q-bio.GN↗

arXiv2012

An open source MATLAB program for fast numerical Feynman integral calculations for open quantum system dynamics on GPUs

This MATLAB program calculates the dynamics of the reduced density matrix of an open quantum system modeled by the Feynman-Vernon model. The user gives the program a vector describing the coordinate of an open quantum system, a hamiltonian matrix describing its energy, and a spectral distribution function and temperature describing the environment's influence on it, in addition to the open quantum system's intial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open quantum system at all (or some) moments specified by that grid of times. This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time-propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integal actually becomes the rate limiting step for most cases tested so far. The overhead of transfrring information from the CPU to the GPU and back seems to have negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU.

quant-ph↗