55 research outputs found
Detecting Multiple Communities Using Quantum Annealing on the D-Wave System
A very important problem in combinatorial optimization is partitioning a
network into communities of densely connected nodes; where the connectivity
between nodes inside a particular community is large compared to the
connectivity between nodes belonging to different ones. This problem is known
as community detection, and has become very important in various fields of
science including chemistry, biology and social sciences. The problem of
community detection is a twofold problem that consists of determining the
number of communities and, at the same time, finding those communities. This
drastically increases the solution space for heuristics to work on, compared to
traditional graph partitioning problems. In many of the scientific domains in
which graphs are used, there is the need to have the ability to partition a
graph into communities with the ``highest quality'' possible since the presence
of even small isolated communities can become crucial to explain a particular
phenomenon. We have explored community detection using the power of quantum
annealers, and in particular the D-Wave 2X and 2000Q machines. It turns out
that the problem of detecting at most two communities naturally fits into the
architecture of a quantum annealer with almost no need of reformulation. This
paper addresses a systematic study of detecting two or more communities in a
network using a quantum annealer
Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics
In Born-Oppenheimer molecular dynamics (BOMD) simulations based on density
functional theory (DFT), the potential energy and the interatomic forces are
calculated from an electronic ground state density that is determined by an
iterative self-consistent field optimization procedure, which in practice never
is fully converged. The calculated energies and the forces are therefore only
approximate, which may lead to an unphysical energy drift and instabilities.
Here we discuss an alternative shadow BOMD approach that is based on a backward
error analysis. Instead of calculating approximate solutions for an underlying
exact regular BO potential, we do the opposite. Instead, we calculate the exact
electron density, energies, and forces, but for an underlying approximate
shadow BO potential. In this way the calculated forces are conservative with
respect to the shadow potential and generate accurate molecular trajectories
with long-term energy stability. We show how such shadow BO potentials can be
constructed at different levels of accuracy as a function of the integration
time step, dt, from the minimization of a sequence of systematically
improvable, but approximate, shadow energy density functionals. For each
functional there is a corresponding ground state BO potential. These pairs of
shadow energy functionals and potentials are higher-level generalizations of
the original "0th-level" shadow energy functionals and potentials used in
extended Lagrangian BOMD [Eur. Phys. J. B vol. 94, 164 (2021)]. The proposed
shadow energy functionals and potentials are useful only within this dynamical
framework, where also the electronic degrees of freedom are propagated together
with the atomic positions and velocities. The theory is general and can be
applied to MD simulations using approximate DFT, Hartree-Fock or semi-empirical
methods, as well as to coarse-grained flexible charge models.Comment: 16 pages, 3 figure
A fast, dense Chebyshev solver for electronic structure on GPUs
Matrix diagonalization is almost always involved in computing the density
matrix needed in quantum chemistry calculations. In the case of modest matrix
sizes ( 5000), performance of traditional dense diagonalization
algorithms on modern GPUs is underwhelming compared to the peak performance of
these devices. This motivates the exploration of alternative algorithms better
suited to these types of architectures. We newly derive, and present in detail,
an existing Chebyshev expansion algorithm [W. Liang et al, J. Chem. Phys. 2003]
whose number of required matrix multiplications scales with the square root of
the number of terms in the expansion. Focusing on dense matrices of modest
size, our implementation on GPUs results in large speed ups when compared to
diagonalization. Additionally, we improve upon this existing method by
capitalizing on the inherent task parallelism and concurrency in the algorithm.
This improvement is implemented on GPUs by using CUDA and HIP streams via the
MAGMA library and leads to a significant speed up over the serial-only approach
for smaller ( 1000) matrix sizes. Lastly, we apply our technique to a
model system with a high density of states around the Fermi level which
typically presents significant challenges.Comment: Submitted to Journal of Chemical Physics Communication
Quantum Isomer Search
Isomer search or molecule enumeration refers to the problem of finding all
the isomers for a given molecule. Many classical search methods have been
developed in order to tackle this problem. However, the availability of quantum
computing architectures has given us the opportunity to address this problem
with new (quantum) techniques. This paper describes a quantum isomer search
procedure for determining all the structural isomers of alkanes. We first
formulate the structural isomer search problem as a quadratic unconstrained
binary optimization (QUBO) problem. The QUBO formulation is for general use on
either annealing or gate-based quantum computers. We use the D-Wave quantum
annealer to enumerate all structural isomers of all alkanes with fewer carbon
atoms (n < 10) than Decane (C10H22). The number of isomer solutions increases
with the number of carbon atoms. We find that the sampling time needed to
identify all solutions scales linearly with the number of carbon atoms in the
alkane. We probe the problem further by employing reverse annealing as well as
a perturbed QUBO Hamiltonian and find that the combination of these two methods
significantly reduces the number of samples required to find all isomers.Comment: 20 pages, 9 figure
Matrix Diagonalization as a Board Game: Teaching an Eigensolver the Fastest Path to Solution
Matrix diagonalization is at the cornerstone of numerous fields of scientific
computing. Diagonalizing a matrix to solve an eigenvalue problem requires a
sequential path of iterations that eventually reaches a sufficiently converged
and accurate solution for all the eigenvalues and eigenvectors. This typically
translates into a high computational cost. Here we demonstrate how
reinforcement learning, using the AlphaZero framework, can accelerate Jacobi
matrix diagonalizations by viewing the selection of the fastest path to
solution as a board game. To demonstrate the viability of our approach we apply
the Jacobi diagonalization algorithm to symmetric Hamiltonian matrices that
appear in quantum chemistry calculations. We find that a significant
acceleration can often be achieved. Our findings highlight the opportunity to
use machine learning as a promising tool to improve the performance of
numerical linear algebra.Comment: 14 page
Eigenvector Centrality Distribution for Characterization of Protein Allosteric Pathways
Determining the principal energy pathways for allosteric communication in
biomolecules, that occur as a result of thermal motion, remains challenging due
to the intrinsic complexity of the systems involved. Graph theory provides an
approach for making sense of such complexity, where allosteric proteins can be
represented as networks of amino acids. In this work, we establish the
eigenvector centrality metric in terms of the mutual information, as a mean of
elucidating the allosteric mechanism that regulates the enzymatic activity of
proteins. Moreover, we propose a strategy to characterize the range of the
physical interactions that underlie the allosteric process. In particular, the
well known enzyme, imidazol glycerol phosphate synthase (IGPS), is utilized to
test the proposed methodology. The eigenvector centrality measurement
successfully describes the allosteric pathways of IGPS, and allows to pinpoint
key amino acids in terms of their relevance in the momentum transfer process.
The resulting insight can be utilized for refining the control of IGPS
activity, widening the scope for its engineering. Furthermore, we propose a new
centrality metric quantifying the relevance of the surroundings of each
residue. In addition, the proposed technique is validated against experimental
solution NMR measurements yielding fully consistent results. Overall, the
methodologies proposed in the present work constitute a powerful and cost
effective strategy to gain insight on the allosteric mechanism of proteins
Multilevel Combinatorial Optimization Across Quantum Architectures
Emerging quantum processors provide an opportunity to explore new approaches
for solving traditional problems in the post Moore's law supercomputing era.
However, the limited number of qubits makes it infeasible to tackle massive
real-world datasets directly in the near future, leading to new challenges in
utilizing these quantum processors for practical purposes. Hybrid
quantum-classical algorithms that leverage both quantum and classical types of
devices are considered as one of the main strategies to apply quantum computing
to large-scale problems. In this paper, we advocate the use of multilevel
frameworks for combinatorial optimization as a promising general paradigm for
designing hybrid quantum-classical algorithms. In order to demonstrate this
approach, we apply this method to two well-known combinatorial optimization
problems, namely, the Graph Partitioning Problem, and the Community Detection
Problem. We develop hybrid multilevel solvers with quantum local search on
D-Wave's quantum annealer and IBM's gate-model based quantum processor. We
carry out experiments on graphs that are orders of magnitudes larger than the
current quantum hardware size, and we observe results comparable to
state-of-the-art solvers in terms of quality of the solution
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