24 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
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
Multilevel Combinatorial Optimization Across Quantum Architectures
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the Post Moore\u27s 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\u27s quantum annealer and IBM\u27s gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size and observe results comparable to state-of-the-art solvers
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
Molecular Dynamics on Quantum Annealers
In this work we demonstrate a practical prospect of using quantum annealers
for simulation of molecular dynamics. A methodology developed for this goal,
dubbed Quantum Differential Equations (QDE), is applied to propagate classical
trajectories for the vibration of the hydrogen molecule in several regimes:
nearly harmonic, highly anharmonic, and dissociative motion. The results
obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly
converge to the analytical reference solution. Several alternative strategies
for such calculations are explored and it was found that the most accurate
results and the best efficiency are obtained by combining the quantum annealer
with classical post-processing (greedy algorithm). Importantly, the QDE
framework developed here is entirely general and can be applied to solve any
system of first-order ordinary nonlinear differential equations using a quantum
annealer
Variational Quantum Eigensolver with Reduced Circuit Complexity
The variational quantum eigensolver (VQE) is one of the most promising
algorithms to find eigenvalues and eigenvectors of a given Hamiltonian on noisy
intermediate-scale quantum (NISQ) devices. A particular application is to
obtain ground or excited states of molecules. The practical realization is
currently limited by the complexity of quantum circuits. Here we present a
novel approach to reduce quantum circuit complexity in VQE for electronic
structure calculations. Our algorithm, called ClusterVQE, splits the initial
qubit space into subspaces (qubit clusters) which are further distributed on
individual (shallower) quantum circuits. The clusters are obtained based on
quantum mutual information reflecting maximal entanglement between qubits,
whereas entanglement between different clusters is taken into account via a new
"dressed" Hamiltonian. ClusterVQE therefore allows exact simulation of the
problem by using fewer qubits and shallower circuit depth compared to standard
VQE at the cost of additional classical resources. In addition, a new gradient
measurement method without using an ancillary qubit is also developed in this
work. Proof-of-principle demonstrations are presented for several molecular
systems based on quantum simulators as well as an IBM quantum device with
accompanying error mitigation. The efficiency of the new algorithm is
comparable to or even improved over qubit-ADAPT-VQE and iterative Qubit Coupled
Cluster (iQCC), state-of-the-art circuit-efficient VQE methods to obtain
variational ground state energies of molecules on NISQ hardware. Above all, the
new ClusterVQE algorithm simultaneously reduces the number of qubits and
circuit depth, making it a potential leader for quantum chemistry simulations
on NISQ devices