42 research outputs found
Quantum Optimization of Fully-Connected Spin Glasses
The Sherrington-Kirkpatrick model with random couplings is programmed
on the D-Wave Two annealer featuring 509 qubits interacting on a Chimera-type
graph. The performance of the optimizer compares and correlates to simulated
annealing. When considering the effect of the static noise, which degrades the
performance of the annealer, one can estimate an improvement on the comparative
scaling of the two methods in favor of the D-Wave machine. The optimal choice
of parameters of the embedding on the Chimera graph is shown to be associated
to the emergence of the spin-glass critical temperature of the embedded
problem.Comment: includes supplemental materia
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
The next few years will be exciting as prototype universal quantum processors
emerge, enabling implementation of a wider variety of algorithms. Of particular
interest are quantum heuristics, which require experimentation on quantum
hardware for their evaluation, and which have the potential to significantly
expand the breadth of quantum computing applications. A leading candidate is
Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates
between applying a cost-function-based Hamiltonian and a mixing Hamiltonian.
Here, we extend this framework to allow alternation between more general
families of operators. The essence of this extension, the Quantum Alternating
Operator Ansatz, is the consideration of general parametrized families of
unitaries rather than only those corresponding to the time-evolution under a
fixed local Hamiltonian for a time specified by the parameter. This ansatz
supports the representation of a larger, and potentially more useful, set of
states than the original formulation, with potential long-term impact on a
broad array of application areas. For cases that call for mixing only within a
desired subspace, refocusing on unitaries rather than Hamiltonians enables more
efficiently implementable mixers than was possible in the original framework.
Such mixers are particularly useful for optimization problems with hard
constraints that must always be satisfied, defining a feasible subspace, and
soft constraints whose violation we wish to minimize. More efficient
implementation enables earlier experimental exploration of an alternating
operator approach to a wide variety of approximate optimization, exact
optimization, and sampling problems. Here, we introduce the Quantum Alternating
Operator Ansatz, lay out design criteria for mixing operators, detail mappings
for eight problems, and provide brief descriptions of mappings for diverse
problems.Comment: 51 pages, 2 figures. Revised to match journal pape
Resource Efficient Gadgets for Compiling Adiabatic Quantum Optimization Problems
A resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a inline image-local, optimization Hamiltonian is developed. This result is important because adiabatic quantum algorithms are often most easily formulated using many-body interactions but experimentally available interactions are generally 2-body. In this context, the efficiency of a reduction gadget is measured by the number of ancilla qubits required as well as the amount of control precision needed to implement the resulting Hamiltonian. First, methods of applying these gadgets to obtain 2-local Hamiltonians using the least possible number of ancilla qubits are optimized. Next, a novel reduction gadget which minimizes control precision and a heuristic which uses this gadget to compile 3-local problems with a significant reduction in control precision are shown. Finally, numerics are presented which indicate a substantial decrease in the resources required to implement randomly generated, 3-body optimization Hamiltonians when compared to other methods in the literature.Chemistry and Chemical Biolog
Data-Side Efficiencies for Lightweight Convolutional Neural Networks
We examine how the choice of data-side attributes for two important visual
tasks of image classification and object detection can aid in the choice or
design of lightweight convolutional neural networks. We show by experimentation
how four data attributes - number of classes, object color, image resolution,
and object scale affect neural network model size and efficiency. Intra- and
inter-class similarity metrics, based on metric learning, are defined to guide
the evaluation of these attributes toward achieving lightweight models.
Evaluations made using these metrics are shown to require 30x less computation
than running full inference tests. We provide, as an example, applying the
metrics and methods to choose a lightweight model for a robot path planning
application and achieve computation reduction of 66% and accuracy gain of 3.5%
over the pre-method model.Comment: 10 pages, 5 figures, 6 table
Exploring Network-Related Optimization Problems Using Quantum Heuristics
Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics.One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer
Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management
We present the mapping of a class of simplified air traffic management (ATM)
problems (strategic conflict resolution) to quadratic unconstrained boolean
optimization (QUBO) problems. The mapping is performed through an original
representation of the conflict-resolution problem in terms of a conflict graph,
where nodes of the graph represent flights and edges represent a potential
conflict between flights. The representation allows a natural decomposition of
a real world instance related to wind-optimal trajectories over the Atlantic
ocean into smaller subproblems, that can be discretized and are amenable to be
programmed in quantum annealers. In the study, we tested the new programming
techniques and we benchmark the hardness of the instances using both classical
solvers and the D-Wave 2X and D-Wave 2000Q quantum chip. The preliminary
results show that for reasonable modeling choices the most challenging
subproblems which are programmable in the current devices are solved to
optimality with 99% of probability within a second of annealing time.Comment: Paper accepted for publication on: IEEE Transactions on Intelligent
Transportation System
Quantum-accelerated constraint programming
Constraint programming (CP) is a paradigm used to model and solve constraint
satisfaction and combinatorial optimization problems. In CP, problems are
modeled with constraints that describe acceptable solutions and solved with
backtracking tree search augmented with logical inference. In this paper, we
show how quantum algorithms can accelerate CP, at both the levels of inference
and search. Leveraging existing quantum algorithms, we introduce a
quantum-accelerated filtering algorithm for the global
constraint and discuss its applicability to a broader family of global
constraints with similar structure. We propose frameworks for the integration
of quantum filtering algorithms within both classical and quantum backtracking
search schemes, including a novel hybrid classical-quantum backtracking search
method. This work suggests that CP is a promising candidate application for
early fault-tolerant quantum computers and beyond.Comment: published in Quantu