16 research outputs found
Exponentially Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians
We study the performance of the D-Wave 2X quantum annealing machine on
systems with well-controlled ground-state degeneracy. While obtaining the
ground state of a spin-glass benchmark instance represents a difficult task,
the gold standard for any optimization algorithm or machine is to sample all
solutions that minimize the Hamiltonian with more or less equal probability.
Our results show that while naive transverse-field quantum annealing on the
D-Wave 2X device can find the ground-state energy of the problems, it is not
well suited in identifying all degenerate ground-state configurations
associated to a particular instance. Even worse, some states are exponentially
suppressed, in agreement with previous studies on toy model problems [New J.
Phys. 11, 073021 (2009)]. These results suggest that more complex driving
Hamiltonians are needed in future quantum annealing machines to ensure a fair
sampling of the ground-state manifold.Comment: 6 pages, 5 figures, 1 tabl
Comparing Three Generations of D-Wave Quantum Annealers for Minor Embedded Combinatorial Optimization Problems
Quantum annealing is a novel type of analog computation that aims to use
quantum mechanical fluctuations to search for optimal solutions of Ising
problems. Quantum annealing in the Transverse Ising model, implemented on
D-Wave QPUs, are available as cloud computing resources. In this article we
report concise benchmarks across three generations of D-Wave quantum annealers,
consisting of four different devices, for the NP-Hard combinatorial
optimization problems unweighted maximum clique and unweighted maximum cut on
random graphs. The Ising, or equivalently QUBO, formulation of these problems
do not require auxiliary variables for order reduction, and their overall
structure and weights are not highly complex, which makes these problems simple
test cases to understand the sampling capability of current D-Wave quantum
annealers. All-to-all minor embeddings of size , with relatively uniform
chain lengths, are used for a direct comparison across the Chimera, Pegasus,
and Zephyr device topologies. A grid search over annealing times and the minor
embedding chain strengths is performed in order to determine the level of
reasonable performance for each device and problem type. Experiment metrics
that are reported are approximation ratios for non-broken chain samples and
chain break proportions. How fairly the quantum annealers sample optimal
maximum cliques, for instances which contain multiple maximum cliques, is also
quantified using entropy of the measured ground state distributions. The newest
generation of quantum annealing hardware, which has a Zephyr hardware
connectivity, performed the best overall with respect to approximation ratios
and chain break frequencies
IASCAR: Incremental Answer Set Counting by Anytime Refinement
Answer set programming (ASP) is a popular declarative programming paradigm
with various applications. Programs can easily have many answer sets that
cannot be enumerated in practice, but counting still allows quantifying
solution spaces. If one counts under assumptions on literals, one obtains a
tool to comprehend parts of the solution space, so-called answer set
navigation. However, navigating through parts of the solution space requires
counting many times, which is expensive in theory. Knowledge compilation
compiles instances into representations on which counting works in polynomial
time. However, these techniques exist only for CNF formulas, and compiling ASP
programs into CNF formulas can introduce an exponential overhead. This paper
introduces a technique to iteratively count answer sets under assumptions on
knowledge compilations of CNFs that encode supported models. Our anytime
technique uses the inclusion-exclusion principle to improve bounds by over- and
undercounting systematically. In a preliminary empirical analysis, we
demonstrate promising results. After compiling the input (offline phase), our
approach quickly (re)counts.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP