45 research outputs found
Performance Models for Split-execution Computing Systems
Split-execution computing leverages the capabilities of multiple
computational models to solve problems, but splitting program execution across
different computational models incurs costs associated with the translation
between domains. We analyze the performance of a split-execution computing
system developed from conventional and quantum processing units (QPUs) by using
behavioral models that track resource usage. We focus on asymmetric processing
models built using conventional CPUs and a family of special-purpose QPUs that
employ quantum computing principles. Our performance models account for the
translation of a classical optimization problem into the physical
representation required by the quantum processor while also accounting for
hardware limitations and conventional processor speed and memory. We conclude
that the bottleneck in this split-execution computing system lies at the
quantum-classical interface and that the primary time cost is independent of
quantum processor behavior.Comment: Presented at 18th Workshop on Advances in Parallel and Distributed
Computational Models [APDCM2016] on 23 May 2016; 10 page
Approximate Approximation on a Quantum Annealer
Many problems of industrial interest are NP-complete, and quickly exhaust
resources of computational devices with increasing input sizes. Quantum
annealers (QA) are physical devices that aim at this class of problems by
exploiting quantum mechanical properties of nature. However, they compete with
efficient heuristics and probabilistic or randomised algorithms on classical
machines that allow for finding approximate solutions to large NP-complete
problems. While first implementations of QA have become commercially available,
their practical benefits are far from fully explored. To the best of our
knowledge, approximation techniques have not yet received substantial
attention. In this paper, we explore how problems' approximate versions of
varying degree can be systematically constructed for quantum annealer programs,
and how this influences result quality or the handling of larger problem
instances on given set of qubits. We illustrate various approximation
techniques on both, simulations and real QA hardware, on different seminal
problems, and interpret the results to contribute towards a better
understanding of the real-world power and limitations of current-state and
future quantum computing.Comment: Proceedings of the 17th ACM International Conference on Computing
Frontiers (CF 2020
Dual-Matrix Domain-Wall: A Novel Technique for Generating Permutations by QUBO and Ising Models with Quadratic Sizes
The Ising model is defined by an objective function using a quadratic formula
of qubit variables. The problem of an Ising model aims to determine the qubit
values of the variables that minimize the objective function, and many
optimization problems can be reduced to this problem. In this paper, we focus
on optimization problems related to permutations, where the goal is to find the
optimal permutation out of the possible permutations of elements. To
represent these problems as Ising models, a commonly employed approach is to
use a kernel that utilizes one-hot encoding to find any one of the
permutations as the optimal solution. However, this kernel contains a large
number of quadratic terms and high absolute coefficient values. The main
contribution of this paper is the introduction of a novel permutation encoding
technique called dual-matrix domain-wall, which significantly reduces the
number of quadratic terms and the maximum absolute coefficient values in the
kernel. Surprisingly, our dual-matrix domain-wall encoding reduces the
quadratic term count and maximum absolute coefficient values from and
to and , respectively. We also demonstrate the
applicability of our encoding technique to partial permutations and Quadratic
Unconstrained Binary Optimization (QUBO) models. Furthermore, we discuss a
family of permutation problems that can be efficiently implemented using
Ising/QUBO models with our dual-matrix domain-wall encoding.Comment: 26 pages, 9 figure
Adiabatic Quantum Graph Matching with Permutation Matrix Constraints
Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems with emerging quantum computing technology and propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. We investigate several ways to inject permutation matrix constraints in a quadratic unconstrained binary optimization problem which can be mapped to quantum hardware. We focus on obtaining a sufficient spectral gap, which further increases the probability to measure optimal solutions and valid permutation matrices in a single run. We perform our experiments on the quantum computer D-Wave 2000Q (2^11 qubits, adiabatic). Despite the observed discrepancy between simulated adiabatic quantum computing and execution on real quantum hardware, our reformulation of permutation matrix constraints increases the robustness of the numerical computations over other penalty approaches in our experiments. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures, which opens up multiple new directions for solving matching problems in 3D computer vision and graphics