Insights on Training Neural Networks for QUBO Tasks
LMU Munich（慕尼黑大学）
Thomas Gabor, Sebastian Feld, Hila Safi, Thomy Phan, Claudia Linnhoff-Popien
备注：
6 pages, 5 figures, accepted at the 1st International Workshop on Quantum Software Engineering (Q-SE 2020) at ICSE 2020 and to be published in the corresponding proceedings
Current hardware limitations restrict the potential when solving quadratic unconstrained binary optimization (QUBO) problems via the quantum approximate optimization algorithm (QAOA) or quantum annealing (QA). Thus, we consider training neural networks in this context. We first discuss QUBO problems that originate from translated instances of the traveling salesman problem (TSP): Analyzing this representation via autoencoders shows that there is way more information included than necessary to solve the original TSP. Then we show that neural networks can be used to solve TSP instances from both QUBO input and autoencoders' hiddenstate representation. We finally generalize the approach and successfully train neural networks to solve arbitrary QUBO problems, sketching means to use neuromorphic hardware as a simulator or an additional co-processor for quantum computing.
Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks
Fakultät für Physik und Erdsystemwissenschaften, Universität Leipzig（莱比锡大学物理与地球科学系）；Data Cybernetics（数据认知科学）；Zentrum für Optische Quantentechnologien, Universität Hamburg（汉堡大学光学量子技术中心）
We analyze the transformation of QUBO from its conventional Boolean presentation into an equivalent spin glass problem with coupled $\pm1$ spin variables exposed to a site-dependent external field. We find that in a widely used testbed for QUBO these fields tend to be rather large compared to the typical coupling and many spins in each optimal configurations simply align with the fields irrespective of their constraints. Thereby, the testbed instances tend to exhibit large redundancies - seemingly independent variables which contribute little to the hardness of the problem, however. We demonst…
We report on a case study in programming an early quantum annealer to attack optimization problems related to operational planning. While a number of studies have looked at the performance of quantum annealers on problems native to their architecture, and others have examined performance of select problems stemming from an application area, ours is one of the first studies of a quantum annealer's performance on parametrized families of hard problems from a practical domain. We explore two different general mappings of planning problems to quadratic unconstrained binary optimization (QUBO) prob…
We present a map from the travelling salesman problem (TSP), a prototypical NP-complete combinatorial optimisation task, to the ground state associated with a system of many-qudits. Conventionally, the TSP is cast into a quadratic unconstrained binary optimisation (QUBO) problem, that can be solved on an Ising machine. The size of the corresponding physical system's Hilbert space is $2^{N^2}$, where $N$ is the number of cities considered in the TSP. Our proposal provides a many-qudit system with a Hilbert space of dimension $2^{N\log_2N}$, which is considerably smaller than the dimension of th…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of multiple patterns and algorithms, and show how it can be applied in the context of Quadratic Unconstrained Binary Optimization (QUBO) problems. We start by presenting a visual approach to quantum computing, which avoids a heavy-reliance on quantum mechanics, linear algebra, or complex mathematical notation, and favors geometrical intuition and computing paradigm…
TECNALIA（泰克纳利亚）；Basque Research and Technology Alliance (BRTA)（巴斯克研究与技术联盟（BRTA））
Despite being considered as the next frontier in computation, Quantum Computing is still in an early stage of development. Indeed, current commercial quantum computers suffer from some critical restraints, such as noisy processes and a limited amount of qubits, among others, that affect the performance of quantum algorithms. Despite these limitations, researchers have devoted much effort to propose different frameworks for efficiently using these Noisy Intermediate-Scale Quantum (NISQ) devices. One of these procedures is D'WAVE Systems' quantum-annealer, which can be use to solve optimization …
Is Quantum Optimization Ready? An Effort Towards Neural Network Compression using Adiabatic Quantum Computing
Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR)（高性能计算研究所（IHPC），科技研究局（A*STAR））；Huadian Coal Industry Group Co. Ltd.（华电煤炭工业集团有限公司）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）
United Technologies Research Center（联合技术研究中心）；SRI International（SRI国际）
Given a Boolean formula $ϕ(x)$ in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly $e$ clauses, for all values of $e$. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the \emph{hardness} of the problem instance. Consequently, in real-world scenarios, this problem is typically infeas…
ILP-based Resource Optimization Realized by Quantum Annealing for Optical Wide-area Communication Networks -- A Framework for Solving Combinatorial Problems of a Real-world Application by Quantum Annealing
Practical insights on the effect of different encodings, ansätze and measurements in quantum and hybrid convolutional neural networks
Quantum Lab, CTIC Centro Tecnol\'ogico, Parque Cient\'ifico Tecnol\'ogico de Gij\'on, Asturias, Spain；Eurecat, Centre Tecnol\`ogic de Catalunya, Multimedia Technologies, Barcelona, Spain；Centre de Visi\'o per Computador (CVC), Barcelona, Spain.；Fsas International Quantum Center (Fujitsu), Santiago de Compostela, Spain.
