arXiv subjects

Sebastian Feld

Publications and source records attributed to Sebastian Feld.

At least 73 records · Page 4Linked to original sources

arXiv2023

Solving (Max) 3-SAT via Quadratic Unconstrained Binary Optimization

We introduce a novel approach to translate arbitrary 3-SAT instances to Quadratic Unconstrained Binary Optimization (QUBO) as they are used by quantum annealing (QA) or the quantum approximate optimization algorithm (QAOA). Our approach requires fewer couplings and fewer physical qubits than the current state-of-the-art, which results in higher solution quality. We verified the practical applicability of the approach by testing it on a D-Wave quantum annealer.

quant-ph↗

arXiv2023

Clever Design, Unexpected Obstacles: Insights on Implementing a Quantum Boltzmann Machine

We have implemented a gated-based quantum version of a restricted Boltzmann machine for approximating the ground state of a Pauli-decomposed qubit Hamiltonian. During the implementation and evaluation, we have noticed a variety of unexpected topics. It starts from limitations due to the structure of the algorithm itself and continues with constraints induced by specific quantum software development kits, which did not (yet) support necessary features for an efficient implementation. In this paper we systematically summarize our findings and categorize them according to their relevance for the implementation of similar quantum algorithms. We also discuss the feasibility of executing such implementations on current NISQ devices.

quant-ph↗

arXiv2022

Characterizing Qubit Traffic of a Quantum Intranet aiming at Modular Quantum Computers

Quantum many-core processors are envisioned as the ultimate solution for the scalability of quantum computers. Based upon Noisy Intermediate-Scale Quantum (NISQ) chips interconnected in a sort of quantum intranet, they enable large algorithms to be executed on current and close future technology. In order to optimize such architectures, it is crucial to develop tools that allow specific design space explorations. To this aim, in this paper we present a technique to perform a spatio-temporal characterization of quantum circuits running in multi-chip quantum computers. Specifically, we focus on the analysis of the qubit traffic resulting from operations that involve qubits residing in different cores, and hence quantum communication across chips, while also giving importance to the amount of intra-core operations that occur in between those communications. Using specific multi-core performance metrics and a complete set of benchmarks, our analysis showcases the opportunities that the proposed approach may provide to guide the design of multi-core quantum computers and their interconnects.

cs.ET↗

arXiv2022

Algorithmic QUBO Formulations for k-SAT and Hamiltonian Cycles

Quadratic unconstrained binary optimization (QUBO) can be seen as a generic language for optimization problems. QUBOs attract particular attention since they can be solved with quantum hardware, like quantum annealers or quantum gate computers running QAOA. In this paper, we present two novel QUBO formulations for $k$-SAT and Hamiltonian Cycles that scale significantly better than existing approaches. For $k$-SAT we reduce the growth of the QUBO matrix from $O(k)$ to $O(log(k))$. For Hamiltonian Cycles the matrix no longer grows quadratically in the number of nodes, as currently, but linearly in the number of edges and logarithmically in the number of nodes. We present these two formulations not as mathematical expressions, as most QUBO formulations are, but as meta-algorithms that facilitate the design of more complex QUBO formulations and allow easy reuse in larger and more complex QUBO formulations.

cs.DS↗

arXiv2022

How to Approximate any Objective Function via Quadratic Unconstrained Binary Optimization

Quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (QA). We present a toolkit of methods to transform almost arbitrary problems to QUBO by (i) approximating them as a polynomial and then (ii) translating any polynomial to QUBO. We showcase the usage of our approaches on two example problems (ratio cut and logistic regression).

quant-ph↗

arXiv2022

Full-stack quantum computing systems in the NISQ era: algorithm-driven and hardware-aware compilation techniques

The progress in developing quantum hardware with functional quantum processors integrating tens of noisy qubits, together with the availability of near-term quantum algorithms has led to the release of the first quantum computers. These quantum computing systems already integrate different software and hardware components of the so-called "full-stack", bridging quantum applications to quantum devices. In this paper, we will provide an overview on current full-stack quantum computing systems. We will emphasize the need for tight co-design among adjacent layers as well as vertical cross-layer design to extract the most from noisy intermediate-scale quantum (NISQ) processors which are both error-prone and severely constrained in resources. As an example of co-design, we will focus on the development of hardware-aware and algorithm-driven compilation techniques.

quant-ph↗

arXiv2022

Topological-Graph Dependencies and Scaling Properties of a Heuristic Qubit-Assignment Algorithm

The qubit-mapping problem aims to assign and route qubits of a quantum circuit onto a NISQ device in an optimized fashion, with respect to some cost function. Finding an optimal solution to this problem is known to scale exponentially in computational complexity; as such, it is imperative to investigate scalable qubit-mapping solutions for NISQ computation. In this work, a noise-aware heuristic qubit-assignment algorithm (which assigns initial placements for qubits in a quantum algorithm to qubits on a NISQ device, but does not route qubits during the quantum algorithm's execution) is presented and compared against the optimal \textit{brute-force} solution, as well as a trivial qubit assignment, with the aim to quantify the performance of our heuristic qubit-assignment algorithm. We find that for small, connected-graph algorithms, our heuristic-assignment algorithm faithfully lies in between the effective upper and lower bounds given by the brute-force and trivial qubit-assignment algorithms. Additionally, we find that the topological-graph properties of quantum algorithms with over six qubits play an important role in our heuristic qubit-assignment algorithm's performance on NISQ devices. Finally, we investigate the scaling properties of our heuristic algorithm for quantum processors with up to 100 qubits; here, the algorithm was found to be scalable for quantum-algorithms which admit path-like graphs. Our findings show that as the size of the quantum processor in our simulation grows, so do the benefits from utilizing the heuristic qubit-assignment algorithm, under particular constraints for our heuristic algorithm. This work thus characterizes the performance of a heuristic qubit-assignment algorithm with respect to the topological-graph and scaling properties of a quantum algorithm which one may wish to run on a given NISQ device.

quant-ph↗

arXiv2022

A context-aware gate set tomography characterization of superconducting qubits

The efficiency of Quantum Characterisation, Verification, and Validation (QCVV) protocols highly hinges on the agreement between the assumed noise model and the underlying error mechanisms. As a matter of fact, errors in Quantum Processing Units (QPUs) incorporate various aspects of context-dependability which are overlooked by the majority of the commonly used QCVV protocols. As QCVV protocols are indispensable when it comes to characterizing and evaluating quantum operations, there is a serious need for a detailed characterization taking into account such aspects. In this work, we address these shortcomings by designing a context-aware version of the gate set tomography (GST) protocol. Our experiment selection approach is based on a polynomial quantification of the accumulation of errors within the designed circuits. Using simulated QPUs, we show that this technique enables a characterization with an inaccuracy reaching $10^{-5}$. Furthermore, we use our proposed protocol to experimentally infer context-dependent errors, namely crosstalk and memory effects, in a publicly accessible cloud-based superconducting qubits platform. Our results show that when the GST is upgraded to include such features of context-awareness, a large coherence in the errors is observed. These findings open up possibilities of drastically reducing the errors within the currently demonstrated QPUs.

quant-ph↗

arXiv2020

Predictive Collision Management for Time and Risk Dependent Path Planning

Autonomous agents such as self-driving cars or parcel robots need to recognize and avoid possible collisions with obstacles in order to move successfully in their environment. Humans, however, have learned to predict movements intuitively and to avoid obstacles in a forward-looking way. The task of collision avoidance can be divided into a global and a local level. Regarding the global level, we propose an approach called "Predictive Collision Management Path Planning" (PCMP). At the local level, solutions for collision avoidance are used that prevent an inevitable collision. Therefore, the aim of PCMP is to avoid unnecessary local collision scenarios using predictive collision management. PCMP is a graph-based algorithm with a focus on the time dimension consisting of three parts: (1) movement prediction, (2) integration of movement prediction into a time-dependent graph, and (3) time and risk-dependent path planning. The algorithm combines the search for a shortest path with the question: is the detour worth avoiding a possible collision scenario? We evaluate the evasion behavior in different simulation scenarios and the results show that a risk-sensitive agent can avoid 47.3% of the collision scenarios while making a detour of 1.3%. A risk-averse agent avoids up to 97.3% of the collision scenarios with a detour of 39.1%. Thus, an agent's evasive behavior can be controlled actively and risk-dependent using PCMP.

cs.LG↗

arXiv2020

A Flexible Pipeline for the Optimization of CSG Trees

CSG trees are an intuitive, yet powerful technique for the representation of geometry using a combination of Boolean set-operations and geometric primitives. In general, there exists an infinite number of trees all describing the same 3D solid. However, some trees are optimal regarding the number of used operations, their shape or other attributes, like their suitability for intuitive, human-controlled editing. In this paper, we present a systematic comparison of newly developed and existing tree optimization methods and propose a flexible processing pipeline with a focus on tree editability. The pipeline uses a redundancy removal and decomposition stage for complexity reduction and different (meta-)heuristics for remaining tree optimization. We also introduce a new quantitative measure for CSG tree editability and show how it can be used as a constraint in the optimization process.

cs.AI↗

arXiv2020

A Quantum Annealing Algorithm for Finding Pure Nash Equilibria in Graphical Games

We introduce Q-Nash, a quantum annealing algorithm for the NP-complete problem of Fnding pure Nash equilibria in graphical games. The algorithm consists of two phases. The first phase determines all combinations of best response strategies for each player using classical computation. The second phase finds pure Nash equilibria using a quantum annealing device by mapping the computed combinations to a quadratic unconstrained binary optimization formulation based on the Set Cover problem. We empirically evaluate Q-Nash on D-Wave's Quantum Annealer 2000Q using different graphical game topologies. The results with respect to solution quality and computing time are compared to a Brute Force algorithm and the Iterated Best Response heuristic.

cs.GT↗

arXiv2020

Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA

Hybrid quantum-classical algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. The solution quality of QAOA depends to a high degree on the parameters chosen by the classical optimizer at each iteration. However, the solution landscape of those parameters is highly multi-dimensional and contains many low-quality local optima. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical optimizer to find better parameter more easily and hence results in an improved performance. We empirically demonstrate that this approach can reach a significant better solution quality for the Knapsack Problem.

quant-ph↗

arXiv2020

Accelerating Evolutionary Construction Tree Extraction via Graph Partitioning

Extracting a Construction Tree from potentially noisy point clouds is an important aspect of Reverse Engineering tasks in Computer Aided Design. Solutions based on algorithmic geometry impose constraints on usable model representations (e.g. quadric surfaces only) and noise robustness. Re-formulating the problem as a combinatorial optimization problem and solving it with an Evolutionary Algorithm can mitigate some of these constraints at the cost of increased computational complexity. This paper proposes a graph-based search space partitioning scheme that is able to accelerate Evolutionary Construction Tree extraction while exploiting parallelization capabilities of modern CPUs. The evaluation indicates a speed-up up to a factor of $46.6$ compared to the baseline approach while resulting tree sizes increased by $25.2\%$ to $88.6\%$.

cs.GR↗

arXiv2020

The Holy Grail of Quantum Artificial Intelligence: Major Challenges in Accelerating the Machine Learning Pipeline

We discuss the synergetic connection between quantum computing and artificial intelligence. After surveying current approaches to quantum artificial intelligence and relating them to a formal model for machine learning processes, we deduce four major challenges for the future of quantum artificial intelligence: (i) Replace iterative training with faster quantum algorithms, (ii) distill the experience of larger amounts of data into the training process, (iii) allow quantum and classical components to be easily combined and exchanged, and (iv) build tools to thoroughly analyze whether observed benefits really stem from quantum properties of the algorithm.

quant-ph↗

arXiv2020

Insights on Training Neural Networks for QUBO Tasks

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.

quant-ph↗

arXiv2020

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.

quant-ph↗

arXiv2020

Trajectory annotation using sequences of spatial perception

In the near future, more and more machines will perform tasks in the vicinity of human spaces or support them directly in their spatially bound activities. In order to simplify the verbal communication and the interaction between robotic units and/or humans, reliable and robust systems w.r.t. noise and processing results are needed. This work builds a foundation to address this task. By using a continuous representation of spatial perception in interiors learned from trajectory data, our approach clusters movement in dependency to its spatial context. We propose an unsupervised learning approach based on a neural autoencoding that learns semantically meaningful continuous encodings of spatio-temporal trajectory data. This learned encoding can be used to form prototypical representations. We present promising results that clear the path for future applications.

cs.LG↗

arXiv2020

Bayesian Surprise in Indoor Environments

This paper proposes a novel method to identify unexpected structures in 2D floor plans using the concept of Bayesian Surprise. Taking into account that a person's expectation is an important aspect of the perception of space, we exploit the theory of Bayesian Surprise to robustly model expectation and thus surprise in the context of building structures. We use Isovist Analysis, which is a popular space syntax technique, to turn qualitative object attributes into quantitative environmental information. Since isovists are location-specific patterns of visibility, a sequence of isovists describes the spatial perception during a movement along multiple points in space. We then use Bayesian Surprise in a feature space consisting of these isovist readings. To demonstrate the suitability of our approach, we take "snapshots" of an agent's local environment to provide a short list of images that characterize a traversed trajectory through a 2D indoor environment. Those fingerprints represent surprising regions of a tour, characterize the traversed map and enable indoor LBS to focus more on important regions. Given this idea, we propose to use "surprise" as a new dimension of context in indoor location-based services (LBS). Agents of LBS, such as mobile robots or non-player characters in computer games, may use the context surprise to focus more on important regions of a map for a better use or understanding of the floor plan.

cs.LG↗