Paper-QO-EN

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Quality Diversity for Variational Quantum Circuit Optimization

Quality Diversity for Variational Quantum Circuit Optimization

Maximilian Zorn, Jonas Stein, Maximilian Balthasar Mansky, Philipp Altmann, Michael Kölle, and Claudia Linnhoff-Popien

Abstract

Optimizing the architecture of variational quantum circuits (VQCs) is crucial for advancing quantum computing (QC) towards practical applications. Current methods range from static ansatz design and evolutionary methods to machine learned VQC optimization, but are either slow, sample inefficient or require infeasible circuit depth to realize advantages. Quality diversity (QD) search methods combine diversity-driven optimization with user-specified features that offer insight into the optimization quality of circuit solution candidates. However, the choice of quality measures and the representational modeling of the circuits to allow for optimization with the current state-of-the-art QD methods like covariance matrix adaptation (CMA), is currently still an open problem. In this work we introduce a directly matrix-based circuit engineering, that can be readily optimized with QD-CMA methods and evaluate heuristic circuit quality properties like expressivity and gate-diversity as quality measures. We empirically show superior circuit optimization of our QD optimization w.r.t. speed and solution score against a set of robust benchmark algorithms from the literature on a selection of NP-hard combinatorial optimization problems.

In progress

Accelerated VQE: Parameter Recycling for Similar Recurring Problem Instances

Accelerated VQE: Parameter Recycling for Similar Recurring Problem Instances

Tobias Rohe, Maximilian Balthasar Mansky, Michael Kölle, Jonas Stein, Leo Sünkel, and Claudia Linnhoff-Popien

Abstract

Training the Variational Quantum Eigensolver (VQE) is a task that requires substantial compute. We propose the use of concepts from transfer learning to considerably reduce the training time when solving similar problem instances. We demonstrate that its utilisation leads to accelerated convergence and provides a similar quality of results compared to circuits with parameters initialised around zero. Further, transfer learning works better when the distance between the source-solution is close to that of the target-solution. Based on these findings, we present an accelerated VQE approach tested on the MaxCut problem with a problem size of 12 nodes solved with two different circuits utilised. We compare our results against a random baseline and non transfer learning trained circuits. Our experiments demonstrate that transfer learning can reduce training time by around 93\% in post-training, relative to identical circuits without the use of transfer learning. The accelerated VQE approach beats the standard approach by seven, respectively nine percentage points in terms of solution quality, if the early-stopping is considered. In settings where time-to-solution or computational costs are critical, this approach provides a significant advantage, having an improved trade-off between training effort and solution quality.

In progress

From Problem to Solution: A General Pipeline to Solve Optimisation Problems on Quantum Hardware

From Problem to Solution: A General Pipeline to Solve Optimisation Problems on Quantum Hardware

Tobias Rohe, Simon Grätz, Michael Kölle, Sebastian Zielinski, Jonas Stein, and Claudia Linnhoff-Popien

Abstract

On account of the inherent complexity and novelty of quantum computing (QC), as well as the expected lack of expertise of many of the stakeholders involved in its development, QC software development projects are exposed to the risk of being conducted in a crowded and unstructured way, lacking clear guidance and understanding. This paper presents a comprehensive quantum optimisation development pipeline, novel in its depth of 22 activities across multiple stages, coupled with project management insights, uniquely targeted to the late noisy intermediate-scale quantum (NISQ) and early post-NISQ eras. We have extensively screened literature and use-cases, interviewed experts, and brought in our own expertise to develop this general quantum pipeline. The proposed solution pipeline is divided into five stages: Use-case Identification, Solution Draft, Pre-Processing, Execution and Post-Processing. Additionally, the pipeline contains two review points to address the project management view, the inherent risk of the project and the current technical maturity of QC technology. This work is intended as an orientation aid and should therefore increase the chances of success of quantum software projects.

In progress

Quantum Circuit Construction and Optimization through Hybrid Evolutionary Algorithms

Quantum Circuit Construction and Optimization through Hybrid Evolutionary Algorithms

Leo Sünkel, Philipp Altmann, Michael Kölle, Gerhard Stenzel, Thomas Gabor, and Claudia Linnhoff-Popien

Abstract

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In progress

A Constant Measurement Quantum Algorithm for Graph Connectivity

A Constant Measurement Quantum Algorithm for Graph Connectivity

Maximilian Balthasar Mansky, Chonfai Kam, and Claudia Linnhoff-Popien

Abstract

We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary abelian gates taken from ZX calculus. Due to the fusion rule, the two-qubit gates correspond to a large single action on the qubits. The algorithm is general and can handle any undirected graph, including those with repeated edges and self-loops. The depth of the algorithm is variable, depending on the graph, and we derive upper and lower bounds. The algorithm exhibits a state decay that can be remedied with ancilla qubits. We provide a numerical simulation of the algorithm.

In progress

Towards Transfer Learning for Large-Scale Image Classification Using Annealing-Based Quantum Boltzmann Machines

Towards Transfer Learning for Large-Scale Image Classification Using Annealing-Based Quantum Boltzmann Machines

Daniëlle Schuman, Leo Sünkel, Philipp Altmann, Jonas Stein, Christoph Roch, Thomas Gabor, Claudia Linnhoff-Popien

Abstract

 

Quantum Transfer Learning (QTL) recently gained popularity as a hybrid quantum-classical approach for image classification tasks by efficiently combining the feature extraction capabilities of large Convolutional Neural Networks with the potential benefits of Quantum Machine Learning (QML). Existing approaches, however, only utilize gate-based Variational Quantum Circuits for the quantum part of these procedures. In this work we present an approach to employ Quantum Annealing (QA) in QTL-based image classification. Specifically, we propose using annealing-based Quantum Boltzmann Machines as part of a hybrid quantum-classical pipeline to learn the classification of real-world, large-scale data such as medical images through supervised training. We demonstrate our approach by applying it to the three-class COVID-CT-MD dataset, a collection of lung Computed Tomography (CT) scan slices. Using Simulated Annealing as a stand-in for actual QA, we compare our method to classical transfer learning, using a neural network of the same order of magnitude, to display its improved classification performance. We find that our approach consistently outperforms its classical baseline in terms of test accuracy and AUC-ROC-Score and needs less training epochs to do this.

Published in: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)

Evidence that PUBO outperforms QUBO when solving continuous optimization problems with the QAOA

Evidence that PUBO outperforms QUBO when solving continuous optimization problems with the QAOA

Jonas Stein, Farbod Chamanian, Maximilian Zorn, Jonas Nüßlein, Sebastian Zielinski, Michael Kölle, Claudia Linnhoff-Popien

Abstract

 

Quantum computing provides powerful algorithmic tools that have been shown to outperform established classical solvers in specific optimization tasks. A core step in solving optimization problems with known quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) is the problem formulation. While quantum optimization has historically centered around Quadratic Unconstrained Optimization (QUBO) problems, recent studies show, that many combinatorial problems such as the TSP can be solved more efficiently in their native Polynomial Unconstrained Optimization (PUBO) forms. As many optimization problems in practice also contain continuous variables, our contribution investigates the performance of the QAOA in solving continuous optimization problems when using PUBO and QUBO formulations. Our extensive evaluation on suitable benchmark functions, shows that PUBO formulations generally yield better results, while requiring less qubits. As the multi-qubit interactions needed for the PUBO variant have to be decomposed using the hardware gates available, i.e., currently single- and two-qubit gates, the circuit depth of the PUBO approach outscales its QUBO alternative roughly linearly in the order of the objective function. However, incorporating the planned addition of native multi-qubit gates such as the global Mølmer-Sørenson gate, our experiments indicate that PUBO outperforms QUBO for higher order continuous optimization problems in general.
 
GECCO ’23 Companion: Proceedings of the Companion Conference on Genetic and Evolutionary Computation
Pages 2254 – 2262
https://doi.org/10.1145/3583133.3596358

Approximative Lookup-Tables and Arbitrary Function Rotations for Facilitating NISQ-Implementations of the HHL and Beyond

Approximative Lookup-Tables and Arbitrary Function Rotations for Facilitating NISQ-Implementations of the HHL and Beyond

Petros Stougiannidis, Jonas Stein, David Bucher, Sebastian Zielinski, Claudia Linnhoff-Popien, and Sebastian Feld

Abstract

Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is prohibitive on near-term quantum computers. Aiming to facilitate such NISQ-implementations, we propose a novel circuit approximation technique that enhances the arithmetic subrou-tines in the HHL, which resemble a particularly resource-demanding component in small-scale settings. For this, we provide a description of the algorithmic implementation of space-efficient rotations of polynomial functions that do not demand explicit arithmetic calculations inside the quantum circuit. We show how these types of circuits can be reduced in depth by providing a simple and powerful approximation technique. Moreover, we provide an algorithm that converts lookup-tables for arbitrary function rotations into a structure that allows an application of the approximation technique. This allows implementing approximate rotation circuits for many polynomial and non-polynomial functions. Experimental results obtained for realistic early-application dimensions show significant improve-ments compared to the state-of-the-art, yielding small circuits while achieving good approximations.

Published in: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)


Influence of Different 3SAT-to-QUBO Transformations on the Solution Quality of Quantum Annealing: A Benchmark Study

Influence of Different 3SAT-to-QUBO Transformations on the Solution Quality of Quantum Annealing: A Benchmark Study

Sebastian Zielinski, Jonas Nüßlein, Jonas Stein, Thomas Gabor, Claudia Linnhoff-Popien, Sebastian Feld

Abstract

To solve 3sat instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an empirical benchmark study, in which we compare four structurally different QUBO transformations for the 3sat problem with regards to the solution quality on D-Wave’s Advantage_system4.1. We show that the choice of QUBO transformation can significantly impact the number of correct solutions the quantum annealer returns. Furthermore, we show that the size of a QUBO instance (i.e., the dimension of the QUBO matrix) is not a sufficient predictor for solution quality, as larger QUBO instances may produce better results than smaller QUBO instances for the same problem. We also empirically show that the number of different quadratic values of a QUBO instance, combined with their range, can significantly impact the solution quality.

In progress

Pattern QUBOs: Algorithmic Construction of 3SAT-to-QUBO Transformations

Pattern QUBOs: Algorithmic Construction of 3SAT-to-QUBO Transformations

Sebastian Zielinski, Jonas Nüßlein, Jonas Stein, Thomas Gabor, Claudia Linnhoff-Popien, Sebastian Feld

Abstract

One way of solving 3sat instances on a quantum computer is to transform the 3sat instances into instances of Quadratic Unconstrained Binary Optimizations (QUBOs), which can be used as an input for the QAOA algorithm on quantum gate systems or as an input for quantum annealers. This mapping is performed by a 3sat-to-QUBO transformation. Recently, it has been shown that the choice of the 3sat-to-QUBO transformation can significantly impact the solution quality of quantum annealing. It has been shown that the solution quality can vary up to an order of magnitude difference in the number of correct solutions received, depending solely on the 3sat-to-QUBO transformation. An open question is: what causes these differences in the solution quality when solving 3sat-instances with different 3sat-to-QUBO transformations? To be able to conduct meaningful studies that assess the reasons for the differences in the performance, a larger number of different 3sat-to-QUBO transformations would be needed. However, currently, there are only a few known 3sat-to-QUBO transformations, and all of them were created manually by experts, who used time and clever reasoning to create these transformations. In this paper, we will solve this problem by proposing an algorithmic method that is able to create thousands of new and different 3sat-to-QUBO transformations, and thus enables researchers to systematically study the reasons for the significant difference in the performance of different 3sat-to-QUBO transformations. Our algorithmic method is an exhaustive search procedure that exploits properties of 4×4
dimensional pattern QUBOs, a concept which has been used implicitly in the creation of 3sat-to-QUBO transformations before, but was never described explicitly. We will thus also formally and explicitly introduce the concept of pattern QUBOs in this paper.

In progress

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