ADMM-Surrogate
Mixed-integer linear programs or mixed-binary linear programs are an important optimization problem and interesting object for quantum computing. This notebook shows how a mixed-binary problem can be optimized with the help of a quantum computer. Two different optimization strategies are implemented; a strategy inspired by classical ADMM algorithms and another one using a Kriging surrogate model on top. Both of them use the VQE algorithm to optimize the binary problem. They can be used and tested with different ansatz functions and optimizers for VQE. Currently mixed-binary equality constraints and intervals for the continuous variables are supported.
Scenario-based route planning to safeguard automotive driving functions (TSP)
The demonstrator shows the QAOA implementation created as part of the project for the »Traveling Salesperson Problem«. In addition, an algorithm for partitioning the TSP developed in the course of the project will be demonstrated. The algorithm, which is based on A*, splits large TSP instances into several smaller ones so that they can be solved on the quantum computer. This approach is hybrid, whereby the partitioning takes place on a classical computer and only the difficult combinatorial »core« of the problem is solved on a quantum computer. Our QAOA implementation is embedded into this algorithm and can alternatively be exchanged with classical solver for comparison. In order to guide the choices of our method on which subinstanced to generate, several heuristics have been developed. This includes notably a small neural network that can estimate the expected length of a TSP instance.
Optimization of Charging Schedules for Electric Cars (EMP)
In this demonstrator, we use four Notebooks to show how to solve an energy use case on a quantum computer. In the first notebook, we introduce the use case, show how it can be formulated as a mathematical optimization problem and derive a Python implementation. In the second notebook, we explain both the theory of the quantum algorithm QAOA and its implementation in Qiskit using the energy use case. In the third notebook, we implement a transpilation pipeline with which QAOA circuits can be executed on real IBM quantum computers. We also explain how the results of a quantum computer can be processed with a big data library. In the last notebook, we present and discuss a series of experiments performed on the IBM Quantum System n in Ehningen ( »ibmq_ehningen«). In the second phase of the project we focus on the execution of application scenarios on real quantum computers, in particular on the IBM Quantum System One in Ehningen. This allows us to demonstrate the technological status and future potential of quantum computing using a real application example. For this purpose, we provide systematic series of problem instances of different sizes and coupling strengths (i.e. of different degrees of difficulty) and show their implementation -- from the classical model to the post-processing of the quantum computing solution (end-to-end run). The demonstrator will be published on this page at the end of the project in spring 2024.
Optimal cutting layouts for metal parts manufacturing (BPP)
The 2D irregular strip packing problem consists in finding the position and orientation of a set of polygons commonly referred to as »pieces« into a strip, i.e. a rectangular-shaped container with imposed and fixed height and variable length, such that: all the pieces fit completely inside the container, no two pieces intersect or »overlap« and the container's length is minimum. This problem is of significant economic importance as it allows the Manufacturing Industry to minimize its costs for materials such as fabric, leather, carton, wood, plastic, glass, ceramic or metal which are used for producing elementary parts composing finished products, such as cloths, cars, ships, electrical appliances, machines and packaging. The problem is also is great ecological importance, as it allows to reduce the industrial consumption of natural resources and the amount of industrial waste. Our solution is a hybrid quantum-classical algorithm that decomposes the problem into a rectangle packing problem and instances of the Traveling Salesman Problem (TSP). The TSP is solved by the Quantum Approximate Optimization Algorithm (QAOA) which is executed on the IBM Quantum System One, located in Ehningen, Germany. Our solution allows an arbitrary number of orientations of the pieces, scales up to a hundred pieces and is able to solve optimally a special class of "puzzle-like" problems.
Zero-Noise Extrapolation
The idea of Zero-Noise Extrapolation (ZNE) is based on the assumption that it is possible to increase the strength of the noise in a quantum circuit, e.g. by inserting additional gates. If the strength of the noise is changed several times (single, triple, fivefold error strength), a fit through the measured points can subsequently be performed. This extrapolates to the error-free case.
Since the main errors are caused by faulty CNOT gates, the simplest method is to replace each CNOT gate with 3 (or even 5) CNOT gates and thus amplify the error by a factor of 3 (or 5). In the fault-free case, this would not change the circuit.
The Python library developed in the project is used in all algorithms in which expected values are calculated. In the Jupyter Notebook example, we demonstrate the application of the ZNE for the HHL algorithm with 4 qubits. This algorithm solves a two-dimensional, linear system of equations. The function 𝐹 that interests us is the norm of the corresponding solution.
Error Mitigation Service
The »Error Mitigation Service« was developed as part of the SEQUOIA project and can be used to reduce the effects of errors in noisy measurement results of a quantum computer. It is available as an open source project on GitHub. This service enables the creation and management of calibration and mitigation data for various QPU vendors. It also allows users to improve their execution results based on newly generated or existing mitigation data. The Error Mitigation Service currently implements several methods, such as Mthree or TPNM for IBMQ and IonQ. It also supports error mitigation for results obtained on quantum simulators with emulated noise. Users can choose between full noise models and noise models containing only readout errors.
Optimization of Job Schedules in Discrete Manufacturing (JSP)
In this demonstrator we show how to solve a job shop scheduling (JSP) use case on a quantum computer in the form of a Jupyter Notebook.
In the notebook we introduce the use case, show how it can be formulated in a mathematical optimization problem (time indexed JSP QUBO), and explain how this problem can be implemented in Python.
After solving the QUBO using a classical optimizer (CPLEX), we show how the QUBO can be transformed into an ising model which is then solved on a quantum computer (ibmq_ehningen) using the Quantum Approximate Optimization Algorithm (QAOA).
Finally, we analyze the shot samples of the algorithm.
Route planning of truck fleets in supply chain management (TSP / SPP)
In this demonstrator we show how a vehicle routing problem (VRP) can be solved on the quantum computer. A VRP is a generalized Traveling Salesperson Problem (TSP) in which a round trip has to be divided among several agents (trucks). The Jupyter Notebook first explains how a VRP can be understood as a so-called Quadratic Unbounded Binary Optimization (QUBO) problem and then how it can be coded for the quantum computer. Examples are used to illustrate how many qubits are required to solve each problem. Finally, it is possible to interactively execute the QAOA algorithm (as a simulation) for a single example and to change optimization parameters and the circuit depth. In the second phase of the project, we systematically investigated the DWave hardware in terms of TSP to achieve better performance. We looked at the asymmetric and symmetric distribution of the cities to see if symmetry helps in finding the correct solution and found that this is indeed the case. We will carry out the calculations in the second project phase with the VQE algorithm instead of QAOA. This was run interactively (as a simulation) for a single example, whereby the optimization parameters and the circuit depth were changed. The demonstrator will be published at the end of the project in spring 2024 published on this page.
Computational fluid dynamics (VQLS)
In this demonstrator, we show how to solve partial differential equations on a quantum computer using a linear system of equations. Three Jupyter Notebooks make up the demonstrator. In the first notebook, the theory for converting partial differential equations into linear systems of equations using finite difference methods is presented together with an interactive code for solving the equations. The quantum algorithm VQLS is the focus of the second and third notebook. The second notebook discusses the theory and implementation of the global cost function, explains the code and illustrates the results using an illustrative example. In the third notebook we use another simple example to discuss local cost function theory and implementation.
Quantum Application Lifecycle Management (QuAntiL): Modularised interface architecture for workflow-based execution of quantum software
This work has been carried out in close cooperation with the PlanQK-project.
Disclaimer
The interactive demonstrator notebooks have been licensed under the Apache licence (version 2.0). The files may only be used in accordance with the licence. A copy of the licence can be downloaded from http://www.apache.org/licenses/LICENSE-2.0 Except as required by applicable law or agreed to in writing, software distributed under this licence is distributed on an »AS IS« basis, without warranties or conditions of any kind, either express or implied. See the licence for the specific rights and restrictions associated with it.
This is a research prototype. Liability for loss of profit, loss of production, business interruption, loss of use, loss of data and information, financing costs and other financial and consequential damage is excluded, except in cases of gross negligence, intent and personal injury.