Trainable Variational Quantum-Multiblock ADMM Algorithm for Generation Scheduling

The advent of quantum computing can potentially revolutionize how complex problems are solved. This paper proposes a two-loop quantum-classical solution algorithm for generation scheduling by infusing quantum computing, machine learning, and distributed optimization. The aim is to facilitate employing noisy near-term quantum machines with a limited number of qubits to solve practical power system optimization problems such as generation scheduling. The outer loop is a 3-block quantum alternative direction method of multipliers (QADMM) algorithm that decomposes the generation scheduling problem into three subproblems, including one quadratically unconstrained binary optimization (QUBO) and two non-QUBOs. The inner loop is a trainable quantum approximate optimization algorithm (T-QAOA) for solving QUBO on a quantum computer. The proposed T-QAOA translates interactions of quantum-classical machines as sequential information and uses a recurrent neural network to estimate variational parameters of the quantum circuit with a proper sampling technique. T-QAOA determines the QUBO solution in a few quantum-learner iterations instead of hundreds of iterations needed for a quantum-classical solver. The outer 3-block ADMM coordinates QUBO and non-QUBO solutions to obtain the solution to the original problem. The conditions under which the proposed QADMM is guaranteed to converge are discussed. Two mathematical and three generation scheduling cases are studied. Analyses performed on quantum simulators and classical computers show the effectiveness of the proposed algorithm. The advantages of T-QAOA are discussed and numerically compared with QAOA which uses a stochastic gradient descent-based optimizer.Comment: 11 page

Optimizing Information Gathering for Environmental Monitoring Applications

The goal of environmental monitoring is to collect information from the environment and to generate an accurate model for a specific phenomena of interest. We can distinguish environmental monitoring applications into two macro areas that have different strategies for acquiring data from the environment. On one hand the use of fixed sensors deployed in the environment allows a constant monitoring and a steady flow of information coming from a predetermined set of locations in space. On the other hand the use of mobile platforms allows to adaptively and rapidly choose the sensing locations based on needs. For some applications (e.g. water monitoring) this can significantly reduce costs associated with monitoring compared with classical analysis made by human operators. However, both cases share a common problem to be solved. The data collection process must consider limited resources and the key problem is to choose where to perform observations (measurements) in order to most effectively acquire information from the environment and decrease the uncertainty about the analyzed phenomena. We can generalize this concept under the name of information gathering. In general, maximizing the information that we can obtain from the environment is an NP-hard problem. Hence, optimizing the selection of the sampling locations is crucial in this context. For example, in case of mobile sensors the problem of reducing uncertainty about a physical process requires to compute sensing trajectories constrained by the limited resources available, such as, the battery lifetime of the platform or the computation power available on board. This problem is usually referred to as Informative Path Planning (IPP). In the other case, observation with a network of fixed sensors requires to decide beforehand the specific locations where the sensors has to be deployed. Usually the process of selecting a limited set of informative locations is performed by solving a combinatorial optimization problem that model the information gathering process. This thesis focuses on the above mentioned scenario. Specifically, we investigate diverse problems and propose innovative algorithms and heuristics related to the optimization of information gathering techniques for environmental monitoring applications, both in case of deployment of mobile and fixed sensors. Moreover, we also investigate the possibility of using a quantum computation approach in the context of information gathering optimization

Synthetic Aperture Radar Image Segmentation with Quantum Annealing

In image processing, image segmentation is the process of partitioning a digital image into multiple image segment. Among state-of-the-art methods, Markov Random Fields (MRF) can be used to model dependencies between pixels, and achieve a segmentation by minimizing an associated cost function. Currently, finding the optimal set of segments for a given image modeled as a MRF appears to be NP-hard. In this paper, we aim to take advantage of the exponential scalability of quantum computing to speed up the segmentation of Synthetic Aperture Radar images. For that purpose, we propose an hybrid quantum annealing classical optimization Expectation Maximization algorithm to obtain optimal sets of segments. After proposing suitable formulations, we discuss the performances and the scalability of our approach on the D-Wave quantum computer. We also propose a short study of optimal computation parameters to enlighten the limits and potential of the adiabatic quantum computation to solve large instances of combinatorial optimization problems.Comment: 13 pages, 6 figures, to be published in IET Radar, Sonar and Navigatio

Towards Quantum Belief Propagation for LDPC Decoding in Wireless Networks

We present Quantum Belief Propagation (QBP), a Quantum Annealing (QA) based decoder design for Low Density Parity Check (LDPC) error control codes, which have found many useful applications in Wi-Fi, satellite communications, mobile cellular systems, and data storage systems. QBP reduces the LDPC decoding to a discrete optimization problem, then embeds that reduced design onto quantum annealing hardware. QBP's embedding design can support LDPC codes of block length up to 420 bits on real state-of-the-art QA hardware with 2,048 qubits. We evaluate performance on real quantum annealer hardware, performing sensitivity analyses on a variety of parameter settings. Our design achieves a bit error rate of $10^{-8}$ in 20 $\mu$s and a 1,500 byte frame error rate of $10^{-6}$ in 50 $\mu$s at SNR 9 dB over a Gaussian noise wireless channel. Further experiments measure performance over real-world wireless channels, requiring 30 $\mu$s to achieve a 1,500 byte 99.99$\%$ frame delivery rate at SNR 15-20 dB. QBP achieves a performance improvement over an FPGA based soft belief propagation LDPC decoder, by reaching a bit error rate of $10^{-8}$ and a frame error rate of $10^{-6}$ at an SNR 2.5--3.5 dB lower. In terms of limitations, QBP currently cannot realize practical protocol-sized ($\textit{e.g.,}$ Wi-Fi, WiMax) LDPC codes on current QA processors. Our further studies in this work present future cost, throughput, and QA hardware trend considerations

Squeezing and quantum approximate optimization

Variational quantum algorithms offer fascinating prospects for the solution of combinatorial optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations therein remain unclear. Here, we shed light on this open issue by establishing a tight connection to the seemingly unrelated field of quantum metrology: Metrological applications employ quantum states of spin-ensembles with a reduced variance to achieve an increased sensitivity, and we cast the generation of such squeezed states in the form of finding optimal solutions to a combinatorial MaxCut problem with an increased precision. By solving this optimization problem with a quantum approximate optimization algorithm (QAOA), we show numerically as well as on an IBM quantum chip how highly squeezed states are generated in a systematic procedure that can be adapted to a wide variety of quantum machines. Moreover, squeezing tailored for the QAOA of the MaxCut permits us to propose a figure of merit for future hardware benchmarks.Comment: 8+7 pages, 4+8 figure