Model Predictive Control for Finite Input Systems using the D-Wave Quantum Annealer

Abstract

The D-Wave quantum annealer has emerged as a novel computational architecture that is attracting significant interest, but there have been only a few practical algorithms exploiting the power of quantum annealers. Here we present a model predictive control (MPC) algorithm using a quantum annealer for a system allowing a finite number of input values. Such an MPC problem is classified as a non-deterministic polynomial-time-hard combinatorial problem, and thus real-time sequential optimization is difficult to obtain with conventional computational systems. We circumvent this difficulty by converting the original MPC problem into a quadratic unconstrained binary optimization problem, which is then solved by the D-Wave quantum annealer. Two practical applications, namely stabilization of a spring-mass-damper system and dynamic audio quantization, are demonstrated. For both, the D-Wave method exhibits better performance than the classical simulated annealing method. Our results suggest new applications of quantum annealers in the direction of dynamic control problems. 2/11 11/11

Implementation of Quantum Annealing: A Systematic Review

“…It was discovered that 75 combinations of metrics and state-of-theart methods were mapped and compared out of which 60 (80%) stated that the QA performed better, 7 (9.33%) stated they have equivalent performance, and 8 (10.67%) showed that QA has lower performance. The most widely used stateof-the-art method for comparison was found to be simulated annealing as indicated by 21 (42%) of the 50 research which include [130], [149], [152], [154], [161], [168], [171], [189], [212], [217], [218], [223], [229], [238], [239], [242], [243], [246], [249], [251], [252]. This is due to the fact that QA is analogous to simulated annealing (classical approach) but in substitution of thermal activation by quantum tunneling.…”

How to Solve Combinatorial Optimization Problems Using Real Quantum Machines: A Recent Survey

“…Starting from D-Wave One with 128 qubits released in 2011, Advantage with currently available 5640 qubits, and Advantage 2 with more than 7000 qubits are being developed. They have a very large number of qubits compared to the limited number of qubits of current general-purpose quantum computers; thus, COP can be effectively solved using QA technology [6], [7], [34]. Therefore, all of the studies to be discussed in this survey use D-Wave quantum annealer to solve practical-scale COPs.…”

“…C OMBINATORIAL optimization problem (COP) is the problem of finding the optimal solution from a set of feasible solutions [1]- [5]. It is closely related to various fields such as computer science, software engineering, and applied mathematics [6], [7]. Due to the nature of COP, the complexity of the problem increases rapidly as the size of the feasible solution space increases, making it difficult to find an optimal solution [8].…”

Control Implemented on Quantum Computers: Effects of Noise, Nondeterminism, and Entanglement

“…In the process systems engineering field, quantum computers (primarily the D-Wave quantum annealer, though with some analysis of an IBM quantum computer in ref ) have been utilized for fault detection and for optimization related to energy systems. − Applications of quantum computers for control to date have included, for example, the application of fuzzy logic control, reinforcement learning, − and model predictive control (MPC; an optimization-based and model-based control law − ) implemented on a quantum annealer . However, this is a relatively limited set of investigations that does not provide enough data for deeply understanding benefits and limitations of control implemented on quantum computers.…”