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Journal of Experimental and Theoretical Physics Letters

Quantum-Assisted Open-Pit Optimization

Georgii Vitalievich Paradezhenko, Anastasiia A. Pervishko, D. Yudin

Published Mar 1, 2024• 1 citation
Publisher

Abstract

With the recent advances in experimental realization of multi-qubit systems the idea of delegating certain real-life optimization tasks to a quantum computer becomes viable. In particular, we herein examine a variational quantum algorithm applied to a three-dimensional problem of open-pit mining, where the core of the classical optimization loop is provided by the probabilistic tensor sampling method. The developed technique is challenged against conventional optimization routines subjected to the essential optimization issues in variational quantum algorithms such as barren plateaus and multiple local minima. We demonstrate that the probabilistic tensor train-based approach allows one to steadily identify the ground state of a given system.

DOI
10.1134/s0021364023604256

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With the recent advances in experimental realization of multi-qubit systems the idea of delegating certain real-life optimization tasks to a quantum computer becomes viable. In particular, we herein examine a variational quantum algorithm applied to a three-dimensional problem of open-pit mining, where the core of the classical optimization loop is provided by the probabilistic tensor sampling method. The developed technique is challenged against conventional optimization routines subjected to the essential optimization issues in variational quantum algorithms such as barren plateaus and multiple local minima. We demonstrate that the probabilistic tensor train-based approach allows one to steadily identify the ground state of a given system.
The determination of optimal open-pit profiles is a well-studied combinatorial optimization problem, with profound technical and conceptual relevance in computational mining. The ongoing evolution of quantum computing hardware and the recent advances of heuristic quantum algorithms make it worthwhile to explore the solution of the open-pit mining problem on quantum computers. In this work, we cast the open-pit mining problem as a Hamiltonian ground-state search problem, which in turn we solve with a dedicated implementation of the variational quantum eigensolver algorithm, and we propose a domain decomposition approach to extend the reach of today's small scale quantum hardware. The procedure is demonstrated on IBMQ devices using four qubits. This is the first example, to the best of our knowledge, of open-pit profile calculations being performed on quantum hardware.
Determining the ultimate pit profile that maximizes the profit while minimizing the cost of mine extraction is a fundamental problem in open-pit mining. The development of quantum computing hardware and advances in heuristic quantum algorithms make it possible to explore quantum computing as a solution for the ultimate pit problem. Here, we cast the ultimate pit problem as a Hamiltonian ground-state search problem, which we approximately solve using the variational quantum eigensolver algorithm. Moreover, we use a domain decomposition approach to extend the reach of today's small-scale quantum hardware. We demonstrate the procedure on IBMQ devices using four qubits. To the best of our knowledge, this is the first attempt to use heuristic quantum algorithms to map small-scale instances of the ultimate pit problem on quantum hardware.
Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum-inspired tensor-network-based algorithm for general locally constrained combinatorial optimization problems. Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem, then encodes the constraints directly into a tensor network state and solves the optimal solution by evolving the system to the ground state of the Hamiltonian. We demonstrate our algorithm with the open-pit mining problem, which results in a quadratic asymptotic time complexity. Our numerical results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems.
This paper presents the application of a quantum optimization technique to a mining problem. A mine planning problem in an open-pit mine is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) model and solved using the Quantum Approximate Optimization Algorithm (QAOA). The problem seeks to maximize the monetary benefit while respecting precedence constraints between blocks and extraction capacity limitations. The methodology is validated through a fictitious copper deposit case study, where the quantum algorithm identifies the optimal extraction, a result validated with Gurobi solver. Although the approach demonstrates technical feasibility, the scalability limitations of current quantum simulators restrict applications to large-scale problems. This work establishes fundamental foundations for applying quantum computing to mine planning challenges and represents a step toward leveraging quantum computational advantages for NP-hard problems in the mining industry.
The problem of the neural network optimization is local minima and flat areas. According to quantum-inspired methods, quantum mechanics, superposition, entanglement and interference are inspirational in order to possibly surpass these constraints in a more efficient manner. Variational quantum algorithms use parameterized quantum circuits parameterized quantum circuits (ansatz) to optimize weights. Quantum kernel methods also take advantage of quantum embeddings in order to transform features better. Hybrid quantum-classical systems incorporate quantum-inspired processing with already known reliability of optimization. There are, however, serious weaknesses that limit implementation. There are exponentially decreasing gradients due to the barren plateau phenomenon that makes it hard to train at scale. The modern quantum machines have a 0.1-1% error and a microsecond coherence time. The overheads in state preparation, the cost of measurement, circuit depth, and poor qubit connectivity are still impediments. The quantum-inspired classical algorithms, which include the tensor networks and optimization heuristics and run-on standard computers, are the most effective in the near future. These come with small advances in certain areas without involving quantum hardware. Although both quantum kernel methods and variational approaches show theoretical potential, the advantages are still small (relative to the advantages of optimized classical methods). Recent evaluations show that quantum benefits are more constrained than originally claimed them to be. Real quantum applications benefits in neural network optimization may only happen 10-20 years ahead, notwithstanding failure resistant quantum hardware and algorithm developments.
Abstract Optimization drives advances in quantum science and machine learning, yet most generative models aim to mimic data rather than to discover optimal answers to challenging problems. Here we present a variational generative optimization network that learns to map simple random inputs into high quality solutions across a variety of quantum tasks. We demonstrate that the network rapidly identifies entangled states exhibiting an optimal advantage in entanglement detection when allowing classical communication, attains the ground state energy of an eighteen spin model without encountering the barren plateau phenomenon that hampers standard hybrid algorithms, and—after a single training run—outputs multiple orthogonal ground states of degenerate quantum models. Because the method is model agnostic, parallelizable and runs on current classical hardware, it can accelerate future variational optimization problems in quantum information, quantum computing and beyond.