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IEEE International Conference on Quantum Computing and Engineering (QCE)

Application of the Variational Quantum Eigensolver to the Ultimate Pit Problem

Yousef Hindy, Jessica Pointing, Meltem Tolunay, Sreeram Venkatarao, Mário Motta, Joseph A. Latone

Published Sep 17, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1109/qce57702.2023.00083

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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.
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.
Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to 18.6×18.6\times18.6× shallower and use up to 12×12\times12× fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least 3.6×3.6\times3.6× less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.
Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to 18.6×18.6\times18.6× shallower and use up to 12×12\times12× fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least 3.6×3.6\times3.6× less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.
Abstract Combinatorial optimization models a vast range of industrial processes aiming at improving their efficiency. In general, solving this type of problem exactly is computationally intractable. Therefore, practitioners rely on heuristic solution approaches. Variational quantum algorithms are optimization heuristics that can be demonstrated with available quantum hardware. In this case study, we apply four variational quantum heuristics running on IBM’s superconducting quantum processors to the job shop scheduling problem. Our problem optimizes a steel manufacturing process. A comparison on 5 qubits shows that the recent filtering variational quantum eigensolver (F-VQE) converges faster and samples the global optimum more frequently than the quantum approximate optimization algorithm (QAOA), the standard variational quantum eigensolver (VQE), and variational quantum imaginary time evolution (VarQITE). Furthermore, F-VQE readily solves problem sizes of up to 23 qubits on hardware without error mitigation post processing.
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 Profitable Tour Problem is a well-known NP-hard optimization challenge central to tourism planning, aiming to maximize collected profit while minimizing travel costs. While classical heuristics provide approximate solutions, they often struggle with finding globally optimal routes. This paper explores the application of near-term quantum computing to this problem. We propose a framework based on the Variational Quantum Eigensolver to find high-quality solutions for the Profitable Tour Problem. The core of our contribution is a novel methodology for constructing a constraint-aware variational ansatz that directly encodes the problem's hard constraints. This approach circumvents the need for large penalty terms in the Hamiltonian problem, which are often a source of optimization challenges. We validate our method through numerical simulations on a representative tourism scenario of up to 25 qubits. The results demonstrate the viability of the approach, achieving high solution accuracy consistent with brute-force enumeration for smaller instances. This work serves as a proof-of-concept for applying Variational Quantum Eigensolver to complex tourism optimization problems and provides a basis for future exploration on real quantum hardware.