Quantum Algorithms: A Potential Game-Changer for Geologic Fracture Network Modeling

Quantum algorithms could revolutionize how we solve linear systems, which are crucial in fields such as medicine, finance, and science. However, these algorithms come with challenges, including the need to satisfy algorithm-specified constraints and the complexity of transporting information to and from the quantum computer. This paper explores these issues in the context of geologic fracture networks, which are too large to solve entirely with classical approaches. The paper also discusses methods for state preparation and information extraction that human developers use, even on noisy near-term quantum hardware.

How Can Quantum Algorithms Revolutionize Geologic Fracture Networks?

Quantum algorithms can potentially revolutionize the way we solve linear systems, which are essential components of problems in various fields such as medicine, finance, urban development, and natural or applied science. These algorithms can provide an exponential speedup over classical linear solvers, but this remarkable gain does not come without its challenges.

The problems of interest must be curated to satisfy algorithm-specified constraints. Moreover, the quantum algorithms must account for the complexity of transporting information to and from the quantum computer via processes that bear little resemblance to classical counterparts. Otherwise, all theoretical intrigue aside, quantum linear-systems algorithms become toothless. We know the algorithm could compute the solution exponentially faster than possible classically, but we can neither supply the problem nor extract the solution efficiently enough to benefit from this speedup.

These difficulties are further complicated by context-specific considerations. For example, it would be pointless to prepare and solve a linear system if we cannot extract information that is of practical relevance for the problem at hand. Consequently, efficient approaches for both preparing the system to be solved and extracting useful information from quantum computers are as important as quantum algorithms themselves.

What Are the Challenges and Solutions in Applying Quantum Algorithms to Geologic Fracture Networks?

This paper addresses these issues within the context of quantum algorithms for geologic fracture networks. Linear systems representing fracture networks are too large to solve in their entirety with even the most sophisticated classical approaches, and reducing problem size requires methods such as upscaling, which supply only approximate solutions that may neglect important features of the network.

For example, when small fractures are neglected, a network exhibiting percolation—complete connectivity of a fracture region—might no longer manifest that effect. Such modeling issues make geologic fracture problems a prime candidate for benefiting from the speedup provided by quantum algorithms, so long as we can satisfy the algorithmic constraints and provide efficient state preparation and information extraction.

Previous work has addressed solving fracture flow problems with quantum algorithms while making assumptions about the auxiliary issues. This work addresses two further requirements for solving geologic fracture flow systems with quantum algorithms: efficient system state preparation and efficient information extraction.

How Can Quantum Algorithms Improve the Modelling of Geologic Fracture Networks?

The remainder of the paper proceeds as follows. We first provide an introduction to modeling geologic fracture networks with linear systems, including the relationship to quantum algorithms. We then present methods for state preparation and information extraction that have acceptable complexities and that are readily usable by human developers, including on noisy near-term quantum hardware.

We include toy examples for both the state preparation and information extraction approaches to clarify method usage. Finally, we conclude with a brief discussion of future work, which includes empirical study of efficient start-to-finish solution of varying-scale geologic fracture problems on newly-available higher-qubit, less error-prone quantum hardware.

What is the Future of Quantum Algorithms in Geophysics?

Simulating geologic fracture networks is one of the most challenging problems in geophysics, in part because of the large range over which fractures exist. Systems modeling fractures with sizes between 10^6 and 10^4 m cannot be solved accurately in their entirety on classical machines, and they sometimes cannot be accurately upscaled either.

Specifically, information lost during upscaling pertains to small fractures that can have a critical effect on the fracture network. For example, the smallest fractures can determine whether the network crosses a percolation threshold, which has a substantial impact on fluid flow.

Quantum algorithms for solving linear systems are not burdened by the same constraints as their classical counterparts. The properties of quantum mechanics endow them with a fundamentally different approach to problem-solving, which could potentially revolutionize the field of geophysics.