Quantum Computational Intelligence For Traveltime Seismic Inversion
Quantum Computational Intelligence For Traveltime Seismic Inversion
Quantum Computational Intelligence For Traveltime Seismic Inversion
A. Albino (SENAI CIMATEC), O. Pires (SENAI CIMATEC), R. F. De Souza (SENAI CIMATEC), P. Nogueira (SENAI CIMATEC),
E. Nascimento (SENAI CIMATEC)
Copyright 2022, SBGf - Sociedade Brasileira de Geofı́sica. in an unusual tomographic challenge, implementing a high-
Este texto foi preparado para a apresentação no IX Simpósio Brasileiro de Geofı́sica, resolution algorithm adequate for quantum computing.
Curitiba, 4 a 6 de outubro de 2022. Seu conteúdo foi revisado pelo Comitê Técnico
do IX SimBGf, mas não necessariamente representa a opinião da SBGf ou de seus
Zhao & Zhang (2016) introduced a new stochastic
associados. É proibida a reprodução total ou parcial deste material para propósitos inversion method based on the Quantum Metropolis-
comerciais sem prévia autorização da SBGf.
Hastings method to deal with pre-stack seismic inversion
problems. Zhu et al. (2020) propose a finite difference
Abstract (FD) method solution based on enhanced quantum particle
swarm optimization (QPSO). Their numerical dispersion
Quantum computation is in its early stage of
analysis shows that the optimized FD scheme based on the
implementation. Its capacity has been growing in the
improved QPSO algorithm has a wider spectral coverage
last years but its application in several fields of sciences
and the accuracy error is controlled within a valid range,
is still restricted to oversimplified problems. In this stage,
which means that the improved QPSO algorithm has better
it is important to identify the situations where quantum
capability to find precise global solutions.
computing presents the most promising results to be
prepared when the technology is ready to be deployed. Quantum computing was first proposed by Feynman
The geophysics field has several areas which are limited (1982) as an alternative to solve problems, intractable to
by the current computation capability, among them the classical computing, by performing computational tasks
so-called seismic inversion is one of the most important using quantum phenomena. Algorithms that exploit these
ones, which are strong candidates to benefit from quantum properties have been developed in the last decades,
computing. In this work, we implement an approach for as well as the construction of quantum devices to
traveltime seismic inversion through a near-term quantum perform such tasks, as summarized in Preskill (2021).
algorithm based on gradient-free quantum circuit learning. Current quantum devices still have a considerable noise
We demonstrate that a quantum computer with thousands rate. These devices are called Noisy Intermediate
of qubits, even if noisy, can solve geophysical problems. Scale Quantum (NISQ) computers and handle a relatively
In addition, we compared the convergence of the method small amount of successive operations on an initial
with the variational quantum algorithms. state before the state decoherence processes take place.
However, given these limitations, with the effort of the
scientific community, new noise mitigation techniques and
Introduction algorithms capable of dealing with NISQ computers called
Retrieving the subsurface parameters through seismic Variational Quantum Algorithms (VQAs) have emerged,
inversion is essential for understanding earthquake as can be seen in Cerezo et al. (2021); Zhou et al.
dynamics, dam monitoring, mapping ore deposits, and oil (2020); Peruzzo et al. (2014); Egger et al. (2021). In
reservoirs exploration. However, the application of seismic the works developed by Havlı́ček et al. (2019); Liu et al.
inversion in all these contexts has required an advance in (2021), it was proved mathematically, and demonstrated
computational geoscience, especially when involving 3D through experiments, that NISQ computers can provide an
seismic wave propagation in complex earth environments. exponential advantage in supervised learning problems. In
For these reasons, any new computational techniques with Deshpande et al. (2022), an experiment was performed
possibilities to speed up calculations must be explored to demonstrate a quantum advantage in a mathematically
by the community. Since commercial quantum computing well-defined problem, using a photonic quantum device.
has becoming reality, the geophysical community already More recently, the experiment carried out by Huang
started to prospect its possible uses, for instance . Moradi et al. (2022), demonstrated an exponential advantage in
et al. (2018) provide a perspective of the most suitable a practical problem of learning properties of quantum
method to solve the wave equation, highlighting that systems.
wave equation solution can be performed through linear Many of the problems in geophysics can be modeled and
system equations so that such systems are appropriate for solved through solutions of systems of linear equations.
quantum algorithms being able to solve with exponential Therefore, investigating quantum algorithms capable of
speedup. Greer & O’Malley (2020) introduced an performing such tasks is an important step towards the
iterative algorithm to solve PDE-constrained optimization application of quantum computing in geophysics. The
problems on a quantum annealer. They then used this work proposed by Harrow et al. (2009), addresses a way
method to invert the velocity parameters of the subsurface to use quantum computers to solve linear systems with
using a hybrid approach of classical and quantum exponential advantage over the best classical method.
computing considering some simple models in their The method is known as Harrow Hassidim Lloyd (HHL)
seismic experiments. Sarkar & Levin (2018) addressed Algorithm and takes advantage of Quantum Phase
how to explore the potential power of quantum computing Estimation (QPE) to achieve quantum advantage, which