Quantum computation with applications in seismic problems

Shahpoor Moradi and Daniel Trad

ABSTRACT

In this report, we motivate the need for quantum computation in seismic problems. We also developed a MATLAB package that simulates the well-known quantum algorithms for general n-qubit states. There are several software packages available to simulate the quan-tum algorithms on classical computers. These packages are useful for expertise in quantum physics. We construct a MATLAB package that aims to simulate the well-known quantum algorithms such as Grover Database Search (GDS) and Quantum Fourier Transform (QFT). This package provides non-experts in quantum physics to play with the simple algorithms to undrestand how quantum algorithms work on an actual quantum computer. The first part of the report deals with the basics of quantum computing, including the definition of ket, bra and various types of quantum gates such as CNOT, SWAP and controlled-U gates. Afterwards, we focus on quantum algorithms for GDS and QFT in detail. Future works will also address the quantum simulation of finite difference modeling needed for seismic wave modeling and inversion. Upcoming part II focuses on the numerical simulation of part I, namely, MATLAB codes for the quantum computational basis generator, random qubit generator with the probability distribution, simulation of GDS and QFT algorithms for general n-qubit states.

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