A quantum algorithm for traveltime tomography

Jorge E. Monsegny, Daniel O. Trad, Donald C. Lawton

Quantum computation is described as a promising paradigm for the future. One of their advantages is the quantum parallelism, that consists in solving many instances of the same problem in a single run. This can be done due to the possibility to set a quantum system in a superposition of states. Although its main limitation is that only one of the states can be read at the end, it is possible to increase the chances of the state we are looking for. In this report we show a framework to pose the traveltime tomography problem, usually solved using gradient methods, as a quantum computing algorithm. This algorithm does a global exploration of the model space using the quantum parallelism. Then it manipulates the quantum phase of their states to increase the chances of reading the model that produces the global minimum. In that way we can read the tomography answer at the end of the quantum computation. Something important to notice is that there is no need to compute gradients or Hessians but only to do forward modelling and residual calculation. In this report we introduce only the notions needed to solve the inverse problem and we show a small example step by step to illustrate how the quantum algorithm works. The algorithm has been coded and run in a quantum simulator.