### Abstract

Quantum computing promises to solve efficiently some crucial problems in scientific computing such as computational chemistry, linear systems solving and partial differential equations. Even if actual quantum algorithms for these kind of problems are curently unpractical due to hardware limitations such as coherence times or gate errors, implementing them using quantum simulators is particularly interesting. Algorithmic complexity and real implementation requirements can be evaluated this way, giving a first insight into what might come and what will be possible. This talk will explain how we implemented a 1-dimensional wave equation solver using Hamiltonian simulation on a quantum emulator. The ressource requirements on a quantum computer will also be studied and commented. This talk will end with a quick overview of ongoing and future work in this topic.

Location

École Polytechnique

Route de Saclay, Palaiseau, 91128

**CORRECTION:** We found a bug in the implementation after the presentation. Consequently, the results presented at the end are invalidated: the wave equation solver was not ensuring that the result obtained was within the target precision of the true result.

After fixing the bug, the total number of gates increased. The number of required qubits did not change.

###### PhD student in Quantum Computing

I am a doctoral student currently involved in a PhD on quantum computing algorithms and how they can be applied to speed-up scientific computing.