Digital quantum simulator for the time-dependent Dirac equation using discrete-time quantum walks

• URL: http://arxiv.org/abs/2305.19568v1
• Date: Wed, 31 May 2023 05:36:57 GMT
• Title: Digital quantum simulator for the time-dependent Dirac equation using discrete-time quantum walks
• Authors: Shigetora Miyashita, Takahiko Satoh, Michihiko Sugawara, Naphan Benchasattabuse, Ken M. Nakanishi, Michal Hajdu\v{s}ek, Hyensoo Choi, Rodney Van Meter
• Abstract summary: We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Our findings indicate that relativistic dynamics is achievable with quantum computers.
• Score: 0.7036032466145112
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in non-relativistic regimes efficiently. However, only some studies have attempted to simulate relativistic dynamics due to its theoretical and computational difficulty. By leveraging the convergence of discrete-time quantum walks to the Dirac equation, we develop a quantum spectral method that approximates smooth solutions with exponential convergence. This mitigates errors in implementing potential functions and reduces the overall gate complexity that depends on errors. We demonstrate that our approach does not require additional operations compared to the asymptotic gate complexity of non-relativistic real-space algorithms. Our findings indicate that simulating relativistic dynamics is achievable with quantum computers and can provide insights into relativistic quantum physics and chemistry.

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