On the physics of Trotterization

Quantum computing is a new mode of computation that allows qualitative advantage over classical computers for certain tasks. One such task is calculating the lowest energy states of quantum systems. In the near term, a promising quantum algorithm for this task is the variational quantum eigensolver (VQE). In order to realize a VQE, one needs to choose a good ansatz for the ground state. The accuracy of the approximation of the VQE essentially depends on the chosen ansatz. Motivated by unitary coupled cluster (UCC) theory in quantum chemistry, the UCC-ansatz has emerged as a standard in the context of VQEs. Implementation on a quantum circuit for this ansatz however, requires a Suzuki-Trotter approximation. In this thesis, we identify two key approaches in this ”Trotterization” method. We investigate the behaviors of the resulting Trotterization schemes. We found a drastic, system-dependent variation in the performances of the different Trotterization schemes. Therefore we recognize...Show moreQuantum computing is a new mode of computation that allows qualitative advantage over classical computers for certain tasks. One such task is calculating the lowest energy states of quantum systems. In the near term, a promising quantum algorithm for this task is the variational quantum eigensolver (VQE). In order to realize a VQE, one needs to choose a good ansatz for the ground state. The accuracy of the approximation of the VQE essentially depends on the chosen ansatz. Motivated by unitary coupled cluster (UCC) theory in quantum chemistry, the UCC-ansatz has emerged as a standard in the context of VQEs. Implementation on a quantum circuit for this ansatz however, requires a Suzuki-Trotter approximation. In this thesis, we identify two key approaches in this ”Trotterization” method. We investigate the behaviors of the resulting Trotterization schemes. We found a drastic, system-dependent variation in the performances of the different Trotterization schemes. Therefore we recognize that the choice of Trotterization scheme might be crucial for quantum advantage in the near future. Based on the analysis in this research, we propose a system-adapted criterion for efficient Trotterization choice. On top of that, we suggest a new VQE ansatz. For certain systems, this ansatz approximates the ground state considerably more accurately than the other ansatzes considered in this project.Show less

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On the physics of Trotterization