I limited the search space by fixing the number of particles and freezing some qubits. As the number of particles increases, the search space grows exponentially, making it difficult to find the ground state.
My first idea is to fix the number of particles to 4, which contributed to limiting the number of basis states. To construct a particle-preserving ansatz, I combined Givens rotation gates and phase rotation gates, which can be implemented with low circuit depth on the ion trap quantum computer.
My second idea is to freeze some qubits to reduce the search space. It is easy to understand that the molecular orbitals with lower energy are more likely to be occupied and the orbitals with higher energy are more likely to be empty. Therefore, I searched which orbitals are likely to be occupied or empty and froze them.
In addition, I applied error mitigation techniques and gradient-free optimization methods to reduce the effect of noise. For the ion trap quantum computer, the dominant noise sources are the depolarizing noise and the measurement error. It is known that the depolarizing noise can be mitigated by amplifying the measurement results. The measurement error can be mitigated by applying the inverse of the measurement error to the measurement results.
In parameter optimization, I used the Nakanishi-Fujii-Todo method, which does not require the gradient of the objective function. I found that the method can be applied not only to Pauli rotation gates but also to Givens rotation gates and phase rotation gates.
Team name:
The Soshun
Team members:
Soshun Naito
Project Description:
I limited the search space by fixing the number of particles and freezing some qubits. As the number of particles increases, the search space grows exponentially, making it difficult to find the ground state. My first idea is to fix the number of particles to 4, which contributed to limiting the number of basis states. To construct a particle-preserving ansatz, I combined Givens rotation gates and phase rotation gates, which can be implemented with low circuit depth on the ion trap quantum computer. My second idea is to freeze some qubits to reduce the search space. It is easy to understand that the molecular orbitals with lower energy are more likely to be occupied and the orbitals with higher energy are more likely to be empty. Therefore, I searched which orbitals are likely to be occupied or empty and froze them.
In addition, I applied error mitigation techniques and gradient-free optimization methods to reduce the effect of noise. For the ion trap quantum computer, the dominant noise sources are the depolarizing noise and the measurement error. It is known that the depolarizing noise can be mitigated by amplifying the measurement results. The measurement error can be mitigated by applying the inverse of the measurement error to the measurement results. In parameter optimization, I used the Nakanishi-Fujii-Todo method, which does not require the gradient of the objective function. I found that the method can be applied not only to Pauli rotation gates but also to Givens rotation gates and phase rotation gates.
Presentation:
https://github.com/SoshunNaito/quantum-algorithm-grand-challenge/blob/main/QAGC_Presentation.pdf
Source code:
https://github.com/SoshunNaito/quantum-algorithm-grand-challenge