Zhancheng Yao, Martin Sandberg, et al.
MRS Fall Meeting 2024
The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual reduction in circuit depth conferred by variational approaches, this algorithm also enjoys several advantages compared to previously proposed ones. For instance, variational approaches suffer from the need for a large number of measurements. However, the grid encoding of first quantized Hamiltonians only requires measuring in position and momentum bases, irrespective of the system size. Their combination with variational approaches is therefore particularly attractive. Moreover, heuristic variational forms can be employed to overcome the limitation of the hard decomposition of Trotterized first quantized Hamiltonians into quantum gates. We apply this quantum algorithm to the dynamics of several systems in one and two dimensions. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches. We show how they can be significantly attenuated through subspace diagonalization at a cost of an additional 2-qubit gates where is the number of dimensions and is the total number of grid points.
Zhancheng Yao, Martin Sandberg, et al.
MRS Fall Meeting 2024
Marco Antonio Guimaraes Auad Barroca, Rodrigo Neumann Barros Ferreira, et al.
Paraty Quantum Information School and Workshop 2023
Tanvi Gujarati, Nam Nguyen, et al.
ACS Fall 2024
Ismail Akhalwaya, Shashanka Ubaru, et al.
ICLR 2024