Non-unitary Trotter circuits for imaginary time evolution

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• Chiara Leadbeater, University of Cambridge
• Wednesday 03 May 2023, 14:30-15:00
• Unilever Lecture Theatre, Yusuf Hamied Department of Chemistry.

If you have a question about this talk, please contact Lisa Masters.

First Year PhD Report

We propose an imaginary time equivalent of the well-established Pauli gadget primitive for Trotter-decomposed real time evolution on quantum circuits [1]. Imaginary time evolution (ITE) is widely used for obtaining the ground state of a system on classical hardware. Near-term implementations on quantum hardware rely on heuristics, compromising their accuracy [2,3]. As a result, there is growing interest in the development of more natively quantum algorithms. Since it is not possible to implement a non-unitary gate deterministically, we resort to the implementation of probabilistic imaginary time evolution (PITE) algorithms [4-6], which rely on a unitary quantum circuit to simulate a block encoding of the ITE operator – that is, they rely on successful ancillary measurements to evolve the system non-unitarily. This scheme was tested on the transverse Ising model and the fermionic Hubbard model and is demonstrated to converge to the ground state of the system.

[1] C. Leadbeater, N. Fitzpatrick, D. Muñoz Ramo, and A. J. W. Thom, (2023), arXiv: 2304.07917. [2] T. Jones, S. Endo, S. McArdle, X. Yuan, and S. C. Benjamin, Physical Review A 99 , 10.1103/physreva.99.062304 (2019). [3] M. Motta, C. Sun, A. T. K. Tan, M. J. O’Rourke, E. Ye, A. J. Minnich, F. G. S. L. Brandão, and G. K.-L. Chan, Nature Physics 16, 205 (2020). [4] T. Liu, J.-G. Liu, and H. Fan, Quantum Information Processing 20, 10.1007/s11128-021-03145-6 (2021). [5] G.-L. Zhang, D. Liu, and M.-H. Yung, Scientific Reports 11, 13795 (2021). [6] T. Kosugi, Y. Nishiya, H. Nishi, and Y.-i. Matsushita, Phys. Rev. Research 4, 033121 (2022).

This talk is part of the Theory - Chemistry Research Interest Group series.

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