email: yu_tong at berkeley dot edu

I am moving to Caltech as an IQIM Postdoctoral Scholar. I obtained my Ph.D. in Applied Mathematics from UC Berkeley in 2022, advised by Lin Lin, and my B.S. degree in computational mathematics from Peking University in 2017. I am broadly interested numerical analysis, quantum computing, computational physics, and computational chemistry.

**Quantum algorithms:** Quantum computers are naturally suited to solve problems arising in quantum chemistry, for which classical algorithms suffer from high computational cost and low accuracy. I am interested in developing quantum algorithms to solve problems such as estimting the ground energy, Green's function, etc., as well as addressing problems in practical implementations on near-term devices.

**Tensor network methods:** Tensor networks provide us with the basic tools to understand quantum systems. They also offer useful computational methods in solving quantum chemistry and quantum physics problems. I am interested in both theoretical analysis of existing tensor network algorithms and the development of new ones.

**Quantum embedding methods:** Given the prohibitive computational cost of dealing with a quantum system of large size on a classical computer, a natural idea is to decompose the system into smaller subsystems and solve for each subsystem. The interaction between a subsystem and the environment leads to many interesting computational tasks.

[1] G. H. Low, Y. Su, **Y. Tong**, M. C. Tran, *On the complexity of implementing Trotter steps*
[arXiv:2211.09133]

[2] H.-Y. Huang, **Y. Tong**, D. Fang, Y. Su, *Learning many-body Hamiltonians with Heisenberg-limited scaling*
[arXiv:2210.03030]
[QIP 2023 Talk]

[3] D. Fang, L. Lin, **Y. Tong**, *Time-marching based quantum solvers for time-dependent linear differential equations*
[arXiv:2208.06941]

[4] Y. Dong, L. Lin, **Y. Tong**, *Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices*
[arXiv:2204.05955]

[5] N. Abrahamsen, **Y. Tong**, N. Bao, Y. Su, N. Wiebe, *Entanglement area law for 1D gauge theories and bosonic systems *
[arXiv:2203.16012]
[QIP 2023 Talk]

[6] **Y. Tong**, V. V. Albert, J. R. McClean, J. Preskill, Y. Su, *Provably accurate simulation of gauge theories and bosonic systems *
[arXiv:2110.06942]
[QIP 2022 Talk]

[7] L. Lin and **Y. Tong**, *Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers*, PRX Quantum
[doi]
[arXiv:2102.11340]

[8] **Y. Tong**, D. An, N. Wiebe, L. Lin, *Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions*, Phys. Rev. A
[doi]
[arXiv:2008.13295]

[9] L. Lin and **Y. Tong**, *Near-optimal ground state preparation*, Quantum
[doi]
[arXiv:2002.12508]
[QIP 2021 Talk]

[10] L. Lin and **Y. Tong**, *Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems*, Quantum
[doi]
[arXiv:1910.14596]

[11] L. Lin and **Y. Tong**, *Low-rank representation of tensor network operators with long-range pairwise interactions*, SIAM J. Sci. Comput.
[doi]
[arXiv:1909.02206]

[12] X. Wu, M. Lindsey, T. Zhou, **Y. Tong**, and L. Lin, *Enhancing robustness and efficiency of density matrix embedding theory via semidefinite programming and local correlation potential fitting*, Phys. Rev. B
[doi]
[arXiv:2003.00873]

[13] X. Wu, Z.-H. Cui, **Y. Tong**, M. Lindsey, G. K.-L. Chan, and L. Lin, *Projected density matrix embedding theory with applications to the two-dimensional Hubbard model*, J. Chem. Phys.
[doi]
[arXiv:1905.00886]