The Complexity of Quantum Dynamics

IQOQI Quantum Seminar

The power of quantum computers originates from the high complexity ofquantum dynamics. In this talk, I will explore how this complexity arises underthe dynamics of a local Hamiltonian. In the first part, I will introduce acluster expansion method that allows for tight accounting of localityconstraints [1]. The expansion converges at short times, indicating a lowdegree of complexity. Indeed, in this regime, the method leads to anefficient classical algorithm for computing local observables and non-localquantities such as the Loschmidt echo. In the second part of the talk, I willdiscuss quantum algorithms that extend to longer evolution times. Thealgorithms are designed to extract physically relevant observables in anoise-resilient way [2, 3]. I will conclude with an outlook on the utility ofnoisy quantum devices for quantum simulation.

[1] D. S. Wild and Á. M. Alhambra, PRX Quantum 4, 020340 (2023).
[2] Y. Yang, A. Christianen, S. Coll-Vinent, V. Smelyanskiy, M. C. Bañuls, T.E. O’Brien, D. S. Wild, J. I. Cirac, PRX Quantum 4, 030320 (2023).
[3] Y. Yang, A. Christianen, M. C. Bañuls, D. S. Wild, J. I. Cirac, arXiv:2308.10796.

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