Integrating subsystem embedding subalgebras and coupled cluster Green’s function: a theoretical foundation for quantum embedding in excitation manifold

Bo Peng, Karol Kowalski

arXiv:2310.17172Electronic StructureJan 12, 20243 citations

Quantum

Hybrid quantum-classical approach for coupled-cluster Green's function theory

Trevor Keen, Bo Peng, Karol Kowalski, Pavel Lougovski, Steven Johnston

Published Mar 30, 2022• 8 citations

Publisher

Abstract

DOI: 10.22331/q-2022-03-30-675

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Hybrid quantum-classical approach for coupled-cluster Green's function theory

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Integrating subsystem embedding subalgebras and coupled cluster Green’s function: a theoretical foundation for quantum embedding in excitation manifold

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arXiv:2310.17172Electronic StructureJan 12, 20243 citations

T

gates that grows as $ \mathcal{O} \left(N^5 \right)$ per time step to calculate the impurity Green's function in the time domain, where

N

is the total number of energy levels in the AIM. Since the number of

T

gates is analogous to the computational time complexity of a classical simulation, we achieve an order of magnitude improvement over a classical CCGF calculation of the same order, which requires $ \mathcal{O} \left(N^6 \right)$ computational resources per time step.

δ

in time

\mathrm{poly}(n,δ^{-1})

, and (2) estimate the partition function at inverse temperature

β

to relative precision

δ

in time

\mathrm{poly}(n,β,δ^{-1})

, where

n

is the system size. These results improve the previous best-known complexity for ground-state energy estimation from quasipolynomial to polynomial time, while establishing for the first time rigorous polynomial-time guarantees for simulating impurity models in thermal equilibrium. On the other hand, we find that simulating dynamical properties of impurity models is hard for classical computers but easy on a quantum computer. As a canonical example, we show that computing their nonequilibrium Green's functions captures the full power of quantum computation, even at finite temperature. Taken together, our results rule out superpolynomial quantum speedups for computing static properties, but provide an avenue for quantum advantage in simulating impurity physics out of equilibrium.