Effective calculation of the Green's function in the time domain on near-term quantum processors

Libbi, Francesco; Rizzo, Jacopo; Tacchino, Francesco; Marzari, Nicola; Tavernelli, Ivano

doi:10.48550/arxiv.2203.12372

Cited by 1 publication

(2 citation statements)

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“…The orthogonalized Krylov states are defined iteratively in Eqs. (10)(11)(12). As discussed there, these states are linear combinations of powers of Ĥ applied to the state |χ 0 =c † |GS .…”

Section: B Basis For the Green's Functionmentioning

confidence: 99%

“…[9][10][11] propose to reduce the circuit depth required for the time evolution by using a variational quantum algorithm (VQA), where the accuracy of the time evolution relies on the accuracy of the variational quantum circuit optimization. A recent work proposes to use the McLachlan variational principle to compute the GF in real time [10,12].…”

Section: Introductionmentioning

confidence: 99%

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Quantum subspace expansion algorithm for Green's functions

Jamet¹,

Agarwal²,

Rungger³

2022

Preprint

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We present an algorithm to compute Green's functions on quantum computers for interacting electron systems, which is a challenging task on conventional computers. It uses a continued fraction representation based on the Lanczos method, where the wave functions are expanded as linear combination of basis states within a quantum subspace. While on conventional computers the cost of the computation grows exponentially with system size, limiting the method to small systems, by representing the basis states on a quantum computer one may overcome this exponential scaling barrier. We propose a two-level multigrid Trotter time evolution for an efficient preparation of the basis states in a quantum circuit, which takes advantage of the robustness of the subspace expansion against Trotter errors. Using a quantum emulator we demonstrate the algorithm for the Hubbard model on a Bethe lattice with infinite coordination, which we map to a 16 qubit Anderson impurity model within the dynamical mean field theory. Our algorithm computes the Green's function accurately for both the metallic and Mott insulating regimes, with a circuit depth several orders of magnitude below what has been proposed using time evolution. The two-level multigrid time evolution reduces the number of Trotter steps required to compute the Green's function to about four to six. We therefore expect that the method can be used on near term quantum computers for moderate system sizes, while allowing for scalability to larger circuit depths and qubit numbers on future fault tolerant quantum computers.

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Section: B Basis For the Green's Functionmentioning

confidence: 99%