Unraveling correlated material properties with noisy quantum computers:
Natural orbitalized variational quantum eigensolving of extended impurity
models within a slave-boson approach
- URL: http://arxiv.org/abs/2108.10780v2
- Date: Tue, 1 Mar 2022 13:59:02 GMT
- Title: Unraveling correlated material properties with noisy quantum computers:
Natural orbitalized variational quantum eigensolving of extended impurity
models within a slave-boson approach
- Authors: Pauline Besserve, Thomas Ayral
- Abstract summary: We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy.
We solve a two-impurity embedded model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm.
This paves the way to a controlled solution of the Hubbard model with larger and larger embedded problems solved by quantum computers.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose a method for computing space-resolved correlation properties of
the two-dimensional Hubbard model within a quantum-classical embedding strategy
that uses a Noisy, Intermediate Scale Quantum (NISQ) computer to solve the
embedded model. While previous approaches were limited to purely local,
one-impurity embedded models, requiring at most four qubits and relatively
shallow circuits, we solve a two-impurity model requiring eight qubits with an
advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm.
This iterative scheme, dubbed Natural Orbitalization (NOization), gradually
transforms the single-particle basis to the approximate Natural-Orbital basis,
in which the ground state can be minimally expressed, at the cost of measuring
the one-particle reduced density-matrix of the embedded problem. We show that
this transformation tends to make the variational optimization of existing (but
too deep) ansatz circuits faster and more accurate, and we propose an ansatz,
the Multireference Excitation Preserving (MREP) ansatz, that achieves great
expressivity without requiring a prohibitive gate count. The one-impurity
version of the ansatz has only one parameter, making the ground state
preparation a trivial step, which supports the optimal character of our
approach. Within a Rotationally Invariant Slave Boson embedding scheme that
requires a minimal number of bath sites and does not require computing the full
Green's function, the NOization combined with the MREP ansatz allow us to
compute accurate, space-resolved quasiparticle weights and static self-energies
for the Hubbard model even in the presence of noise levels representative of
current NISQ processors. This paves the way to a controlled solution of the
Hubbard model with larger and larger embedded problems solved by quantum
computers.
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