Dynamic, Symmetry-Preserving, and Hardware-Adaptable Circuits for Quantum Computing Many-Body States and Correlators of the Anderson Impurity Model
We present a hardware-reconfigurable ansatz on $N_q$-qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with $N_{\text{imp}}+N_{\text{bath}}=N_q/2$ sites, which conserves total charge and spin z-component within each variational search subspace. The many-...
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Main Authors | , , , , , , , |
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Format | Journal Article |
Language | English |
Published |
23.05.2024
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Subjects | |
Online Access | Get full text |
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Summary: | We present a hardware-reconfigurable ansatz on $N_q$-qubits for the
variational preparation of many-body states of the Anderson impurity model
(AIM) with $N_{\text{imp}}+N_{\text{bath}}=N_q/2$ sites, which conserves total
charge and spin z-component within each variational search subspace. The
many-body ground state of the AIM is determined as the minimum over all minima
of $O(N_q^2)$ distinct charge-spin sectors. Hamiltonian expectation values are
shown to require $\omega(N_q) < N_{\text{meas.}} \leq
O(N_{\text{imp}}N_{\text{bath}})$ symmetry-preserving, parallelizable
measurement circuits, each amenable to post-selection. To obtain the
one-particle impurity Green's function we show how initial Krylov vectors can
be computed via mid-circuit measurement and how Lanczos iterations can be
computed using the symmetry-preserving ansatz. For a single-impurity Anderson
model with a number of bath sites increasing from one to six, we show using
numerical emulation that the ease of variational ground-state preparation is
suggestive of linear scaling in circuit depth and sub-quartic scaling in
optimizer complexity. We therefore expect that, combined with time-dependent
methods for Green's function computation, our ansatz provides a useful tool to
account for electronic correlations on early fault-tolerant processors.
Finally, with a view towards computing real materials properties of interest
like magnetic susceptibilities and electron-hole propagators, we provide a
straightforward method to compute many-body, time-dependent correlation
functions using a combination of time evolution, mid-circuit
measurement-conditioned operations, and the Hadamard test. |
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DOI: | 10.48550/arxiv.2405.15069 |