Dynamic, Symmetry-Preserving, and Hardware-Adaptable Circuits for Quantum Computing Many-Body States and Correlators of the Anderson Impurity Model

• URL: http://arxiv.org/abs/2405.15069v1
• Date: Thu, 23 May 2024 21:41:28 GMT
• Title: Dynamic, Symmetry-Preserving, and Hardware-Adaptable Circuits for Quantum Computing Many-Body States and Correlators of the Anderson Impurity Model
• Authors: Eric B. Jones, Cody James Winkleblack, Colin Campbell, Caleb Rotello, Edward D. Dahl, Matthew Reynolds, Peter Graf, Wesley Jones,
• Abstract summary: Hamiltonian expectation values are shown to require $omega(N_q) N_textmeas. leq O(N_textimpN_textbath)$ symmetry-preserving, parallel measurement circuits. Our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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