Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model

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_{imp}+N_{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 ω(N_{q})<N_{meas.}≤O(N_{imp}N_{bath}) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green's function we show how initial Krylov vectors can be computed via midcircuit 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 seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic 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, midcircuit measurement-conditioned operations, and the Hadamard test.