Fig. 2: Quantum circuits for Krylov quantum diagonalization.
From: Krylov diagonalization of large many-body Hamiltonians on a quantum processor
a Each circuit performs the controlled preparation of an initial state within the target particle sector, followed by a Trotterized time evolution. b The controlled preparation prepares a computational basis state in which the Hamming weight corresponds to the number of particles for the given experiment, controlled on the auxiliary qubit. Since the heavy-hex lattice can be edgewise three-colored (colors given in the figure by red, green, and blue), both the controlled preparation and the Trotterized time evolution can be implemented using sequences of three unique two-qubit gate layers interleaved with single-qubit rotations. See the main text for details. c Each layer of two-qubit gates is Pauli twirled in order to tailor the noise to a sparse Pauli-Lindblad noise model Λ43,44, preceded by its amplification ΛG for PEA. Note that adjacent layers of single-qubit gates, originating from either the source circuit, the twirling, or the noise amplification layer, are always combined in a single layer; they are left unmerged in the figure for clarity. d (12 + 1)-qubit example of the CZ layers.
