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Abstract Hybrid quantum-classical approaches offer potential solutions to quantum chemistry problems, yet they often manifest as constrained optimization problems. Here, we explore the interconnection between constrained optimization and generalized eigenvalue problems through the Unitary Coupled Cluster (UCC) excitation generators. Inspired by the generator coordinate method, we employ these UCC excitation generators to construct non-orthogonal, overcomplete many-body bases, projecting the system Hamiltonian into an effective Hamiltonian, which bypasses issues such as barren plateaus that heuristic numerical minimizers often encountered in standard variational quantum eigensolver (VQE). Diverging from conventional quantum subspace expansion methods, we introduce an adaptive scheme that robustly constructs the many-body basis sets from a pool of the UCC excitation generators. This scheme supports the development of a hierarchical ADAPT quantum-classical strategy, enabling a balanced interplay between subspace expansion and ansatz optimization to address complex, strongly correlated quantum chemical systems cost-effectively, setting the stage for more advanced quantum simulations in chemistry. 

This article investigates block-level interference exploitation (IE) precoding for multiuser multiple-input-single-output (MU-MISO) downlink systems. To overcome the need for symbol-level IE precoding to frequently update the precoding matrix, we propose to jointly optimize all the precoders or transmit signals within a transmission block. The resultant precoders only need to be updated once per block, and while not necessarily constant over all the symbol slots, we refer to the technique as block-level slot-variant IE precoding. Through a careful examination of the optimal structure and the explicit duality inherent in block-level power minimization (PM) and signal-to-interference-plus-noise ratio (SINR) balancing (SB) problems, we discover that the joint optimization can be decomposed into subproblems with smaller variable sizes. As a step further, we propose block-level slot-invariant IE precoding by adding a structural constraint on the slot-variant IE precoding to maintain a constant precoder throughout the block. A novel linear precoder for IE is further presented, and we prove that the proposed slot-variant and slot-invariant IE precoding share an identical solution when the number of symbol slots does not exceed the number of users. Numerical simulations demonstrate that the proposed precoders achieve a significant complexity reduction compared against benchmark schemes, without sacrificing performance.