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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. 

Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is that quantum noise is highly unstable and thus it is likely to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the quantum approximate optimization algorithm and the variational quantum eigensolver with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step toward improving the reliability of VQAs influenced by shifted noise from the parameter optimization perspective 

Abstract The baryonic Tully–Fisher relation (BTFR) has applications in galaxy evolution as a test bed for the galaxy–halo connection and in observational cosmology as a redshift-independent secondary distance indicator. This analysis leverages the 31,000+ galaxy Arecibo Legacy Fast ALFA (AreciboL-band Feed Array) Survey (ALFALFA) sample—which provides redshifts, velocity widths, and Hicontent for a large number of gas-bearing galaxies in the local universe—to fit and test an extensive local universe BTFR. The fiducial relation is fit using a 3000-galaxy subsample of ALFALFA, and is shown to be consistent with the full sample. This BTFR is designed to be as inclusive of ALFALFA and comparable samples as possible. Velocity widths measured via an automated method andM_bproxies extracted from survey data can be uniformly and efficiently measured for other samples, giving this analysis broad applicability. We also investigate the role of sample demographics in determining the best-fit relation. We find that the best-fit relations are changed significantly by changes to the sample mass range and to second order by changes to mass sampling, gas fraction, different stellar mass and velocity width measurements. We use a subset of ALFALFA with demographics that reflect the full sample to measure a robust BTFR slope of 3.30 ± 0.06. We apply this relation and estimate source distances, finding general agreement with flow-model distances as well as average distance uncertainties of ∼0.17 dex for the full ALFALFA sample. We demonstrate the utility of these distance estimates by applying them to a sample of sources in the Virgo vicinity, recovering signatures of infall consistent with previous work.