Algorithm Overview: Performs VQE with an algorithm called Rotoselect[1] as the optimizer. This method optimizes parameters one by one to minimize the expected value obtained by fixing all parameters except for one, similar to the Nakanishi-Fujii-Todo[2] method. The difference is that in Rotoselect, not only parameters but also rotation angles are optimized.

[1] https://quantum-journal.org/papers/q-2021-01-28-391/

[2] https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.043158

Algorithm Overview: Performs VQE with HardwareEfficient Real ansatz, Simultaneous Perturbation Stochastic Approximation (SPSA) Optimizer, and Stochastic Shots allocator. Furthermore, it performs Linear Zero Noise Extrapolation three times and outputs the minimum value from the results of VQE and ZNE.

Algorithm Overview: Performs VQE using Simultaneous Perturbation Stochastic Approximation (SPSA) Optimizer and Proportional shots allocator. The ansatz uses the Symmetry Preserving ansatz[1], and the Givens Rotation Gate only on interconnections between unexcited and excited qubits are more useful with large coefficients.

[1] https://www.nature.com/articles/s41534-019-0240-1

Algorithm Overview: Updates the circuit representing the orbital rotation, U, so that E(U) is minimized, where E(U)=<HF|U^\dag H U |HF>. This optimization updates all parameters of the Givens rotation once. Here, E(U) is calculated by measuring the 1RDM <HF|U^\dag a_i^\dag a_j U|HF>. Furthermore, Quantum-Selected Configuration Interaction(QSCI) [1] is performed on U|HF>, and the energy is calculated. The 1RDM measured data is reused, so no new measurements are taken. U is updated on-the-fly, and the minimum value of the QSCI energy is output.

[1] https://arxiv.org/abs/2302.11320