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1. Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer

   https://doi.org/10.1039/d2sc05371c  

   Asthana, Ayush; Kumar, Ashutosh; Abraham, Vibin; Grimsley, Harper; Zhang, Yu; Cincio, Lukasz; Tretiak, Sergei; Dub, Pavel A.; Economou, Sophia E.; Barnes, Edwin; et al (March 2023, Chemical Science)

   We present a new hybrid quantum algorithm to estimate molecular excited and charged states on near-term quantum computers following any VQE-based ground state estimation. 

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2. Boosting quantum amplitude exponentially in variational quantum algorithms

   https://doi.org/10.1088/2058-9565/acf4ba  

   Kyaw, Thi Ha; Soley, Micheline B; Allen, Brandon; Bergold, Paul; Sun, Chong; Batista, Victor S; Aspuru-Guzik, Alán (October 2023, Quantum Science and Technology)

   Abstract We introduce a family of variational quantum algorithms, which we coin as quantum iterative power algorithms (QIPAs), and demonstrate their capabilities as applied to global-optimization numerical experiments. Specifically, we demonstrate the QIPA based on a double exponential oracle as applied to ground state optimization of theH₂molecule, search for the transmon qubit ground-state, and biprime factorization. Our results indicate that QIPA outperforms quantum imaginary time evolution (QITE) and requires a polynomial number of queries to reach convergence even with exponentially small overlap between an initial quantum state and the final desired quantum state, under some circumstances. We analytically show that there exists an exponential amplitude amplification at every step of the variational quantum algorithm, provided the initial wavefunction has non-vanishing probability with the desired state and that the unique maximum of the oracle is given by ${\lambda }_1>0$, while all other values are given by the same value $0<{\lambda }_2<{\lambda }_1$(hereλcan be taken as eigenvalues of the problem Hamiltonian). The generality of the global-optimization method presented here invites further application to other problems that currently have not been explored with QITE-based near-term quantum computing algorithms. Such approaches could facilitate identification of reaction pathways and transition states in chemical physics, as well as optimization in a broad range of machine learning applications. The method also provides a general framework for adaptation of a class of classical optimization algorithms to quantum computers to further broaden the range of algorithms amenable to implementation on current noisy intermediate-scale quantum computers. 

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3. Magnetic field effects on the quantum spin liquid behaviors of NaYbS2

   https://doi.org/10.1007/s44214-022-00011-z  

   Wu, Jiangtao; Li, Jianshu; Zhang, Zheng; Liu, Changle; Gao, Yong Hao; Feng, Erxi; Deng, Guochu; Ren, Qingyong; Wang, Zhe; Chen, Rui; et al (December 2022, Quantum Frontiers)

   Abstract Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides Equation missing<#comment/>(Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between Equation missing<#comment/>and Equation missing<#comment/>ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the Equation missing<#comment/>ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions. 

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4. Pathway Selectivity in 2D Electronic‐Vibrational Spectroscopy with Quantum Light

   https://doi.org/10.1002/lpor.202401576  

   Jadoun, Deependra; Yadalam, Hari K; Harbola, Upendra; Chernyak, Vladimir Y; Kizmann, Matthias; Mukamel, Shaul (April 2025, Laser & Photonics Reviews)

   Abstract Pathway selectivity in quantum spectroscopy with entangled photons is a powerful spectroscopic tool. Phase‐matched signals involving classical light contain contributions from multiple material pathways, whereas quantum spectroscopy may allow the selection of individual pathways. 2D electronic‐vibrational spectroscopy (2DEVS) is a four‐wave mixing technique which employs visible and infrared entangled photons. It is showed how the three contributing pathways—ground state bleach, excited state absorption, and excited state emission—can be separated by photon‐number‐resolved coincidence measurements. Entangled photons thus reveal spectral features not visible in the classical signal, with an enhanced spectral resolution. 

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5. Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers

   https://doi.org/10.22331/q-2023-10-11-1136  

   Ding, Zhiyan; Lin, Lin (October 2023, Quantum)

   We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis demonstrates that the algorithm exhibits Heisenberg-limited scaling in terms of circuit depth and total cost. Notably, the proposed quantum circuit utilizes just one ancilla qubit, and with appropriate initial state conditions, it achieves significantly shorter circuit depths compared to circuits based on quantum phase estimation (QPE). Numerical results suggest that compared to QPE, the circuit depth can be reduced by around two orders of magnitude under several settings for estimating ground-state and excited-state energies of certain quantum systems. 

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