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Computations of chemical systems' equilibrium properties and non-equilibrium dynamics have been suspected of being a "killer app" for quantum computers. This review highlights the recent advancements of quantum algorithms tackling complex sampling tasks in the key areas of computational chemistry: ground state, thermal state properties, and quantum dynamics calculations. We review a broad range of quantum algorithms, from hybrid quantum-classical to fully quantum, focusing on the traditional Monte Carlo family, including Markov chain Monte Carlo, variational Monte Carlo, projector Monte Carlo, path integral Monte Carlo, etc. We also cover other relevant techniques involving complex sampling tasks, such as quantum-selected configuration interaction, minimally entangled typical thermal states, entanglement forging, and Monte Carlo-flavored Lindbladian dynamics. We provide a comprehensive overview of these algorithms' classical and quantum counterparts, detailing their theoretical frameworks and discussing the potentials and challenges in achieving quantum computational advantages., Comment: 35 pages, 12 figures

ipie is a Python-based auxiliary-field quantum Monte Carlo (AFQMC) package that has undergone substantial improvements since its initial release [J. Chem. Theory Comput., 2022, 19(1): 109-121]. This paper outlines the improved modularity and new capabilities implemented in ipie. We highlight the ease of incorporating different trial and walker types and the seamless integration of ipie with external libraries. We enable distributed Hamiltonian simulations, allowing for multi-GPU simulations of large systems. This development enabled us to compute the interaction energy of a benzene dimer with 84 electrons and 1512 orbitals, which otherwise would not have fit on a single GPU. We also support GPU-accelerated multi-slater determinant trial wavefunctions [arXiv:2406.08314] to enable efficient and highly accurate simulations of large-scale systems. This allows for near-exact ground state energies of multi-reference clusters, [Cu$_2$O$_2$]$^{2+}$ and [Fe$_2$S$_2$(SCH$_3$)]$^{2-}$. We also describe implementations of free projection AFQMC, finite temperature AFQMC, AFQMC for electron-phonon systems, and automatic differentiation in AFQMC for calculating physical properties. These advancements position ipie as a leading platform for AFQMC research in quantum chemistry, facilitating more complex and ambitious computational method development and their applications., Comment: 17 pages, 13 figures

In this work, we report, for the first time, an implementation of fermionic auxiliary-field quantum Monte Carlo (AFQMC) using matrix product state (MPS) trial wavefunctions, dubbed MPS-AFQMC. Calculating overlaps between an MPS trial and arbitrary Slater determinants up to a multiplicative error, a crucial subroutine in MPS-AFQMC, is proven to be #P-hard. Nonetheless, we tested several promising heuristics in successfully improving fermionic phaseless AFQMC energies. We also proposed a way to evaluate local energy and force bias evaluations free of matrix-product operators. This allows for larger basis set calculations without significant overhead. We showcase the utility of our approach on one- and two-dimensional hydrogen lattices, even when the MPS trial itself struggles to obtain high accuracy. Our work offers a new set of tools that can solve currently challenging electronic structure problems with future improvements., Comment: 24 pages, 20 figures

Strong evidence of the existence of the Stochastic Gravitational-Wave Background (SGWB) has been reported by the NANOGrav, PPTA, EPTA and CPTA collaborations. The Bayesian posteriors of the Gravitational-Wave Background (GWB) amplitude and spectrum are compatible with current astrophysical predictions for the GWB from the population of supermassive black hole binaries (SMBHBs). In this paper, we discuss the corrections arising from the extra scalar or vector radiation to the characteristic dimensionless strain in PTA experiments and explore the possibility to detect charges surrounding massive black holes, which could give rise to SGWB with vector or scalar polarizations. The parametrized frequency-dependent characteristic dimensionless strain is used to take a Bayesian analysis and the Bayes factor is also computed for charged and neutral SMBHBs. The Bayesian posterior of GWB tensor amplitude is $\log_{10} A_T=-14.85^{+0.26}_{-0.38}$ and spectral exponent $\alpha=-0.60^{+0.32}_{-0.36}$. The Bayesian posterior for vector or scalar amplitude $A_{V, S}$ is nearly flat and there is nearly no constraint from the current observation data. The Bayesian factor is $0.71$ far less than 100, so the current observation can not support the existence of the charged SMBHB., Comment: 15 pages, 3 figures; Comments are welcome

The accurate sky localization of gravitational wave (GW) sources is an important scientific goal for space-based GW detectors. Due to the effects of gravity on three spacecrafts, it is hard to maintain the equality of the arm length, so the time-delay interferometry (TDI) method is needed to cancel out the laser frequency noise for space-based GW detectors. By considering the first-generation TDI combination, we employ the Fisher information matrix to study the accuracy of sky localizations for future space-based GW detectors and their combined network. The main difference between future space-based GW detectors includes the time-changing orientation of the detector plane, the arm length, the orbital period of spacecrafts and the noise curve. We study the effects of these factors on the accuracy of source localization at different frequencies. We find that the amplitude modulation caused by the rotation of the detector plane can help LISA and Taiji not only to improve the accuracy of source localization but also to enlarge the sky coverage at frequencies below 1 mHz. As the frequency of monochromatic GWs increases, the Doppler modulation becomes dominate and the equatorial pattern appears in the sky map. The effect of arm length on the angular resolution mainly comes from the noise curve and it is almost the same for both heliocentric and geocentric constellations. The orbital period of the spacecrafts has little effect on the angular resolutions. The improvement on the angular resolutions by the network of combined detectors is small compared with a single detector and the angular resolutions are almost the same with and without the TDI combination., Comment: 24 pages, 8 figures

Using the analytic, static and spherically symmetric metric for a Schwarzschild black hole immersed in dark matter (DM) halos with Hernquist type density distribution, we derive analytic formulae for the orbital period and orbital precession, the evolutions of the semi-latus rectum and the eccentricity for eccentric EMRIs with the environment of DM halos. We show how orbital precessions are decreased and even reverse the direction if the density of DM halo is large enough. The presence of local DM halos slows down the decrease of the semi-latus rectum and the eccentricity. Comparing the number of orbital cycles with and without DM halos over one-year evolution before the merger, we find that DM halos with the compactness as small as $10^{-4}$ can be detected. By calculating the mismatch between GW waveforms with and without DM halos, we show that we can use GWs from EMRIs in the environments of galaxies to test the existence of DM halos and detect the compactness as small as $10^{-5}$., Comment: 21 pages, 6 figures

Exciton coherence length (ECL) is an essential concept to characterize the nature of exciton in molecular aggregates for photosynthesis, organic photovoltaics, and light-emitting diodes. ECL has been defined in a number of ways through the variance or purity of the electronic reduced density matrix. However, we find that these definitions fail to present a monotonic relationship with respect to the exciton radiative decay efficiency as it should be when exciton-phonon couplings are taken into accounts. We propose a unified definition of ECL by virtue of sum rule of oscillator strengths. Using the numerically accurate time-dependent matrix product states formalism applied to Frenkel-Holstein models for molecular aggregates in both one- and two-dimensional system, we find our ECL definition exhibits a monotonic relationship with respect to the radiative efficiency and can serve as an efficient and unified description for exciton coherence. We further predict that the two-dimensional aggregates can display maximum superradiance enhancement (SRE) at finite temperature, different from the previous knowledge of SRE-$1/T$ behavior.

The dark matter (DM) distributed around an intermediate massive black hole (IMBH) forms an overdensity region called DM minispike. We consider the binary system which consists of an IMBH with DM minispike and a small black hole inspiralling around the IMBH in eccentric orbits. The factors which affect the evolution of the orbit include the gravity of the system, the dynamical friction and accretion of the small black hole caused by the DM minispike, and the radiation reaction of gravitational waves (GWs). Using the method of osculating orbit, we find that when the semilatus rectum p<<10^5 Rs (Rs is the Schwarzschild radius of the IMBH) the dominated factors are the dynamical friction and accretion from the DM minispike, and the radiation reaction. When p>>10^5 Rs, the gravity from the DM minispike dominates the orbital evolution. The existence of DM minispike leads to the deviation from the Keplerian orbit, such as extra orbital precession, henceforth extra phase shift in the GW waveform. By calculating the signal-to-noise ratio for GWs with and without DM minispikes and the mismatch between them, we show that the effect of the DM minispike in GW waveforms can potentially be detected by future space-based GW detectors such as LISA, Taiji, and Tianqin., Comment: 29 pages, 13 figures, 1 table; Comments are welcome

Intermediate/Extreme mass ratio inspiral (I/EMRI) system provides a good tool to test the nature of gravity in strong field. Based on the method of osculating orbits, we compute the orbital evolutions of I/EMRIs on quasi-elliptic orbits in both Einstein's general relativity and Brans-Dicke theory. The extra monopolar and dipolar channels in Brans-Dicke theory accelerate the orbital decay, so it is important to consider the effects of monopolar and dipolar emissions on the waveform. With the help of accurate orbital motion, we generate waveform templates which include both monopolar and dipolar contributions for I/EMRIs on eccentric orbits in Brans-Dicke theory. With a two-year observation of gravitational waves emitted from I/EMRIs by LISA, we get the most stringent constraint on the Brans-Dicke coupling parameter $\omega_0>10^6$., Comment: Major revision by adding discussions on more mass ratios, but conclusions are strengthened, matched to the published JCAP version

Constructing matrix product operators (MPO) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For DMRG to be conveniently used in different problems described by different Hamiltonians, in this work we propose a new generic algorithm to construct the MPO of an arbitrary operator with a sum-of-products form based on the bipartite graph theory. We show that the method has the following advantages: (i) It is automatic in that only the definition of the operator is required; (ii) It is symbolic thus free of any numerical error; (iii) The complementary operator technique can be fully employed so that the resulting MPO is globally optimal for any given order of degrees of freedom; (iv) The symmetry of the system could be fully employed to reduce the dimension of MPO. To demonstrate the effectiveness of the new algorithm, the MPOs of Hamiltonians ranging from the prototypical spin-boson model and Holstein model to the more complicated ab initio electronic Hamiltonian and the anharmonic vibrational Hamiltonian with sextic force field are constructed. It is found that for the former three cases, our automatic algorithm can reproduce exactly the same MPOs as the optimally hand-crafted ones already known in the literature., Comment: 31 pages, 6 figures