@article{liu_meitei_chin_dutt_tao_chuang_van voorhis_2023, title={Bootstrap Embedding on a Quantum Computer}, volume={19}, ISSN={1549-9618 1549-9626}, url={http://dx.doi.org/10.1021/acs.jctc.3c00012}, DOI={10.1021/acs.jctc.3c00012}, abstractNote={We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.}, number={8}, journal={Journal of Chemical Theory and Computation}, publisher={American Chemical Society (ACS)}, author={Liu, Yuan and Meitei, Oinam R. and Chin, Zachary E. and Dutt, Arkopal and Tao, Max and Chuang, Isaac L. and Van Voorhis, Troy}, year={2023}, month={Mar}, pages={2230–2247} }
 @article{martyn_liu_chin_chuang_2023, title={Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation}, volume={158}, ISSN={0021-9606 1089-7690}, url={http://dx.doi.org/10.1063/5.0124385}, DOI={10.1063/5.0124385}, abstractNote={Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 − δ while only requiring a single copy of the initial state. We subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: Θ‖H‖|t|+ln(1/ϵ)+ln(1/δ). Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.}, number={2}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Martyn, John M. and Liu, Yuan and Chin, Zachary E. and Chuang, Isaac L.}, year={2023}, month={Jan} }
 @book{tan_liu_tran_chuang_2023, title={Error Correction of Quantum Algorithms: Arbitrarily Accurate Recovery Of Noisy Quantum Signal Processing}, DOI={10.48550/arXiv.2301.08542}, abstractNote={The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by $\epsilon < 1$ is introduced. It is shown that while Pauli $Z$-errors are not recoverable without additional resources, Pauli $X$ and $Y$ errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length $O(2^k c^{k^2} d)$ is sufficient to correct any length-$d$ QSP with $c$ unique phases to $k^{th}$-order in error $\epsilon$. Allowing an additional assumption, a lower bound of $\Omega(cd)$ is shown, which is tight for $k = 1$, on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.}, number={2301.085422301.08542}, author={Tan, A.K. and Liu, Y. and Tran, M.C. and Chuang, I.L.}, year={2023} }
 @article{yuan_liu_zhang_wang_2023, title={Observation of a Polarization-Assisted Dipole-Bound State}, volume={145}, ISSN={0002-7863 1520-5126}, url={http://dx.doi.org/10.1021/jacs.3c00246}, DOI={10.1021/jacs.3c00246}, abstractNote={The critical dipole moment to bind an electron was empirically determined to be 2.5 debye, even though smaller values were predicted theoretically. Herein, we report the first observation of a polarization-assisted dipole-bound state (DBS) for a molecule with a dipole moment below 2.5 debye. Photoelectron and photodetachment spectroscopies are conducted for cryogenically cooled indolide anions, where the neutral indolyl radical has a dipole moment of 2.4 debye. The photodetachment experiment reveals a DBS only 6 cm-1 below the detachment threshold along with sharp vibrational Feshbach resonances. Rotational profiles are observed for all of the Feshbach resonances, which are found to have surprisingly narrow linewidths and long autodetachment lifetimes attributed to weak coupling between vibrational motions and the nearly free dipole-bound electron. Calculations suggest that the observed DBS has π-symmetry stabilized by the strong anisotropic polarizability of indolyl.}, number={9}, journal={Journal of the American Chemical Society}, publisher={American Chemical Society (ACS)}, author={Yuan, Dao-Fu and Liu, Yuan and Zhang, Yue-Rou and Wang, Lai-Sheng}, year={2023}, month={Feb}, pages={5512–5522} }
 @article{tan_liu_tran_chuang_2023, title={Perturbative model of noisy quantum signal processing}, volume={107}, ISSN={2469-9926 2469-9934}, url={http://dx.doi.org/10.1103/physreva.107.042429}, DOI={10.1103/PhysRevA.107.042429}, abstractNote={Recent progress in quantum signal processing (QSP) and its generalization, quantum singular value transformation, has led to a grand unification of quantum algorithms. However, inherent experimental noise in quantum devices severely limits the length of realizable QSP sequences. We consider a model of QSP with generic perturbative noise in the signal processing basis and present a diagrammatic notation useful for analyzing such errors. To demonstrate our technique, we study a specific coherent error, that of under- or overrotation of the signal processing operator parametrized by $\ensuremath{\epsilon}\ensuremath{\ll}1$. For this coherent error model, it is shown that while Pauli $Z$ errors are not recoverable without additional resources, Pauli $X$ and $Y$ errors can be arbitrarily suppressed by coherently appending a noisy recovery QSP without the use of additional resources or ancillas. Furthermore, through a careful accounting of errors using our diagrammatic tools, we provide an upper and lower bound on the length of this recovery QSP operator. We anticipate that the perturbative technique and the diagrammatic notation proposed here will facilitate future study of generic noise in QSP and quantum algorithms.}, number={4}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Tan, Andrew K. and Liu, Yuan and Tran, Minh C. and Chuang, Isaac L.}, year={2023}, month={Apr} }
 @book{sinanan-singh_mintzer_chuang_liu_2023, title={Single-shot Quantum Signal Processing Interferometry}, DOI={10.48550/arXiv.2311.13703}, abstractNote={Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics, i.e., the Heisenberg sensing limit, by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy given a single-shot qubit measurement can approach the Heisenberg-limit scaling. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.}, number={2311.137032311.13703}, author={Sinanan-Singh, J. and Mintzer, G.L. and Chuang, I.L. and Liu, Y.}, year={2023} }
 @article{foulon_ray_kim_liu_rubenstein_lordi_2022, title={1/ω electric-field noise in surface ion traps from correlated adsorbate dynamics}, volume={105}, url={http://dx.doi.org/10.1103/physreva.105.013107}, DOI={10.1103/physreva.105.013107}, abstractNote={Ion traps are promising architectures for implementing quantum computers, but they suffer from excessive ``anomalous'' ion motional heating that limit their overall coherence and practicality for scalable quantum computing. The exact microscopic origins of anomalous heating remain an open question, but experiments point to adsorbates on trap electrodes as one likely source. Many different models of anomalous heating have been proposed, but these models have yet to pinpoint the atomistic origin of the experimentally observed $1/\ensuremath{\omega}$ electric-field noise scaling seen in ion traps at frequencies between 0.1--10 MHz. In this work, we show that a model based on previously proposed surface-induced dipole fluctuations on adsorbates, but which also incorporates interparticle interaction dynamics through molecular dynamics simulations of up to multiple monolayers of adsorbates, gives rise to $1/\ensuremath{\omega}$ frequency scaling at the MHz frequencies typically employed in ion traps. These results demonstrate that moderate-to-high densities of adsorbates can give rise to a set of activated motions that produce the $1/\ensuremath{\omega}$ noise observed in ion traps and that collective adsorbate motions produce the observed noise spectra that a noninteracting model does not capture.}, number={1}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Foulon, Benjamin L. and Ray, Keith G. and Kim, Chang-Eun and Liu, Yuan and Rubenstein, Brenda and Lordi, Vincenzo}, year={2022}, month={Jan} }
 @book{ang_carini_chen_chuang_demarco_economou_eickbusch_faraon_fu_girvin_et al._2022, title={Architectures for Multinode Superconducting Quantum Computers}, DOI={10.48550/arXiv.2212.06167}, abstractNote={Many proposals to scale quantum technology rely on modular or distributed designs where individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, a limiting factor of these machines will be internode gates, which may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require a range of techniques, including improvements in entanglement generation, the use of entanglement distillation, and optimized software and compilers, and it remains unclear how improvements to these components interact to affect overall system performance, what performance from each is required, or even how to quantify the performance of each. In this paper, we employ a `co-design' inspired approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. In the case of superconducting MNQCs with microwave-to-optical links, we uncover a tradeoff between entanglement generation and distillation that threatens to degrade performance. We show how to navigate this tradeoff, lay out how compilers should optimize between local and internode gates, and discuss when noisy quantum links have an advantage over purely classical links. Using these results, we introduce a roadmap for the realization of early MNQCs which illustrates potential improvements to the hardware and software of MNQCs and outlines criteria for evaluating the landscape, from progress in entanglement generation and quantum memory to dedicated algorithms such as distributed quantum phase estimation. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.}, number={2212.061672212.06167}, author={Ang, J. and Carini, G. and Chen, Y. and Chuang, I. and DeMarco, M.A. and Economou, S.E. and Eickbusch, A. and Faraon, A. and Fu, K.-M. and Girvin, S.M. and et al.}, year={2022} }
 @article{liu_sinanan-singh_kearney_mintzer_chuang_2021, title={Constructing qudits from infinite-dimensional oscillators by coupling to qubits}, volume={104}, ISSN={2469-9926 2469-9934}, url={http://dx.doi.org/10.1103/physreva.104.032605}, DOI={10.1103/PhysRevA.104.032605}, abstractNote={An infinite dimensional system such as a quantum harmonic oscillator offers a potentially unbounded Hilbert space for computation, but accessing and manipulating the entire state space requires a physically unrealistic amount of energy. When such a quantum harmonic oscillator is coupled to a qubit, for example via a Jaynes-Cummings interaction, it is well known that the total Hilbert space can be separated into independently accessible subspaces of constant energy, but the number of subspaces is still infinite. Nevertheless, a closed four-dimensional Hilbert space can be analytically constructed from the lowest energy states of the qubit-oscillator system. We extend this idea and show how a $d$-dimensional Hilbert space can be analytically constructed, which is closed under a finite set of unitary operations resulting solely from manipulating standard Jaynes-Cummings Hamiltonian terms. Moreover, we prove that the first-order sideband pulses and carrier pulses comprise a universal set for quantum operations on the qubit-oscillator qudit. This work suggests that the combination of a qubit and a bosonic system may serve as hardware-efficient quantum resources for quantum information processing.}, number={3}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Liu, Yuan and Sinanan-Singh, Jasmine and Kearney, Matthew T. and Mintzer, Gabriel and Chuang, Isaac L.}, year={2021}, month={Sep} }
 @article{yuan_zhang_qian_liu_wang_2021, title={Probing the Dipole-Bound State in the 9-Phenanthrolate Anion by Photodetachment Spectroscopy, Resonant Two-Photon Photoelectron Imaging, and Resonant Photoelectron Spectroscopy}, volume={125}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85104370139&partnerID=MN8TOARS}, DOI={10.1021/acs.jpca.1c01563}, abstractNote={Valence-bound anions with a dipolar core can support dipole-bound states (DBSs) below the electron detachment threshold. The highly diffuse DBS observed is usually of σ symmetry with an s-like orbital. Recently, a π-type DBS was observed experimentally in the 9-anthrolate anion (9AT-) and it was shown to be stabilized due to the large anisotropic polarizability of the 9AT core. To confirm the general existence of π-DBS and its structural dependence, here we report an investigation of the 9-phenanthrolate anion (9PT-), which has a different structure and lower symmetry than 9AT-. Photodetachment spectroscopy revealed a DBS 257 cm-1 below the detachment threshold of 9PT- at 19 627 cm-1 (2.4334 eV). Resonant two-photon photoelectron imaging indeed showed a π symmetry for the DBS. Similar to that observed in 9AT-, the π-DBS in 9PT- is also stabilized by the anisotropic polarizability of the 9PT core and accessed via nonadiabatic population transfer from the initially populated σ-DBS. Photodetachment spectroscopy unveiled nine above-threshold vibrational resonances of the DBS, resulting in nine highly non-Franck-Condon resonant photoelectron spectra by tuning the detachment laser to the vibrational resonances. The combination of photodetachment spectroscopy and resonant photoelectron spectroscopy allowed frequencies for nine vibrational modes of the 9-phenathroxy radical to be measured, including the six lowest frequency bending modes.}, number={14}, journal={Journal of Physical Chemistry A}, author={Yuan, D.-F. and Zhang, Y.-R. and Qian, C.-H. and Liu, Y. and Wang, L.-S.}, year={2021}, pages={2967–2976} }
 @article{shen_liu_yu_rubenstein_2020, title={Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble}, volume={153}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85097038269&partnerID=MN8TOARS}, DOI={10.1063/5.0026606}, abstractNote={Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi–Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.}, number={20}, journal={Journal of Chemical Physics}, publisher={AIP Publishing}, author={Shen, Tong and Liu, Yuan and Yu, Yang and Rubenstein, Brenda}, year={2020}, pages={204108} }
 @article{liu_zhu_yuan_qian_zhang_rubenstein_wang_2020, title={Observation of a Symmetry-Forbidden Excited Quadrupole-Bound State}, volume={142}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85096609610&partnerID=MN8TOARS}, DOI={10.1021/jacs.0c10552}, abstractNote={We report the observation of a symmetry-forbidden excited quadrupole-bound state (QBS) in the tetracyanobenzene anion (TCNB-) using both photoelectron and photodetachment spectroscopies of cryogenically-cooled anions. The electron affinity of TCNB is accurately measured as 2.4695 eV. Photodetachment spectroscopy of TCNB- reveals selected symmetry-allowed vibronic transitions to the QBS, but the ground vibrational state was not observed because the transition from the ground state of TCNB- (Au symmetry) to the QBS (Ag symmetry) is triply forbidden by the electric and magnetic dipoles and the electric quadrupole. The binding energy of the QBS is found to be 0.2206 eV, which is unusually large due to strong correlation and polarization effects. A centrifugal barrier is observed for near-threshold autodetachment, as well as relaxations from the QBS vibronic levels to the ground and a valence excited state of TCNB-. The current study shows a rare example where symmetry selection rules, rather than the Franck-Condon principle, govern vibronic transitions to a nonvalence state in an anion.}, number={47}, journal={Journal of the American Chemical Society}, author={Liu, Y. and Zhu, G.-Z. and Yuan, D.-F. and Qian, C.-H. and Zhang, Y.-R. and Rubenstein, B.M. and Wang, L.-S.}, year={2020}, pages={20240–20246} }
 @article{yuan_liu_qian_zhang_rubenstein_wang_2020, title={Observation of a π -Type Dipole-Bound State in Molecular Anions}, volume={125}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85090172467&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.125.073003}, abstractNote={We report the observation of a π-type dipole-bound state (π-DBS) in cryogenically cooled deprotonated 9-anthrol molecular anions (9AT^{-}) by resonant two-photon photoelectron imaging. A DBS is observed 191  cm^{-1} (0.0237 eV) below the detachment threshold, and the existence of the π-DBS is revealed by a distinct (s+d)-wave photoelectron angular distribution. The π-DBS is stabilized by the large anisotropic in-plane polarizability of 9AT. The population of the dipole-forbidden π-DBS is proposed to be via a nonadiabatic coupling with the dipole-allowed σ-type DBS mediated by molecular rotations.}, number={7}, journal={Physical Review Letters}, publisher={American Physical Society (APS)}, author={Yuan, Dao-Fu and Liu, Yuan and Qian, Chen-Hui and Zhang, Yue-Rou and Rubenstein, Brenda M. and Wang, Lai-Sheng}, year={2020} }
 @article{yuan_liu_qian_kocheril_zhang_rubenstein_wang_2020, title={Polarization of Valence Orbitals by the Intramolecular Electric Field from a Diffuse Dipole-Bound Electron}, volume={11}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85091191389&partnerID=MN8TOARS}, DOI={10.1021/acs.jpclett.0c02514}, abstractNote={The diffuse electron in a dipole-bound state is spatially well separated from the valence electrons and is known to have negligible effects on the dipole-bound state's molecular structure. Here, we show that a dipole-bound state is observed in deprotonated 4-(2-phenylethynyl)-phenoxide anions, 348 cm-1 below the anion's detachment threshold. The photodetachment of the dipole-bound electron is observed to accompany a simultaneous shakeup process in valence orbitals in this aromatic molecular anion. This shakeup process is due to configuration mixing as a result of valence orbital polarization by the intramolecular electric field of the dipole-bound electron. This observation suggests that dipole-bound anions can serve as a new platform to probe how oriented electric fields influence the valence electronic structure of polyatomic molecules.}, number={18}, journal={Journal of Physical Chemistry Letters}, publisher={American Chemical Society (ACS)}, author={Yuan, Dao-Fu and Liu, Yuan and Qian, Chen-Hui and Kocheril, G. Stephen and Zhang, Yue-Rou and Rubenstein, Brenda M. and Wang, Lai-Sheng}, year={2020}, pages={7914–7919} }
 @article{liu_shen_zhang_rubenstein_2020, title={Unveiling the Finite Temperature Physics of Hydrogen Chains via Auxiliary Field Quantum Monte Carlo}, volume={16}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85088485021&partnerID=MN8TOARS}, DOI={10.1021/acs.jctc.0c00288}, abstractNote={The ability to accurately predict the finite temperature properties and phase diagrams of realistic quantum solids is central to uncovering new phases and engineering materials with novel properties ripe for device applications. Nonetheless, there remain comparatively few many-body techniques capable of elucidating the finite temperature physics of solids from first principles. In this work, we take a significant step towards developing such a technique by generalizing our previous, exact fully ab initio finite temperature Auxiliary Field Quantum Monte Carlo (FT-AFQMC) method to model periodic solids and employing it to uncover the finite temperature physics of periodic hydrogen chains. Our chains' unit cells consist of 10 hydrogen atoms modeled in a minimal basis and we sample 5 k-points from the first Brillouin zone to arrive at a supercell consisting of 50 orbitals and 50 electrons. Based upon our calculations of these chains' many-body energies, free energies, entropies, heat capacities, double and natural occupancies, and charge and spin correlation functions, we outline their metal-insulator and magnetic ordering as a function of both H-H bond distance and temperature. At low temperatures approaching the ground state, we observe both metal-insulator and ferromagnetic-antiferromagnetic crossovers at bond lengths between 0.5 and 0.75 Å. We then demonstrate how this low-temperature ordering evolves into a metallic phase with decreasing magnetic order at higher temperatures. In order to contextualize our results, we compare the features we observe to those previously seen in one-dimensional, half-filled Hubbard models at finite temperature and in ground state hydrogen chains. Interestingly, we identify signatures of the Pomeranchuk effect in hydrogen chains for the first time and show that spin and charge excitations that typically arise at distinct temperatures in the Hubbard model are indistinguishably coupled in these systems. Beyond qualitatively revealing the many-body phase behavior of hydrogen chains in a numerically exact manner without invoking the phaseless approximation, our efforts shed light on the further theoretical developments that will be required to construct the phase diagrams of the more complex transition metal, lanthanide, and actinide solids of longstanding interest to physicists.}, number={7}, journal={Journal of Chemical Theory and Computation}, publisher={American Chemical Society (ACS)}, author={Liu, Yuan and Shen, Tong and Zhang, Hang and Rubenstein, Brenda}, year={2020}, pages={4298–4314} }
 @article{foulon_liu_rosenstein_rubenstein_2019, title={A Language for Molecular Computation}, volume={5}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85076143262&partnerID=MN8TOARS}, DOI={10.1016/j.chempr.2019.11.007}, abstractNote={Advances in molecular computing have been thwarted by the lack of theoretical underpinnings that are both generalizable and experimentally practical. In a recent issue of iScience, Dueñas-Díez and Pérez-Mercader begin to fill this void by illustrating the correspondence between Chomsky’s hierarchy of formal grammars and example chemical automata. Advances in molecular computing have been thwarted by the lack of theoretical underpinnings that are both generalizable and experimentally practical. In a recent issue of iScience, Dueñas-Díez and Pérez-Mercader begin to fill this void by illustrating the correspondence between Chomsky’s hierarchy of formal grammars and example chemical automata. With semiconductor transistor dimensions approaching fundamental physical limits, researchers have revived an age-old question: are there alternative computing paradigms that would enable high-performance computation at molecular scales? The prospect of using molecules for computation is tantalizing given the staggering amount of information that small quantities of chemicals could encode: if every molecule in a flask could be engineered to compute, Avogadrian (>1023) numbers of parallel computations could be performed in just cubic centimeters of volume. Moreover, molecules can undergo collective phase transitions that are inherently nonlinear and possess many degrees of freedom, including vibrational, nuclear, and constitutional states, each of which could be used for information storage and processing on its own intrinsic timescale. Molecular computing may sound far-fetched, but all of biology relies on intricately evolved molecular information processing systems. Despite this promise, many foundational theoretical and experimental questions remain to be resolved before a practical and competitive molecular computer could ever be realized. Thus far, molecular information demonstrations have overwhelmingly focused on molecular data storage and chemical logic gates. Biomolecular examples of information storage have now become somewhat routine, and the past two decades have seen megabytes of chemical data written and read back using DNA, RNA, metabolites, peptides, and polysaccharides.1Organick L. Ang S.D. Chen Y.-J. Lopez R. Yekhanin S. Makarychev K. Racz M.Z. Kamath G. Gopalan P. Nguyen B. et al.Random access in large-scale DNA data storage.Nat. Biotechnol. 2018; 36: 242-248Crossref PubMed Scopus (276) Google Scholar, 2Kennedy E. Arcadia C.E. Geiser J. Weber P.M. Rose C. Rubenstein B.M. Rosenstein J.K. Encoding information in synthetic metabolomes.PLoS One. 2019; 14: e0217364Crossref PubMed Scopus (14) Google Scholar, 3Cafferty B.J. Ten A.S. Fink M.J. Morey S. Preston D.J. Mrksich M. Whitesides G.M. Storage of information using small organic molecules.ACS Cent. Sci. 2019; 5: 911-916Crossref PubMed Scopus (50) Google Scholar More recently, data have also been successfully written to non-biological small molecules, including Ugi reaction products and phenols.4Rosenstein J.K. Rose C. Reda S. Weber P.M. Kim E. Sello J. Geiser J. Kennedy E. Arcadia C. Dombroski A. et al.Principles of Information Storage in Small-Molecule Mixtures.arXiv. 2019; https://arxiv.org/abs/1905.02187Google Scholar,5Arcadia, C.E., Tann, H., Dombroski, A., Ferguson, K., Chen, S.L., Kim, E., Rose, C., Rubenstein, B.M., Reda, S., and Rosenstein, J.K. (2018). Parallelized Linear Classification with Volumetric Chemical Perceptrons. Proceedings of the IEEE Conference on Rebooting Computing, 1–9.Google Scholar Chemical computation, on the other hand, has been significantly more challenging to realize, because the field still lacks a clear theoretical underpinning for general purpose chemical computations that are experimentally viable (see Chen et al.6Chen H.-L. Doty D. Soloveichik D. Deterministic function computation with chemical reaction networks.Nat. Comput. 2014; 13: 517-534Crossref Scopus (79) Google Scholar for the most compelling theory to date). Some of the earliest examples of molecular computing harnessed DNA hybridization to solve optimization problems. In the years since, many efforts have transitioned from designing single-purpose molecules for specific computational demonstrations to designing more universal chemical logic gates that can, in principle, be cascaded to realize more generalizable chemical circuits.7Seelig G. Soloveichik D. Zhang D.Y. Winfree E. Enzyme-free nucleic acid logic circuits.Science. 2006; 314: 1585-1588Crossref PubMed Scopus (1113) Google Scholar At first, many of these gates were designed using biomolecules, but the relatively recent realization that small-molecule chemistries manifest a much wider range of behaviors—and therefore computations—has ushered in the design of small-molecule- and chemical-oscillator-based gates.8de Silva A.P. McClenaghan N.D. Molecular-scale logic gates.Chemistry. 2004; 10: 574-586Crossref PubMed Scopus (591) Google Scholar Nevertheless, designing chemical logic gates amounts to a conservative approach to chemical computing when compared to the human body, which orchestrates everything from learning tasks to homeostasis not via an assemblage of gates but through more computationally complex feedback loops.9Dalchau N. Szép G. Hernansaiz-Ballesteros R. Barnes C.P. Cardelli L. Phillips A. Csikász-Nagy A. Computing with biological switches and clocks.Nat. Comput. 2018; 17: 761-779Crossref PubMed Scopus (22) Google Scholar It is only in the past few years that researchers have explored approaches that go beyond gates by attempting to map small-molecule reactions to more complex mathematical operations.4Rosenstein J.K. Rose C. Reda S. Weber P.M. Kim E. Sello J. Geiser J. Kennedy E. Arcadia C. Dombroski A. et al.Principles of Information Storage in Small-Molecule Mixtures.arXiv. 2019; https://arxiv.org/abs/1905.02187Google Scholar Without a theoretical framework that can guide the integration of these reactions into meaningful computations, however, many of these efforts amount to shooting in the dark. In a recent issue of iScience, Dueñas-Díez and Pérez-Mercader take a step forward by demonstrating one form of computation, formal language recognition, using non-biological reactions.10Dueñas-Díez M. Perez-Mercader J. How Chemistry Computes: Language Recognition by Non-Biochemical Chemical Automata. From Finite Automata to Turing Machines.iScience. 2019; 19: 514-526Abstract Full Text Full Text PDF PubMed Scopus (20) Google Scholar They examine three chemical systems that can be described by three classes of formal grammars of increasing complexity—regular, context-free, and context-sensitive—from Chomsky’s hierarchy. In doing so, they show how reaction network features, such as pH and system-state oscillation, can be employed to perform computational tasks. Their early success points to language-based logic as a potential framework for unifying chemical computation. As a first simple example, the authors build a finite automaton (FA) out of a bimolecular reaction and use it to recognize the L1 regular language. FAs accept or reject patterns based on predefined rules; for elementary bimolecular reactions (A+B→C), the rule is to produce C if both A and B are present, enabling it to recognize the L1 language of strings containing at least one A and B. The reaction “accepts” inputs if C is produced and “rejects” them otherwise. The authors use a precipitation reaction, in which C is detectable on sight, to perform the recognition. To recognize a context-free language, the authors build a 1-stack pushdown automaton (1-PDA) out of a pH reaction network. 1-PDAs are essentially FAs with a stack that can have symbols added (pushed) to and removed (popped) from it. Chemically, this requires (1) a chemical-based stack that can have things added and removed and (2) a way to reject input strings that try to pop symbols from an empty stack. In the authors’ reaction network, the pH level acts as a stack, with pH = 7 indicating empty. This network can recognize the Dyck language of well-balanced pairs (e.g., sets of parentheses) represented by additions of weak acid (“open”) or strong base (“close”). Adding acid pushes to the stack, whereas adding base pops from the stack. Any string that reduces the pH below 7 implies an imbalance and is immediately rejected. Strings read to their end are accepted only if pH = 7, which implies a balanced number of acid and base additions. Recognizing more sophisticated context-sensitive languages requires Turing machines (TMs), which can be built from PDAs with multiple interacting stacks. Thus, chemical TMs need multiple measurable quantities that non-linearly depend on each other. In the Belousov-Zhabotinsky (BZ) oscillatory reaction network, there is a non-linear relationship between oscillation frequency (f) and deviations from the maximum redox potential (D). The authors use f as a stack and D as a symbol-processing counter. These quantities depend on the system’s levels of oxidizing and reducing agents, along with the basicity; adding to each sequentially corresponds to inputting a string made of symbols a, b, and c. Using this mapping, the network can recognize the L3 language (L3 = (an, bn, cn)). There are several reasons to be encouraged by these early but exciting demonstrations. In contrast with some previous proposals for universal chemical computation, Dueñas-Díez and Pérez-Mercader’s is non-biological and yet still practical: each of their automata involves a one-pot reaction and is thus more amenable to future automation. Furthermore, the authors’ realization of several language-recognition tasks in different chemistries provides a correspondence between the complexity of a chemical reaction and the difficulty of the language-recognition task. Increasing reaction complexity from a single bimolecular reaction to a set of coupled reactions demonstrates how specific properties of chemical reaction networks are useful in achieving particular computational goals. This provides much-needed intuition to guide the search for chemical reaction networks in the future. Nonetheless, as the authors concede, this work falls short of establishing a rigorous mapping between chemical reaction networks and automata. So far, this approach seems to offer a new vocabulary to describe existing chemical systems rather than systematic paths for designing future ones. A larger breakthrough would define how to reliably implement a broad family of mathematical forms in chemistry. This will require constraints that allow chemical outputs to be cascaded directly into chemical operators; considerations of yield, speed, and energy; and procedures for determining which sets of formal languages are physically realizable. Here, as in other early work on chemical logic, we must draw an important distinction between observing that a system can be mapped to a Boolean logic gate (for example) versus first defining an arbitrary logic function and then identifying a chemical system that implements it. Questions also remain about how the proposed networks would scale to larger problems. There may be an Avogadrian number of molecules in any macroscale system, but if they cannot be programmed or read independently, then this parallelism is of limited use. Dueñas-Díez and Pérez-Mercader correctly point out that the complexity of an operation (or formal language) corresponds to its computational power. It is useful to remember that electronic logic gates are trivial in isolation, but they are powerful because they can be reliably interconnected into large networks. Outside of biology, it is still challenging to imagine comparable levels of programmable complexity in chemical networks. This is an immense and worthy challenge, and it is our belief that researchers should not settle for small isolated examples of chemical logic. One useful measure of a chemical computation could be the degree to which it saves electronic computations. For example, a chemical computation would show a clear benefit if evaluating an input string of length N would have required O(N3) electronic instructions but only O(N) chemical measurements. In this understandably early example, the simple formal languages that the authors have chosen would require only O(N) instructions to evaluate. Unfortunately, their pH-PDA and BZ systems both still require continuous observation and the same O(N) chemical measurements to classify input sequences as would also be required electronically, limiting their practical value. When considering isolated examples, showing that one chemical system can correspond to one particular computation can feel like painting a bullseye around an arrow. Yet, even if it does not signify the end of the tournament, at least it illustrates the rules of the game and provides targets for which to aim. By providing new examples that describe experimental chemical systems using formal languages, Dueñas-Díez and Pérez-Mercader have uncovered a new path that could bring us closer to the elusive target of scalable molecular computation. This research was supported by funding from the Defense Advanced Research Projects Agency (DARPA W911NF-18-2-0031). The views, opinions, and/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the US government. This research relates to patent PCT/US2019/038301: Methods of Chemical Computation. How Chemistry Computes: Language Recognition by Non-Biochemical Chemical Automata. From Finite Automata to Turing MachinesDueñas-Díez et al.iScienceAugust 6, 2019In BriefChemistry; Chemical Reaction; Computer Science; Theory of Computation Full-Text PDF Open Access}, number={12}, journal={Chem}, publisher={Elsevier BV}, author={Foulon, Benjamin L. and Liu, Yuan and Rosenstein, Jacob K. and Rubenstein, Brenda M.}, year={2019}, pages={3017–3019} }
 @article{liu_ning_wang_2019, title={Double- and multi-slit interference in photodetachment from nanometer organic molecular anions}, volume={150}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85068132120&partnerID=MN8TOARS}, DOI={10.1063/1.5100799}, abstractNote={We present the predictions of double-slit and multislit interference of photoelectrons from a nanometer-size molecular negative ion. The interference clearly appears in both photoelectron angular distributions and photodetachment cross sections. In contrast to the diatomic photoelectron interference via the X-ray photon, the interference in the nanometer-size negative ions can be readily observed via a visible or extreme ultraviolet laser. Therefore, the phenomenon can be realized on a table-top setup, instead of a large accelerator.}, number={24}, journal={Journal of Chemical Physics}, publisher={AIP Publishing}, author={Liu, Yuan and Ning, Chuan-Gang and Wang, Lai-Sheng}, year={2019}, pages={244302} }
 @article{liu_ning_wang_2019, title={Publisher's Note: Double- And multi-slit interference in photodetachment from nanometer organic molecular anions (Journal of Chemical Physics (2019) 150 (244302) DOI: 10.1063/1.5100799)}, volume={151}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85071051456&partnerID=MN8TOARS}, DOI={10.1063/1.5123673}, abstractNote={First Page}, number={7}, journal={Journal of Chemical Physics}, author={Liu, Y. and Ning, C.-G. and Wang, L.-S.}, year={2019} }
 @article{zhu_cheung_liu_qian_wang_2019, title={Resonant two-photon photoelectron imaging and intersystem crossing from excited dipole-bound states of cold anions}, volume={10}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85070360050&partnerID=MN8TOARS}, DOI={10.1021/acs.jpclett.9b01743}, abstractNote={We report the observation of a dipole-bound state (DBS) 659 cm-1 below the electron detachment threshold of cryogenically-cooled deprotonated 4,4'-biphenol anion (bPh-) and nineteen of its lowest vibrational levels. Resonant two-photon photoelectron imaging (R2P-PEI) via the vibrational levels of the DBS display a sharp peak with a constant binding energy. This observation indicates vertical detachment from the vibrational levels of the DBS to the corresponding neutral levels with the conservation of the vibrational energy, suggesting that the highly diffuse electron in the DBS has little effect on the neutral core. The R2P-PEI spectra also exhibit two features at lower binding energies, which come from intersystem crossings from the DBS to two lower-lying valence-bound triplet excited states of bPh-. The current study discloses the first R2P-PEI spectra from vibrational excited states of a DBS and direct spectroscopic evidence of transitions from a DBS to valence-bound states of anions.}, number={15}, journal={Journal of Physical Chemistry Letters}, publisher={American Chemical Society (ACS)}, author={Zhu, Guo-Zhu and Cheung, Ling Fung and Liu, Yuan and Qian, Chen-Hui and Wang, Lai-Sheng}, year={2019}, pages={4339–4344} }
 @article{liu_cho_rubenstein_2018, title={Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo}, volume={14}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85052330648&partnerID=MN8TOARS}, DOI={10.1021/acs.jctc.8b00569}, abstractNote={We present an ab initio auxiliary field quantum Monte Carlo method for studying the electronic structure of molecules, solids, and model Hamiltonians at finite temperature. The algorithm marries the ab initio phaseless auxiliary field quantum Monte Carlo algorithm known to produce high accuracy ground state energies of molecules and solids with its finite temperature variant, long used by condensed matter physicists for studying model Hamiltonian phase diagrams, to yield a phaseless, ab initio finite temperature method. We demonstrate that the method produces internal energies within chemical accuracy of exact diagonalization results across a wide range of temperatures for H2O (STO-3G), C2 (STO-6G), the one-dimensional hydrogen chain (STO-6G), and the multiorbital Hubbard model. Our method effectively controls the phase problem through importance sampling, often even without invoking the phaseless approximation, down to temperatures at which the systems studied approach their ground states and may therefore be viewed as exact over wide temperature ranges. This technique embodies a versatile tool for studying the finite temperature phase diagrams of a plethora of systems whose properties cannot be captured by a Hubbard U term alone. Our results moreover illustrate that the severity of the phase problem for model Hamiltonians far exceeds that for many molecules at all of the temperatures studied.}, number={9}, journal={Journal of Chemical Theory and Computation}, publisher={American Chemical Society (ACS)}, author={Liu, Yuan and Cho, Minsik and Rubenstein, Brenda}, year={2018}, pages={4722–4732} }
 @article{zhu_liu_hashikawa_zhang_murata_wang_2018, title={Probing the interaction between the encapsulated water molecule and the fullerene cages in H<inf>2</inf>O@C<inf>60</inf><sup>-</sup> and H<inf>2</inf>O@C<inf>59</inf>N<sup>-</sup>}, volume={9}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85049235570&partnerID=MN8TOARS}, DOI={10.1039/c8sc01031e}, abstractNote={The guest–host interactions in the H2O@C60 and H2O@C59N endohedral fullerenes are probed by high-resolution photoelectron imaging.}, number={25}, journal={Chemical Science}, publisher={Royal Society of Chemistry (RSC)}, author={Zhu, Guo-Zhu and Liu, Yuan and Hashikawa, Yoshifumi and Zhang, Qian-Fan and Murata, Yasujiro and Wang, Lai-Sheng}, year={2018}, pages={5666–5671} }
 @article{zhu_hashikawa_liu_zhang_cheung_murata_wang_2017, title={High-Resolution Photoelectron Imaging of Cryogenically-Cooled C<inf>59</inf>N<sup>-</sup> and (C<inf>59</inf>N)<inf>2</inf><sup>2-</sup> Azafullerene Anions}, volume={8}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85039064174&partnerID=MN8TOARS}, DOI={10.1021/acs.jpclett.7b03091}, abstractNote={We report a photoelectron imaging study of cryogenically cooled C59N- and (C59N)22- anions produced from electrospray ionization. High-resolution photoelectron spectra are obtained for C59N- for the first time, allowing seven vibrational frequencies of the C59N azafullerene to be measured. The electron affinity of C59N is determined accurately to be 3.0150 ± 0.0007 eV. The observed vibrational features are understood on the basis of calculated frequencies and compared with those of C60 and C59HN. The photoelectron image of (C59N)22-, which has the same mass/charge ratio as C59N-, is also observed, allowing the second electron affinity of the (C59N)2 azafullerene dimer to be measured as 1.20 ± 0.05 eV. The intramolecular Coulomb repulsion of the (C59N)22- dianion is estimated to be 1.96 eV and is investigated theoretically using the electron density difference between (C59N)22- and (C59N)2.}, number={24}, journal={The journal of physical chemistry letters}, publisher={American Chemical Society (ACS)}, author={Zhu, Guo-Zhu and Hashikawa, Yoshifumi and Liu, Yuan and Zhang, Qian-Fan and Cheung, Ling Fung and Murata, Yasujiro and Wang, Lai-Sheng}, year={2017}, pages={6220–6225} }
 @article{zhu_liu_wang_2017, title={Observation of Excited Quadrupole-Bound States in Cold Anions}, volume={119}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85025472003&partnerID=MN8TOARS}, DOI={10.1103/PhysRevLett.119.023002}, abstractNote={We report the first observation of an excited quadrupole-bound state (QBS) in an anion. High-resolution photoelectron imaging of cryogenically cooled 4-cyanophenoxide (4CP^{-}) anions yields an electron detachment threshold of 24 927  cm^{-1}. The photodetachment spectrum reveals a resonant transition 20  cm^{-1} below the detachment threshold, which is attributed to an excited QBS of 4CP^{-} because neutral 4CP has a large quadrupole moment with a negligible dipole moment. The QBS is confirmed by observation of seventeen above-threshold resonances due to autodetachment from vibrational levels of the QBS.}, number={2}, journal={Physical Review Letters}, publisher={American Physical Society (APS)}, author={Zhu, Guo-Zhu and Liu, Yuan and Wang, Lai-Sheng}, year={2017} }
 @article{huang_zhu_liu_wang_2017, title={Photodetachment spectroscopy and resonant photoelectron imaging of cryogenically-cooled deprotonated 2-hydroxypyrimidine anions}, volume={332}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85006320854&partnerID=MN8TOARS}, DOI={10.1016/j.jms.2016.10.021}, abstractNote={We report a photodetachment and high-resolution photoelectron imaging study of cold deprotonated 2-hydroxypyrimidine anions, C4H3N2O−. Photodetachment spectroscopy reveals an excited dipole-bound state (DBS) of C4H3N2O− with a binding energy of 598 ± 5 cm−1 below the detachment threshold of 26,010 ± 5 cm−1. Twenty vibrational levels of the DBS are observed as resonances in the photodetachment spectrum, with three below the detachment threshold and seventeen above the threshold. By tuning the detachment laser to the above-threshold vibrational resonances, highly non-Franck-Condon photoelectron spectra are obtained. Nine fundamental vibrational frequencies are resolved, including six symmetry-forbidden modes. The 598 cm−1 binding energy for the DBS is quite high due to the large dipole moment of the C4H3N2O radical (>6 D). However, no evidence of a second DBS is observed below the detachment threshold.}, journal={Journal of Molecular Spectroscopy}, publisher={Elsevier BV}, author={Huang, Dao-Ling and Zhu, Guo-Zhu and Liu, Yuan and Wang, Lai-Sheng}, year={2017}, pages={86–93} }
 @article{liu_ning_2015, title={Calculation of photodetachment cross sections and photoelectron angular distributions of negative ions using density functional theory}, volume={143}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84944267513&partnerID=MN8TOARS}, DOI={10.1063/1.4932978}, abstractNote={Recently, the development of photoelectron velocity map imaging makes it much easier to obtain the photoelectron angular distributions (PADs) experimentally. However, explanations of PADs are only qualitative in most cases, and very limited works have been reported on how to calculate PAD of anions. In the present work, we report a method using the density-functional-theory Kohn-Sham orbitals to calculate the photodetachment cross sections and the anisotropy parameter β. The spherical average over all random molecular orientation is calculated analytically. A program which can handle both the Gaussian type orbital and the Slater type orbital has been coded. The testing calculations on Li−, C−, O−, F−, CH−, OH−, NH2−, O2−, and S2− show that our method is an efficient way to calculate the photodetachment cross section and anisotropy parameter β for anions, thus promising for large systems.}, number={14}, journal={Journal of Chemical Physics}, publisher={AIP Publishing}, author={Liu, Yuan and Ning, Chuangang}, year={2015}, pages={144310} }
 @article{liu_huang_liu_cheung_dau_ning_wang_2015, title={Vibrational state-selective resonant two-photon photoelectron spectroscopy of AuS<sup>-</sup> via a spin-forbidden excited state}, volume={6}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84923376070&partnerID=MN8TOARS}, DOI={10.1021/acs.jpclett.5b00053}, abstractNote={Vibrational state-selective resonant two-photon photoelectron spectra have been obtained via a triplet intermediate state ((3)Σ(-)) of AuS(-) near its detachment threshold using high-resolution photoelectron imaging of cryogenically cooled AuS(-) anions. Four vibrational levels of the (3)Σ(-) excited state are observed to be below the detachment threshold. Resonant two-photon absorptions through these levels yield vibrational state-selective photoelectron spectra to the (2)Σ final state of neutral AuS with broad and drastically different Franck-Condon distributions, reflecting the symmetries of the vibrational wave functions of the (3)Σ(-) intermediate state. The (3)Σ(-) excited state is spin-forbidden from the (1)Σ(+) ground state of AuS(-) and is accessed due to strong relativistic effects. The nature of the (3)Σ(-) excited state is confirmed by angular distributions of the photoelectron images and quantum calculations.}, number={4}, journal={Journal of Physical Chemistry Letters}, publisher={American Chemical Society (ACS)}, author={Liu, Hong-Tao and Huang, Dao-Ling and Liu, Yuan and Cheung, Ling-Fung and Dau, Phuong Diem and Ning, Chuan-Gang and Wang, Lai-Sheng}, year={2015}, pages={637–642} }
 @article{liu_cheung_ning_2014, title={Assessment of delocalized and localized molecular orbitals through electron momentum spectroscopy}, volume={23}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84902007578&partnerID=MN8TOARS}, DOI={10.1088/1674-1056/23/6/063403}, abstractNote={Recently, there was a hot controversy about the concept of localized orbitals, which was triggered by Grushow's work titled “Is it time to retire the hybrid atomic orbital?” [J. Chem. Educ. 88, 860 (2011)]. To clarify the issue, we assess the delocalized and localized molecular orbitals from an experimental view using electron momentum spectroscopy. The delocalized and localized molecular orbitals based on various theoretical models for CH4, NH3, and H2O are compared with the experimental momentum distributions. Our results show that the delocalized molecular orbitals rather than the localized ones can give a direct interpretation of the experimental (e, 2e) results.}, number={6}, journal={Chinese Physics B}, publisher={IOP Publishing}, author={Liu, Yuan and Cheung, Ling-Fung and Ning, Chuan-Gang}, year={2014}, pages={063403} }
 @phdthesis{liu, title={Calculation of Photoelectron Angular Distributions}, school={Tsinghua University}, author={Liu, Y.} }
 @phdthesis{liu, title={Finite Temperature Physics of Molecules and Solids via Auxiliary Field Quantum Monte Carlo and Observation of p-Type Dipole-Bound States Near the Molecular Threshold}, school={Brown University}, author={Liu, Y.} }