arXiv subjects

Garnet Kin-Lic Chan

Publications and source records attributed to Garnet Kin-Lic Chan.

At least 109 records · Page 6Linked to original sources

arXiv2020

The Ground State Electronic Energy of Benzene

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$ζ$ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around $-863$ m$E_{\text{H}}$. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 m$E_{\text{H}}$), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

physics.chem-ph↗

arXiv2020

Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution

Developing scalable quantum algorithms to study finite-temperature physics of quantum many-body systems has attracted considerable interest due to recent advancements in quantum hardware. However, such algorithms in their present form require resources that exceed the capabilities of current quantum computers except for a limited range of system sizes and observables. Here, we report calculations of finite-temperature properties including energies, static and dynamical correlation functions, and excitation spectra of spin Hamiltonians with up to four sites on five-qubit IBM Quantum devices. These calculations are performed using the quantum imaginary time evolution (QITE) algorithm and made possible by several algorithmic improvements, including a method to exploit symmetries that reduces the quantum resources required by QITE, circuit optimization procedures to reduce circuit depth, and error mitigation techniques to improve the quality of raw hardware data. Our work demonstrates that the ansatz-independent QITE algorithm is capable of computing diverse finite-temperature observables on near-term quantum devices.

quant-ph↗

arXiv2020

Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions

Matrix product states (MPS) and `dressed' ground states of quadratic mean fields (e.g. Gutzwiller projected Slater Determinants) are both important classes of variational wave-functions. This latter class has played important roles in understanding superconductivity and quantum spin-liquids. We present a novel method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic mean-field Hamiltonian, (which in the simplest case is a Slater determinant and in the most general case is a Pfaffian). We also show how to represent products of such states (e.g. determinants times Pfaffians). From this representation one can project to single occupancy and evaluate the entanglement spectra after Gutzwiller projection. We then obtain the MPS and iMPS representation of Gutzwiller projected mean-field states that arise from the variational slave-fermion approach to the $S=1$ Bilinear-Biquadratic (BLBQ) quantum spin chain. To accomplish this, we develop an approach to orthogonalize degenerate iMPS to find all the states in the degenerate ground-state manifold. We find the energies of the MPS and iMPS states match the variational energies closely indicating the method is accurate and there is minimal loss due to truncation error. We then present the first exploration of the entanglement spectra of projected slave-fermion states exploring their qualitative features and finding good qualitative agreement with the respective exact ground state spectra found from DMRG.

cond-mat.str-el↗

arXiv2020

Numerical continuum tensor networks in two dimensions

We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of fermionic projected entangled pair states obtained via a tensor network formulation of multi-grid, and another based on the combination of the fermionic projected entangled pair state with layers of isometric coarse-graining transformations. We first benchmark our approach on the two-dimensional free Fermi gas then proceed to study the two-dimensional interacting Fermi gas with an attractive interaction in the unitary limit, using tensor networks on grids with up to 1000 sites.

cond-mat.str-el↗

arXiv2020

Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks

We demonstrate the power of 2D tensor networks for obtaining large deviation functions of dynamical observables in a classical nonequilibrium setting. Using these methods, we analyze the previously unstudied dynamical phase behavior of the fully 2D asymmetric simple exclusion process with biases in both the x and y directions. We identify a dynamical phase transition, from a jammed to a flowing phase, and characterize the phases and the transition, with an estimate of the critical point and exponents.

cond-mat.stat-mech↗

arXiv2020

Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases

Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and require solving the grand-challenge problem of the many-electron Schrodinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed matter physics and chemistry, while retaining a connection to the paradigmatic Hubbard model. Here we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantum-mechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition and an intricate set of intertwined magnetic orders.

cond-mat.str-el↗

arXiv2020

Quantum algorithms for quantum chemistry and quantum materials science

As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman's idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics, that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal state simulation, and analyze their strengths and weaknesses for future developments.

quant-ph↗

arXiv2020

Recent developments in the PySCF program package

PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PYSCF as a development environment. We then summarize the capabilities of PYSCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PYSCF across the domains of quantum chemistry, materials science, machine learning and quantum information science.

physics.chem-ph↗

arXiv2020

Minimal matrix product states and generalizations of mean-field and geminal wavefunctions

Simple wavefunctions of low computational cost but which can achieve qualitative accuracy across the whole potential energy surface (PES) are of relevance to many areas of electronic structure as well as to applications to dynamics. Here, we explore a class of simple wavefunctions, the minimal matrix product state (MMPS), that generalizes many simple wavefunctions in common use, such as projected mean-field wavefunctions, geminal wavefunctions, and generalized valence bond states. By examining the performance of MMPSs for PESs of some prototypical systems, we find that they yield good qualitative behavior across the whole PES, often significantly improving on the aforementioned ansätze.

physics.chem-ph↗

arXiv2020

Novel algorithms and high-performance cloud computing enable efficient fully quantum mechanical protein-ligand scoring

Ranking the binding of small molecules to protein receptors through physics-based computation remains challenging. Though inroads have been made using free energy methods, these fail when the underlying classical mechanical force fields are insufficient. In principle, a more accurate approach is provided by quantum mechanical density functional theory (DFT) scoring, but even with approximations, this has yet to become practical on drug discovery-relevant timescales and resources. Here, we describe how to overcome this barrier using algorithms for DFT calculations that scale on widely available cloud architectures, enabling full density functional theory, without approximations, to be applied to protein-ligand complexes with approximately 2500 atoms in tens of minutes. Applying this to a realistic example of 22 ligands binding to MCL1 reveals that density functional scoring outperforms classical free energy perturbation theory for this system. This raises the possibility of broadly applying fully quantum mechanical scoring to real-world drug discovery pipelines.

physics.chem-ph↗

arXiv2020

Finite-temperature coupled cluster: Efficient implementation and application to prototypical systems

We discuss the theory and implementation of the finite temperature coupled cluster singles and doubles (FT-CCSD) method including the equations necessary for an efficient implementation of response properties. Numerical aspects of the method including the truncation of the orbital space and integration of the amplitude equations are tested on some simple systems, and we provide some guidelines for applying the method in practice. The method is then applied to the 1D Hubbard model, the uniform electron gas at warm, dense conditions, and some simple materials. The performance on model systems at high temperatures is encouraging: for the 1-dimensional Hubbard model FT-CCSD provides a qualitatively accurate description of finite-temperature correlation effects even at $U = 8$, and it allows for the computation of systematically improvable exchange-correlation energies of the warm, dense UEG over a wide range of conditions. We highlight the obstacles that remain in using the method for realistic {\it ab initio} calculations on materials.

physics.chem-ph↗

arXiv2020

Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

The accurate computation of Hamiltonian ground, excited, and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared to their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs averages through an analog of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit.

quant-ph↗

arXiv2020

Efficient Implementation of Ab Initio Quantum Embedding in Periodic Systems: Density Matrix Embedding Theory

We describe an efficient quantum embedding framework for realistic ab initio density matrix embedding (DMET) calculations in solids. We discuss in detail the choice of orbitals and mapping to a lattice, treatment of the virtual space and bath truncation, and the lattice-to embedded integral transformation. We apply DMET in this ab initio framework to a hexagonal boron nitride monolayer, crystalline silicon, and nickel monoxide in the antiferromagnetic phase, using large embedded clusters with up to 300 embedding orbitals. We demonstrate our formulation of ab initio DMET in the computation of ground-state properties such as the total energy, equation of state, magnetic moment and correlation functions.

cond-mat.str-el↗

arXiv2020

Theoretical Prediction of Magnetic Exchange Coupling Constants from Broken-Symmetry Coupled Cluster Calculations

Exchange coupling constants ($J$) are fundamental to the understanding of spin spectra of magnetic systems. Here we investigate the broken-symmetry (BS) approaches of Noodleman and Yamaguchi in conjunction with coupled cluster (CC) methods to obtain exchange couplings. $J$ values calculated from CC in this fashion converge smoothly towards the FCI result with increasing level of CC excitation. We compare this BS-CC scheme to the complementary EOM-CC approach on a selection of bridged molecular cases and give results from a few other methodologies for context.

physics.chem-ph↗

arXiv2019

Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization

We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D WASEP. We show that with modest resources we can capture the features of the susceptibility in large systems that marks the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems.

cond-mat.stat-mech↗

arXiv2019

Efficient Formulation of Ab Initio Quantum Embedding in Periodic Systems: Dynamical Mean-Field Theory

We present an efficient ab initio dynamical mean-field theory (DMFT) implementation for quantitative simulations in solids. Our DMFT scheme employs ab initio Hamiltonians defined for impurities comprising the full unit cell or a supercell of atoms and for realistic quantum chemical basis sets. We avoid double counting errors by using Hartree-Fock as the low-level theory. Intrinsic and projected atomic orbitals (IAO+PAO) are chosen as the local embedding basis, facilitating numerical bath truncation. Using an efficient integral transformation and coupled-cluster Green's function (CCGF) impurity solvers, we are able to handle embedded impurity problems with several hundred orbitals. We apply our ab initio DMFT approach to study a hexagonal boron nitride monolayer, crystalline silicon, and nickel oxide in the antiferromagnetic phase, with up to 104 and 78 impurity orbitals in spin-restricted and unrestricted cluster DMFT calculations and over 100 bath orbitals. We show that our scheme produces accurate spectral functions compared to both benchmark periodic coupled-cluster computations and experimental spectra.

cond-mat.str-el↗

arXiv2019

Finite temperature density matrix embedding theory

We describe a formulation of the density matrix embedding theory at finite temperature. We present a generalization of the ground-state bath orbital construction that embeds a mean-field finite-temperature density matrix up to a given order in the Hamiltonian, or the Hamiltonian up to a given order in the density matrix. We assess the performance of the finite-temperature density matrix embedding on the 1D Hubbard model both at half-filling and away from it, and the 2D Hubbard model at half-filling, comparing to exact data where available, as well as results from finite-temperature density matrix renormalization group, dynamical mean-field theory, and dynamical cluster approximations. The accuracy of finite-temperature density matrix embedding appears comparable to that of the ground-state theory, with at most a modest increase in bath size, and competitive with that of cluster dynamical mean-field theory.

cond-mat.str-el↗

arXiv2019

A simplified and improved approach to tensor network operators in two dimensions

Matrix product states (MPS) and matrix product operators (MPOs) are one dimensional tensor networks that underlie the modern density matrix renormalization group (DMRG) algorithm. The use of MPOs accounts for the high level of generality and wide range of applicability of DMRG. However, current algorithms for two dimensional (2D) tensor network states, known as projected entangled-pair states (PEPS), rarely employ the associated 2D tensor network operators, projected entangled-pair operators (PEPOs), due to their computational cost and conceptual complexity. To lower these two barriers, we describe how to reformulate a PEPO into a set of tensor network operators that resemble MPOs by considering the different sets of local operators that are generated from sequential bipartitions of the 2D system. The expectation value of a PEPO can then be evaluated on-the-fly using only the action of MPOs and generalized MPOs at each step of the approximate contraction of the 2D tensor network. This technique allows for the simpler construction and more efficient energy evaluation of 2D Hamiltonians that contain finite-range interactions, and provides an improved strategy to encode long-range interactions that is orders of magnitude more accurate and efficient than existing schemes.

cond-mat.str-el↗