arXiv subjects

Garnet Kin-Lic Chan

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

At least 91 records · Page 5Linked to original sources

arXiv2022

Differentiable quantum chemistry with PySCF for molecules and materials at the mean-field level and beyond

We introduce an extension to the PySCF package which makes it automatically differentiable. The implementation strategy is discussed, and example applications are presented to demonstrate the automatic differentiation framework for quantum chemistry methodology development. These include orbital optimization, properties, excited-state energies, and derivative couplings, at the mean-field level and beyond, in both molecules and solids. We also discuss some current limitations and directions for future work.

physics.chem-ph↗

arXiv2022

Systematic electronic structure in the cuprate parent state from quantum many-body simulations

The quantitative description of correlated electron materials remains a modern computational challenge. We demonstrate a numerical strategy to simulate correlated materials at the fully ab initio level beyond the solution of effective low-energy models, and apply it to gain a detailed microscopic understanding across a family of cuprate superconducting materials in their parent undoped states. We uncover microscopic trends in the electron correlations and reveal the link between the material composition and magnetic energy scales via a many-body picture of excitation processes involving the buffer layers. Our work illustrates a path towards a quantitative and reliable understanding of more complex states of correlated materials at the ab initio many-body level.

cond-mat.supr-con↗

arXiv2022

Simulating challenging correlated molecules and materials on the Sycamore quantum processor

Simulating complex molecules and materials is an anticipated application of quantum devices. With strong quantum advantage demonstrated in artificial tasks, we examine how such advantage translates into modeling physical problems of correlated electronic structure. We simulate static and dynamical electronic structure on a superconducting quantum processor derived from Google's Sycamore architecture for two representative correlated electron problems: the nitrogenase iron-sulfur molecular clusters, and $α$-ruthenium trichloride, a proximate spin-liquid material. To do so, we simplify the electronic structure into low-energy spin models that fit on the device. With extensive error mitigation and assistance from classically simulated data, we achieve quantitatively meaningful results deploying about 1/5 of the gate resources used in artificial quantum advantage experiments on a similar architecture. This increases to over 1/2 of the gate resources when choosing a model that suits the hardware. Our work serves to convert artificial measures of quantum advantage into a physically relevant setting.

quant-ph↗

arXiv2022

Using hyper-optimized tensor networks and first-principles electronic structure to simulate experimental properties of the giant {Mn84} torus

The single-molecule magnet {Mn84} is a challenge to theory due to its high nuclearity. Building on our prior work which characterized the structure of the spectrum of this magnet, we directly compute two experimentally accessible observables, the field-dependent magnetization up to 75 T and the temperature-dependent heat capacity, using parameter free theory. In particular, we use first principles calculations to derive short- and long-range exchange interactions, while we compute the exact partition function of the resulting classical Potts and Ising spin models for all 84 Mn $S=2$ spins to obtain the observables. The latter computation is possible because of a simulation methodology that uses hyper-optimized tensor network contraction, borrowing from recent techniques developed to simulate quantum supremacy circuits. We also synthesize the magnet and measure its heat capacity and field-dependent magnetization. We observe good qualitative agreement between theory and experiment, identifying an unusual peak in the heat capacity in both, as well as a plateau in the magnetization. Our work also identifies some limitations of current theoretical modeling in large magnets, such as the sensitivity to small, long-range, exchange couplings.

physics.chem-ph↗

arXiv2022

Matrix product states with large sites

We explore various ways to group orbitals into clusters in a matrix product state (MPS). We explain how a generic cluster MPS can often lead to an increase in computational cost and instead propose a special cluster structure, involving only the first and last orbitals/sites, with a wider scope for computational advantage. This structure is a natural formalism to describe correlated multireference (MR) theories. We demonstrate the flexibility and usefulness of this approach by implementing various uncontracted MR configuration interaction, perturbation and linearized coupled cluster theories using an MPS with large cluster sites. Applications to the nitrogen dimer, the chromium dimer, and benzene, including up to triple excitations in the external space, demonstrate the utility of an MPS with up to two large sites. We use our results to analyze the quality of different multireference approximations.

physics.chem-ph↗

arXiv2022

On the pure state $v$-representability of density matrix embedding theory

Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable in practical calculations. In such a case, the global band gap of the low-level theory vanishes, and this can require additional numerical considerations. We find that both the violation of the exact matching condition and the vanishing low-level gap are related to the assumption that the high-level density matrix blocks are non-interacting pure-state $v$-representable (NI-PS-V), which assumes that the low-level density matrix is constructed following the Aufbau principle. In order to relax the NI-PS-V condition, we develop an augmented Lagrangian method to match the density matrix blocks without referring to the Aufbau principle. Numerical results for 2D Hubbard and hydrogen model systems indicate that in some challenging scenarios, the relaxation of the Aufbau principle directly leads to exact matching of the density matrix blocks, which also yields improved accuracy.

physics.comp-ph↗

arXiv2022

Entanglement in the quantum phases of an unfrustrated Rydberg atom array

We report on the ground state phase diagram of interacting Rydberg atoms in the unfrustrated square lattice array. Using new tensor network algorithms, we scale to large systems in two dimensions while including all long-range interactions, revealing the phases in the bulk and their analogs in accessible finite arrays. We find a greatly altered phase diagram from earlier numerical and experimental studies, and in particular, we uncover an emergent entangled quantum nematic phase that appears in the absence of frustration. Broadly our results yield a conceptual guide for future experiments, while our techniques provide a blueprint for converging numerical studies in other lattices.

cond-mat.str-el↗

arXiv2021

Realizing symmetry-protected topological phases in a spin-1/2 chain with next-nearest neighbor hopping on superconducting qubits

The realization of novel phases of matter on quantum simulators is a topic of intense interest. Digital quantum computers offer a route to prepare topological phases with interactions that do not naturally arise in analog quantum simulators. Here, we report the realization of symmetry-protected topological (SPT) phases of a spin-{1/2} Hamiltonian with next-nearest-neighbor hopping on up to 11 qubits on a programmable superconducting quantum processor. We observe clear signatures of the two distinct SPT phases, such as excitations localized to specific edges and finite string order parameters. Our work advances ongoing efforts to realize novel states of matter with exotic interactions on digital near-term quantum computers.

quant-ph↗

arXiv2021

The Variational Power of Quantum Circuit Tensor Networks

We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multi-scale entanglement renormalization ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than $10^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D/2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground-states.

quant-ph↗

arXiv2021

The Fermionic Quantum Emulator

The fermionic quantum emulator (FQE) is a collection of protocols for emulating quantum dynamics of fermions efficiently taking advantage of common symmetries present in chemical, materials, and condensed-matter systems. The library is fully integrated with the OpenFermion software package and serves as the simulation backend. The FQE reduces memory footprint by exploiting number and spin symmetry along with custom evolution routines for sparse and dense Hamiltonians, allowing us to study significantly larger quantum circuits at modest computational cost when compared against qubit state vector simulators. This release paper outlines the technical details of the simulation methods and key advantages.

quant-ph↗

arXiv2021

Constructing Tensor Network Influence Functionals for General Quantum Dynamics

We describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of the bond dimensions and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.

quant-ph↗

arXiv2021

Low communication high performance ab initio density matrix renormalization group algorithms

There has been recent interest in the deployment of ab initio density matrix renormalization group computations on high performance computing platforms. Here, we introduce a reformulation of the conventional distributed memory ab initio DMRG algorithm that connects it to the conceptually simpler and advantageous sum of sub-Hamiltonians approach. Starting from this framework, we further explore a hierarchy of parallelism strategies, that includes (i) parallelism over the sum of sub-Hamiltonians, (ii) parallelism over sites, (iii) parallelism over normal and complementary operators, (iv) parallelism over symmetry sectors, and (v) parallelism over dense matrix multiplications. We describe how to reduce processor load imbalance and the communication cost of the algorithm to achieve higher efficiencies. We illustrate the performance of our new open-source implementation on a recent benchmark ground-state calculation of benzene in an orbital space of 108 orbitals and 30 electrons, with a bond dimension of up to 6000, and a model of the FeMo cofactor with 76 orbitals and 113 electrons. The observed parallel scaling from 448 to 2800 CPU cores is nearly ideal.

physics.chem-ph↗

arXiv2021

Conservation laws in coupled cluster dynamics at finite-temperature

We extend the finite-temperature Keldysh non-equilibrium coupled cluster theory (Keldysh-CC) [{\it J. Chem. Theory Comput.} \textbf{2019}, 15, 6137-6253] to include a time-dependent orbital basis. When chosen to minimize the action, such a basis restores local and global conservation laws (Ehrenfest's theorem) for all one-particle properties, while remaining energy conserving for time-independent Hamiltonians. We present the time-dependent orbital-optimized coupled cluster doubles method (Keldysh-OCCD) in analogy with the formalism for zero-temperature dynamics, extended to finite temperatures through the time-dependent action on the Keldysh contour. To demonstrate the conservation property and understand the numerical performance of the method, we apply it to several problems of non-equilibrium finite-temperature dynamics: a 1D Hubbard model with a time-dependent Peierls phase, laser driving of molecular H$_2$, driven dynamics in warm-dense silicon, and transport in the single impurity Anderson model.

cond-mat.stat-mech↗

arXiv2021

Externally corrected CCSD with renormalized perturbative triples (R-ecCCSD(T)) and density matrix renormalization group and selected configuration interaction external sources

We investigate the renormalized perturbative triples correction together with the externally corrected coupled-cluster singles and doubles (ecCCSD) method. We take the density matrix renormalization group (DMRG) and heatbath CI (HCI) as external sources for the ecCCSD equations. The accuracy is assessed for the potential energy surfaces of H2O, N2, and F2. We find that the triples correction significantly improves on ecCCSD and we do not see any instability of the renormalized triples with respect to dissociation. We explore how to balance the cost of computing the external source amplitudes with respect to the accuracy of the subsequent CC calculation. In this context, we find that very approximate wavefunctions (and their large amplitudes) serve as an efficient and accurate external source. Finally, we characterize the domain of correlation treatable using the externally corrected method and renormalized triples combination studied in this work via a well-known wavefunction diagnostic.

physics.chem-ph↗

arXiv2020

All-electron Gaussian-based $G_0W_0$ for Valence and Core Excitation Energies of Periodic Systems

We describe an all-electron $G_0W_0$ implementation for periodic systems with $k$-point sampling implemented in a crystalline Gaussian basis. Our full-frequency $G_0W_0$ method relies on efficient Gaussian density fitting integrals and includes both analytic continuation and contour deformation schemes. Due to the compactness of Gaussian bases, no virtual state truncation is required as is seen in many plane-wave formulations. Finite size corrections are included by taking the $q \to 0$ limit of the Coulomb divergence. Using our implementation, we study quasiparticle energies and band structures across a range of systems including molecules, semiconductors, rare gas solids, and metals. We find that the $G_0W_0$ band gaps of traditional semiconductors converge rapidly with respect to the basis size, even for the conventionally challenging case of ZnO. Using correlation-consistent bases of polarized triple-zeta quality, we find the mean absolute relative error of the extrapolated $G_0W_0$@PBE band gaps to be only 5.2% when compared to experimental values. For core excitation binding energies (CEBEs), we find that $G_0W_0$ predictions improve significantly over those from DFT if the $G_0W_0$ calculations are started from hybrid functionals with a high percentage of exact exchange.

cond-mat.mtrl-sci↗

arXiv2020

Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory

We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AFM and SC orders occurs in all parameter sets. The local magnetic moment localizes entirely at the copper sites. The magnetic phase diagram is particularly sensitive to $Δ_{pd}$ and $t_{pp}$, and existing estimates of the charge transfer gap $Δ_{pd}$ appear too large in so-called minimal model parametrizations. The electron-doped side of the phase diagram is qualitatively distinct from hole-doped side and we find an unusual two-peak structure in the SC in the full model parametrization. Examining the SC order at the atomic scale, within the larger scale $d_{x^2 - y^2}$-wave SC pairing order between Cu-Cu and O-O, we also observe a local $p_{x (y)}$ [or $d_{xz (yz)}$]-symmetry modulation of the pair density on the Cu-O bonds. Our work highlights some of the features that arise in a three-band versus one-band picture, the role of the oxygen degrees of freedom in new kinds of atomic-scale SC orders, and the necessity of re-evaluating current parametrizations of the three-band Hubbard model.

cond-mat.str-el↗

arXiv2020

Ab Initio Full Cell GW+DMFT for Correlated Materials

Quantitative prediction of electronic properties in correlated materials requires simulations without empirical truncations and parameters. We present a method to achieve this goal through a new ab initio formulation of dynamical mean-field theory (DMFT). Instead of using small impurities defined in a low-energy subspace, which require complicated downfolded interactions which are often approximated, we describe a full cell $GW$+DMFT approach, where the impurities comprise all atoms in a unit cell or supercell of the crystal. Our formulation results in large impurity problems, which we treat here with efficient quantum chemistry impurity solvers that work on the real-frequency axis, combined with a one-shot $G_0W_0$ treatment of long-range interactions. We apply our full cell approach to bulk Si, two antiferromagnetic correlated insulators NiO and $α$-Fe$_2$O$_3$, and the paramagnetic correlated metal SrMoO$_3$, with impurities containing up to 10 atoms and 124 orbitals. We find that spectral properties, magnetic moments, and two-particle spin correlation functions are obtained in good agreement with experiments. In addition, in the metal oxide insulators, the balanced treatment of correlations involving all orbitals in the cell leads to new insights into the orbital character around the insulating gap.

cond-mat.str-el↗

arXiv2020

A coupled cluster framework for electrons and phonons

We describe a coupled cluster framework for coupled systems of electrons and phonons. Neutral and charged excitations are accessed via the equation-of-motion version of the theory. Benchmarks on the Hubbard-Holstein model allow us to assess the strengths and weaknesses of different coupled cluster approximations which generally perform well for weak to moderate coupling. Finally, we report progress towards an implementation for {\it ab initio} calculations on solids, and present some preliminary results on finite-size models of diamond. We also report the implementation of electron-phonon coupling matrix elements from crystalline Gaussian type orbitals (cGTO) within the PySCF program package.

cond-mat.mtrl-sci↗