Dmitry Lyakh

National Center for Computational Sciences · Scientific Computing

The numerical simulation of quantum circuits is an indispensable tool for development, verification and validation of hybrid quantum-classical algorithms intended for near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulati...

We present ExaTN (Exascale Tensor Networks), a scalable GPU-accelerated C++ library which can express and process tensor networks on shared- as well as distributed-memory high-performance computing platforms, including those equipped with GPU accelerators. Specifically, ExaTN provides the ability to build, transform, and numerically evaluate tensor...

As quantum computing hardware systems continue to advance, the research and development of performant, scalable, and extensible software architectures, languages, models, and compilers is equally as important in order to bring this novel coprocessing capability to a diverse group of domain computational scientists. For the field of quantum chemistr...

Quantum computing offers a new paradigm for advancing high-energy physics research by enabling novel methods for representing and reasoning about fundamental quantum mechanical phenomena. Realizing these ideals will require the development of novel computational tools for modeling and simulation, detection and classification, data analysis, and for...

Quantum computing promises remarkable approaches for processing information, but new tools are needed to compile program representations into the physical instructions required by a quantum computer. Here we present a novel adaptation of the multi-level intermediate representation (MLIR) integrated into a quantum compiler that may be used for check...

Abstract A composable design scheme is presented for the development of hybrid quantum/classical algorithms and workflows for applications of quantum simulation. The proposed object‐oriented approach is based on constructing an expressive set of common data structures and methods that enables programming of a broad variety of complex hybrid quantum...

Quantum computing systems are developing rapidly as powerful solvers for a variety of real-world calculations. Traditionally, many of these same applications are solved using conventional high-performance computing (HPC) systems, which have progressed sharply through decades of hardware and software improvements. Here, we present a perspective on t...

In this paper, we report reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for parallel execution on many compute nodes with optional GPU coprocessing, accomplished via the new ExaTENSOR back end. The resulting ExaCorr mod...

We present a composable design scheme for the development of hybrid quantum/classical algorithms and workflows for applications of quantum simulation. Our object-oriented approach is based on constructing an expressive set of common data structures and methods that enable programming of a broad variety of complex hybrid quantum simulation applicati...

As quantum computing hardware systems continue to advance, the research and development of performant, scalable, and extensible software architectures, languages, models, and compilers is equally as important in order to bring this novel coprocessing capability to a diverse group of domain computational scientists. For the field of quantum chemistr...

The numerical simulation of quantum circuits is an indispensable tool for development, verification and validation of hybrid quantum-classical algorithms on near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. We pre...

In this paper, we report a reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for efficient parallel execution on many compute nodes with optional GPU coprocessing, accomplished via the new ExaTENSOR back end. The resulting...

We present a composable design scheme for the development of hybrid quantum/classical algorithms and workflows for applications of quantum simulation. Our object-oriented approach is based on constructing an expressive set of common data structures and methods that enable programming of a broad variety of complex hybrid quantum simulation applicati...

Domain-specific languages (DSLs) are both pervasive and powerful, but remain difficult to integrate into large projects. As a result, while DSLs can bring distinct advantages in performance, reliability, and maintainability, their use often involves trading off other good software-engineering practices. In this paper, we describe an extension to th...

Quantum programming techniques and software have advanced significantly over the past five years, with a majority focusing on high-level language frameworks targeting remote REST library APIs. As quantum computing architectures advance and become more widely available, lower-level, system software infrastructures will be needed to enable tighter, c...

This is the updated supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at https://www.nature.com/articles/s41586-019-1666-5 Summary of changes relative to the supplementary information dated Octo...

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor¹. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor wi...

Noisy Intermediate-Scale Quantum (NISQ) computers aim to perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving "Quantum Supremacy", a major milestone in quantum computing. NISQ Supremacy requires comparison with a state-of-the-art classical simulator. We report HPC simulations of hard random...

The cluster perturbation series, CPS(D), for coupled cluster singles and doubles excitation energies is considered. It is demonstrated that the second-order model CPS(D-2) is identical to the configuration interaction singles with perturbative doubles, CIS(D) model. The third-order model, CPS(D-3), provides excitation energies of coupled cluster si...

We advocate domain‐specific virtual processors (DSVP) as a portability layer for expressing and executing domain‐specific computational workloads on modern heterogeneous HPC architectures, with applications in quantum chemistry. Specifically, in this article we extend, generalize and better formalize the concept of a domain‐specific virtual process...

The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circu...

The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circu...

Recent computations involving quantum processing units (QPUs) have demonstrated a series of challenges inherent to hybrid classical-quantum programming, compilation, execution, and verification and validation. Despite considerable progress, system-level noise, limited low-level instructions sets, remote access models, and an overall lack of portabi...

Heterogeneous high-performance computing (HPC) systems offer novel architectures which accelerate specific workloads through judicious use of specialized coprocessors. A promising architectural approach for future scientific computations is provided by heterogeneous HPC systems integrating quantum processing units (QPUs). To this end, we present XA...

Heterogeneous high-performance computing (HPC) systems offer novel architectures accommodating specialized processors that accelerate specific workloads. Near-term quantum computing technologies are poised to benefit applications as wide-ranging as quantum chemistry, machine learning, and optimization. A novel approach to scale these applications w...

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalization group approach, H/H2-matrix algebra and fast multipole method...

We introduce the CUDA Tensor Transpose (cuTT) library that implements high-performance tensor transposes for NVIDIA GPUs with Kepler and above architectures. cuTT achieves high performance by (a) utilizing two GPU-optimized transpose algorithms that both use a shared memory buffer in order to reduce global memory access scatter, and by (b) computin...

The recently developed Local Framework for calculating Excitation energies (LoFEx) is extended to the coupled cluster singles and doubles (CCSD) model. In the new scheme, a standard CCSD excitation energy calculation is carried out within a reduced excitation orbital space (XOS), which is composed of localised molecular orbitals and natural transit...

We present a scalable cross-platform hybrid MPI / OpenMP / OpenACC implementation of the Divide-Expand-Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures. The Divide-Expand-Consolidate formalism is designed to reduce the steep computational scaling of conventional many-body methods employed in electronic struct...

The earlier proposed multi-reference state-specific coupled-cluster theory with the complete active space reference [CASCC; Lyakh et al., J. Chem. Phys. 122, 024108 (2005)] suffered from a problem of energy discontinuities when the formal reference state was changing in the calculation of the potential energy curve (PEC). A simple remedy to the dis...

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side,...

While the formalism of multiresolution analysis, based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent‐particle level and, recently, second‐order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the tradi...

The fundamentality of the exponential representation of a second-quantised correlated wave function is emphasised with an accent on the physical sense of cluster amplitudes as cumulants of the correlated ansatz. Three main wave function formalisms, namely, the configuration-interaction theory, the coupled-cluster approach, and the many-body perturb...

The recently developed method [M. Musiał, J. Chem. Phys. 136, 134111 (2012)] to study double electron attached states has been applied to the description of the ground and excited state potential energy curves of the alkali metal dimers. The method is based on the multireference coupled cluster scheme formulated within the Fock space formalism for...

The initial implementation of the triple electron attachment (TEA) equation-of-motion (EOM) coupled cluster (CC) method is presented, aiming at the description of electronic states with three open shell electrons outside a suitably chosen closed shell vacuum. In particular, such an approach can be used for describing dissociation of chemical bonds...

It is known that the Λ-tensor (an array of Lagrange multipliers), necessary for evaluating analytic energy gradients in the coupled-cluster theory, is diagrammatically disconnected in general. This means that the number of non-negligible elements in the Λ-tensor grows faster than linearly with the number of calculated particles. At a formal level,...

In this (first) paper we attempt to generalize the notion of tensor connectivity, subsequently studying how this property is affected in different tensorial operations. We show that the often implied corollary of the linked diagram theorem, namely individual size-extensivity of arbitrary connected closed diagrams, can be violated in Coulomb systems...

Various efforts made to solve quasi-degenerate problems with the coupled cluster (CC) theory are summarized and critically analyzed. Hanrath suggested a simplification for the generalized extensivity test and generalized extensivity and size-extensivity also lead to size-intensivity when one describes intensive physical properties. Nakatsuji sugges...

The multireference state specific coupled cluster theory with a complete active space reference (CASCCSD) is described and its application to calculate electronic ground states is discussed. The working algorithm for the CASCCSD method was derived with a computer-based automated approach that generates the coupled-cluster diagrams and the correspon...

A state-specific coupled cluster (CC) theory with the CAS (complete active space) reference (CASCC) and based on an approach that employs single reference determinant (so-called “formal reference” determinant) in the expression for the wave function has been developed to study electronic excited states with different spatial and spin symmetries. Th...

An alternative route to extend the CCSD(T) approach to multireference problems is presented. The well-known defect of the CCSD(T) model in describing the non-dynamic electron correlation effects is remedied by ‘tailoring’ the underlying coupled-cluster singles and doubles (CCSD) approach and applying the perturbative triples correction to it. The T...

A formulation of an adaptive coupled-cluster theory is presented. The method automatically "adjusts" to any state of an electronic system and converges to the full CI limit, thus being capable of describing both single- and multireference phenomena. Adaptivity is accomplished through a guided selection of a compact set of cluster amplitudes as requ...

The multi-reference state-specific coupled-cluster method with a complete-active-space reference (CASCC) developed by our group has been used to calculate the potential energy curves, spectroscopic parameters, and vibrational levels for the ground (X1Σ+) and excited (B1Σ+) states of 19FH. The working algorithm for the CASCC method was derived with...

The multireference state-specific coupled cluster theory is used for the calculation of the potential energy surfaces (PES) of 11BH molecule in the ground and excited states. The PESs are approximated by a number of analytical functions generalizing the Morse potential. The solution of a radial Schrodinger equation and the values of spectroscopic c...

This work reviews the state-specific multireference coupled-cluster (CC) approaches which have been developed as approximate methods for performing high-level quantum mechanical calculations on quasidegenerate ground and excited states of atomic and molecular systems. The term "quasidegenerate" refers to a state that cannot be described even in the...

The complete-active-space coupled-cluster approach with single and double excitations (CASCCSD) based on the ansatz of Oliphant and Adamowicz [J. Chem. Phys. 94, 1229 (1991); 96, 3739 (1992)] is used to derive an approach termed XCASCCSD for calculating potential energy surfaces of ground and excited electronic states with different multiplicities...

A comprehensive comparison of different quantum-chemical methods applied to calculate the N2 ground state potential energy curve is presented. In the comparison we highlight the multireference state-specific (MRSS) coupled-cluster (CC) approach with the complete-active-space (CAS) reference and with single and double excitations from all reference...

The recently developed CAS(n,m)CCSD method is applied to describe the difficult case of the dissociation of the fluorine molecule, F2. The results of the CASCCSD calculations are compared with the results obtained using the CR-CCSD method, the RMR-CCSD method, and other approaches. We demonstrate that among the methods compared CAS(n,m)CCSD provide...

An algorithm for generation of the spin-orbital diagrammatic representation, the corresponding algebraical formulas, and the computer code of the coupled cluster (CC) method with an arbitrary level of the electronic excitations developed earlier in our laboratory have been employed to generate the CAS(2,2)CCSD code. CAS(2,2)CCSD is the state-specif...

The recently proposed state-specific multi-reference coupled cluster (SSMRCC) theory with the complete active space (CAS) reference has been tested in calculations of the potential energy surfaces of electronically-excited states. The algorithm for the method is derived using the computer-based automated approach for generating the coupled cluster...

The recently proposed multireference state-specific coupled-cluster theory with the complete active space reference has been used to study electronically excited states with different spatial and spin symmetries. The algorithm for the method has been obtained using the computerized approach for automatic generation of coupled-cluster diagrams with...

New cumulative indices which describe the configurational structure and the degree of ‘multi-configurationality’ of the coupled cluster (CC) wave function have been proposed and tested on some model systems. The indices calculated for the coupled cluster wave functions generated with the CCSD (single and double excitations) and CCSDT (single, doubl...

Multiconfigurationality index calculated for the coupled-cluster wave function based on an algorithm developed using a computer-aided generation approach is applied to analyze the multireference state-specific coupled-cluster method with the CAS reference (i.e. the so called the CAS( n,m )CCSD approach). The numerical results concern dissociation o...

An algorithm for generation of the spin-orbital diagrammatic representation, the corresponding algebraical formulas, and the computer code of the coupled-cluster (CC) method with an arbitrary level of the electronic excitations has been developed. The method was implemented in the general case as well as for specific application in the state-specif...