Quantum Fluid Dynamics: An Extended Coupled Cluster Treatment

Bishop, R. F.; Robinson, N. I.; Arponen, J.; Pajanne, E.

doi:10.1007/978-3-642-61330-2_13

Cited by 3 publications

(10 citation statements)

References 10 publications

(13 reference statements)

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“…The crucial feature of both schemes is that corresponding ket and bra states are parametrised independently in a way that does not explicitly preserve their Hermitian-adjoint relationship to one another, and which as a consequence actually breaks it at a general (e.g., SUBn) level of truncation. The underlying reasons for this have been given by Arponen and his co-workers [67,68,101], and are explained below. We introduce the notation {~0[ for the bra ground state, …”

Section: Ccm Formalism Now Divides Into the Normal (Nccm) And Extendementioning

confidence: 94%

“…In particular, the CIM together with the two main modern complete formulations of the CCM which we describe more fully in Sect. 3, and which are known respectively as the normal (NCCM) and emended (ECCM) versions [67], have been shown [68,69] to form a natural closed hierarchy of three increasingly sophisticated parametrisations in which the underlying amplitudes have in-creasing degrees of connectedness. In the same spirit, as we discuss in Sect.…”

Section: Relationships Between Methodsmentioning

confidence: 99%

“…3, each of these three independent cluster methods has also been completely reformulated [67][68][69] via a variational principle, thereby providing further bridges between perturbative and variational techniques. Fifthly, and at the level of possible marriages between various of the methods, we have already mentioned the "correlated coupled cluster theory" [49], which was motivated by a desire to combine the best features of both the CCM and CBF approaches.…”

Section: Relationships Between Methodsmentioning

confidence: 99%

“…It transpires [67,68] that the linked nature of the bottom amplitudes {s,} implies that the NCCM automatically generates diagrams (for the energy, for example) with such a GTO property in the "downward" direction (i.e., backwards in time). Conversely, the fact that the top amplitudes {ai} are generally unlinked implies the absence of a GTO property in the "upward" direction.…”

Section: Sz Ex 6si Elmentioning

confidence: 99%

“…Although we shall not go through the details here, we note that many of the NCCM results of Sect. 3.5 may now be generalised to the ECCM [67,68,101,126]. Many of the key distinguishing features of the ECCM follow from its double exponential structure and hence also its double similarity transform structure,…”

Section: Formal Elements Of the Extended Ccmmentioning

confidence: 99%

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The coupled cluster method

Bishop

Microscopic Quantum Many-Body Theories and Their Applications

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Abstract. The coupled cluster method (CCM) is nowadays widely recognised as providing one of the most powerful, most universally applicable, and numerically most accurate at attainable levels of implementation, of all available ab initio methods of microscopic quantum many-body theory. The number of successful applications of the method to a wide range of physical and chemical systems is impressively large. In almost all such cases the numerical results are either the best or among the best available. A typical example is the electron gas, where the CCM results for the correlation energy agree over the entire metallic density range to within less than one millihartree per electron (or < 1%) with the essentially exact Green's function Monte Carlo results.What has since become known as the normal (NCCM) version of the method was invented some forty years ago to calculate the ground-state energies of closedshell atomic nuclei. Extensions of the CCM have since been developed to calculate excited states, energies of open-shell systems, density matrices and hence other properties, stun rules, and the sub-sum-rules that follow from embedding linear response theory within the NCCM. Further extensions deal with the general dynamics of quantum many-body systems, and with their mixed states appropriate, for example, to their behaviour at nonzero temperatures. More recently, a so-called extended (ECCM) version of the method has been introduced. It has the same ability as the NCCM to describe accurately the local properties of quantum many-body systems, but it also has the potential to describe such global phenomena as phase transitions, spontaneous symmetry breaking, states of topological excitation, and nonequilibrium behaviour.The role of the CCM within modern quantum many-body theory is first surveyed, by a comparison with, and discussion of, the alternative microscopic formulations. We then discuss the method and each of its individual components in considerable detail. Our overall aim is to stress the broad applicability of the method. To that end we introduce and exploit a very general theoretical framework in which to formulate the key ideas and to develop the theory. We end with a brief review of the applications of the method to date.

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Section: Ccm Formalism Now Divides Into the Normal (Nccm) And Extendementioning

confidence: 94%

Section: Relationships Between Methodsmentioning

confidence: 99%

Section: Relationships Between Methodsmentioning

confidence: 99%

Section: Sz Ex 6si Elmentioning

confidence: 99%

Section: Formal Elements Of the Extended Ccmmentioning

confidence: 99%

See 3 more Smart Citations

The coupled cluster method

Bishop

Microscopic Quantum Many-Body Theories and Their Applications

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Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science

Bauman

Kowalski

2022

Mater Theory

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The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems commonly encountered in materials science and chemistry. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces.

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Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

Kowalski

Bauman

2022

Applied Sciences

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We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.

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Quantum Fluid Dynamics: An Extended Coupled Cluster Treatment

Cited by 3 publications

References 10 publications

The coupled cluster method

The coupled cluster method

Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science

Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

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