Reduced density matrix sampling: Self-consistent embedding and multiscale electronic structure on current generation quantum computers

Tilly, Jules; Sriluckshmy, P. V.; Patel, Akashkumar; Fontana, Enrico; Rungger, Ivan; Grant, Edward; Tennyson, Jonathan; Booth, George H.

doi:10.1103/physrevresearch.3.033230

Cited by 43 publications

(73 citation statements)

References 81 publications

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“…In this case, we expect the required ansatz complexity (depth, for example) to express the correction vector to be similar to the required ansatz complexity to describe these excited states, which will again depend on the level of entanglement between the degrees of freedom. Therefore, we expect the scalability of our correction vector ansatz to be comparable to other state-specific VQE-based algorithms [50,61].…”

Section: E Perspectivementioning

confidence: 85%

“…We demonstrate that the Green's func-tion approach to combining the response of the active and external spaces is sufficiently accurate for the LiH system, where the correlation effects are not too strong, and the hybridization between these canonical degrees of freedom is small. Future work will look to expand this approach to other dynamical correlation functions of interest, as well as investigate the use of the approach within a self-consistent dynamical mean-field embedding theory [34,37,50,61,62] and assess the viability of the approach on physical quantum devices.…”

Section: Discussionmentioning

confidence: 99%

“…In order to overcome a restriction to small system sizes due to the limitations of qubit number, we can also seek a multiscale approach, whereby the quantum solution to the Green's function is solved in a strongly correlated subset of the total degrees of freedom, in the presence of a mean-field description of the response outside this. These multi-resolution or embedded approaches to the correlated dynamics are common in many approaches where the full solution is intractable, and where a subspace of the most important correlated physics can be identified, often involving subspaces chosen via locality or energetic arguments [34,[61][62][63][64][65][66][67][68]. In this work, we will demonstrate a simple approach to embed a noisy Green's function, e.g.…”

Section: Active Space Embedding Of Green's Functionsmentioning

confidence: 99%

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A variational quantum eigensolver for dynamic correlation functions

Chen,

Nusspickel,

Tilly

et al. 2021

Preprint

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Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolver (VQE). These coupled quantum-classical algorithms leverage the ability to perform many repeated measurements to avoid the currently prohibitive gate depths often required for exact quantum algorithms, with the restriction of a parameterized circuit to describe the states of interest. In this work, we show how the calculation of zero-temperature dynamic correlation functions defining the linear response characteristics of quantum systems can also be recast into a modified VQE algorithm, which can be incorporated into the current variational quantum infrastructure. This allows for these important physical expectation values describing the dynamics of the system to be directly converged on the frequency axis, and they approach exactness over all frequencies as the flexibility of the parameterization increases. The frequency resolution hence does not explicitly scale with gate depth, which is approximately twice as deep as a ground state VQE. We apply the method to compute the single-particle Green's function of ab initio dihydrogen and lithium hydride molecules, and demonstrate the use of a practical active space embedding approach to extend to larger systems. While currently limited by the fidelity of two-qubit gates, whose number is increased compared to the ground state algorithm on current devices, we believe the approach shows potential for the extraction of frequency dynamics of correlated systems on near-term quantum processors.

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Section: E Perspectivementioning

confidence: 85%

Section: Discussionmentioning

confidence: 99%

Section: Active Space Embedding Of Green's Functionsmentioning

confidence: 99%

See 1 more Smart Citation

A variational quantum eigensolver for dynamic correlation functions

Chen,

Nusspickel,

Tilly

et al. 2021

Preprint

Self Cite

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show abstract

“…Note that orbitals are rarely optimized on the quantum computer, thus this treatment corresponds to a CASCI rather than a CASSCF calculation. 53 In any case, the relevant Hamiltonian can be obtained by a projection to the active space ( PA ),…”

Section: Embedding Approachesmentioning

confidence: 99%

“…49 Among embedding approaches, DMFT 50 and DMET 51 implementations on quantum computers have already been described and the cost of DMET calculations has already been estimated. 52 Energy-weighted DMET 53 and Gutzwiller variational embedding 54 approaches have been tested on current quantum processors. For other choices of ansätze and more recent developments, see a recent survey.…”

Section: Introductionmentioning

confidence: 99%

Quantum Computing in Pharma: A Multilayer Embedding Approach for Near Future Applications

Izsak,

Riplinger,

Blunt

et al. 2022

Preprint

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Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F 2 in a (2,2) active space on Rigetti's Aspen-11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.

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Multireference Methods are Realistic and Useful Tools for Modeling Catalysis

Vitillo

Cramer

Gagliardi

2022

Israel Journal of Chemistry

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Highly correlated systems, in particular those that include transition metals, are ubiquitous in catalysis. The significant static correlation found in such systems is often poorly accounted for using Kohn Sham density functional theory methods, as they are single determinantal in nature. Applications to catalysis of more rigorous and appropriate multiconfigurational methods have been reported in select instances, but their use remains rare. We discuss obstacles that hinder the routine application of multireference (MR) wave function theoretical calculations to catalytic systems and the current state of the art with respect to removing those obstacles.

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Reduced density matrix sampling: Self-consistent embedding and multiscale electronic structure on current generation quantum computers

Cited by 43 publications

References 81 publications

A variational quantum eigensolver for dynamic correlation functions

A variational quantum eigensolver for dynamic correlation functions

Quantum Computing in Pharma: A Multilayer Embedding Approach for Near Future Applications

Multireference Methods are Realistic and Useful Tools for Modeling Catalysis

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