Shreya Verma, Ruhee D’Cunha, Abhishek Mitra, Matthew Hermes, Stephen K. Gray, Matthew Otten* and Laura Gagliardi*,
{"title":"多项式标度局部活动空间幺正选择性耦合簇单双。","authors":"Shreya Verma, Ruhee D’Cunha, Abhishek Mitra, Matthew Hermes, Stephen K. Gray, Matthew Otten* and Laura Gagliardi*, ","doi":"10.1021/acs.jctc.5c00745","DOIUrl":null,"url":null,"abstract":"<p >We present a polynomial-scaling algorithm for the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. In this approach, cluster excitations are selected based on a threshold ϵ determined by the absolute gradients of the LAS-UCCSD energy with respect to cluster amplitudes. Using the generalized Wick’s theorem for multireference wave functions, we derive the gradient expression as a polynomial function of one-, two-, and three-body reduced density matrices and 1- and 2-electron integrals, valid for any multireference wave function. The resulting gradient implementation exhibits a memory scaling of <i></i><math><mi>O</mi></math>(<i>N</i><sup>6</sup>), with <i>N</i> spin orbitals in the combined active space of all fragments. The variational quantum eigensolver is used to optimize the selected cluster excitations on a quantum simulator. By plotting the energy error, defined as the difference between the LAS-USCCSD and corresponding CASCI energies, against the inverse cluster amplitude selection threshold (ϵ<sup>–1</sup>) for polyene chains containing 2 to 5 π-bond units, we establish a relationship between the energy error and the threshold. To further validate the accuracy of LAS-USCCSD, we computed the cis–trans isomerization energy of stilbene (a 20-qubit system) and the magnetic coupling constant of the tris-hydroxo-bridged chromium dimer [Cr<sub>2</sub>(OH)<sub>3</sub>(NH<sub>3</sub>)<sub>6</sub>]<sup>3+</sup> (evaluated as both 12- and 20-qubit systems) using the Qiskit-Qulacs simulator. Assessing such examples is important to determine the practical feasibility of quantum simulations for chemically realistic systems. Toward this goal, with the LAS-USCCSD algorithm we estimated the quantum resources required for simulating an active space of (30e,22o) in [Cr<sub>2</sub>(OH)<sub>3</sub>(NH<sub>3</sub>)<sub>6</sub>]<sup>3+</sup>, a size that remains beyond the reach of current quantum simulators for accurate treatment.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"21 15","pages":"7460–7470"},"PeriodicalIF":5.5000,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Polynomial Scaling Localized Active Space Unitary Selective Coupled Cluster Singles and Doubles\",\"authors\":\"Shreya Verma, Ruhee D’Cunha, Abhishek Mitra, Matthew Hermes, Stephen K. Gray, Matthew Otten* and Laura Gagliardi*, \",\"doi\":\"10.1021/acs.jctc.5c00745\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p >We present a polynomial-scaling algorithm for the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. In this approach, cluster excitations are selected based on a threshold ϵ determined by the absolute gradients of the LAS-UCCSD energy with respect to cluster amplitudes. Using the generalized Wick’s theorem for multireference wave functions, we derive the gradient expression as a polynomial function of one-, two-, and three-body reduced density matrices and 1- and 2-electron integrals, valid for any multireference wave function. The resulting gradient implementation exhibits a memory scaling of <i></i><math><mi>O</mi></math>(<i>N</i><sup>6</sup>), with <i>N</i> spin orbitals in the combined active space of all fragments. The variational quantum eigensolver is used to optimize the selected cluster excitations on a quantum simulator. By plotting the energy error, defined as the difference between the LAS-USCCSD and corresponding CASCI energies, against the inverse cluster amplitude selection threshold (ϵ<sup>–1</sup>) for polyene chains containing 2 to 5 π-bond units, we establish a relationship between the energy error and the threshold. To further validate the accuracy of LAS-USCCSD, we computed the cis–trans isomerization energy of stilbene (a 20-qubit system) and the magnetic coupling constant of the tris-hydroxo-bridged chromium dimer [Cr<sub>2</sub>(OH)<sub>3</sub>(NH<sub>3</sub>)<sub>6</sub>]<sup>3+</sup> (evaluated as both 12- and 20-qubit systems) using the Qiskit-Qulacs simulator. Assessing such examples is important to determine the practical feasibility of quantum simulations for chemically realistic systems. Toward this goal, with the LAS-USCCSD algorithm we estimated the quantum resources required for simulating an active space of (30e,22o) in [Cr<sub>2</sub>(OH)<sub>3</sub>(NH<sub>3</sub>)<sub>6</sub>]<sup>3+</sup>, a size that remains beyond the reach of current quantum simulators for accurate treatment.</p>\",\"PeriodicalId\":45,\"journal\":{\"name\":\"Journal of Chemical Theory and Computation\",\"volume\":\"21 15\",\"pages\":\"7460–7470\"},\"PeriodicalIF\":5.5000,\"publicationDate\":\"2025-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Chemical Theory and Computation\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://pubs.acs.org/doi/10.1021/acs.jctc.5c00745\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"CHEMISTRY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Chemical Theory and Computation","FirstCategoryId":"92","ListUrlMain":"https://pubs.acs.org/doi/10.1021/acs.jctc.5c00745","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
Polynomial Scaling Localized Active Space Unitary Selective Coupled Cluster Singles and Doubles
We present a polynomial-scaling algorithm for the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. In this approach, cluster excitations are selected based on a threshold ϵ determined by the absolute gradients of the LAS-UCCSD energy with respect to cluster amplitudes. Using the generalized Wick’s theorem for multireference wave functions, we derive the gradient expression as a polynomial function of one-, two-, and three-body reduced density matrices and 1- and 2-electron integrals, valid for any multireference wave function. The resulting gradient implementation exhibits a memory scaling of (N6), with N spin orbitals in the combined active space of all fragments. The variational quantum eigensolver is used to optimize the selected cluster excitations on a quantum simulator. By plotting the energy error, defined as the difference between the LAS-USCCSD and corresponding CASCI energies, against the inverse cluster amplitude selection threshold (ϵ–1) for polyene chains containing 2 to 5 π-bond units, we establish a relationship between the energy error and the threshold. To further validate the accuracy of LAS-USCCSD, we computed the cis–trans isomerization energy of stilbene (a 20-qubit system) and the magnetic coupling constant of the tris-hydroxo-bridged chromium dimer [Cr2(OH)3(NH3)6]3+ (evaluated as both 12- and 20-qubit systems) using the Qiskit-Qulacs simulator. Assessing such examples is important to determine the practical feasibility of quantum simulations for chemically realistic systems. Toward this goal, with the LAS-USCCSD algorithm we estimated the quantum resources required for simulating an active space of (30e,22o) in [Cr2(OH)3(NH3)6]3+, a size that remains beyond the reach of current quantum simulators for accurate treatment.
期刊介绍:
The Journal of Chemical Theory and Computation invites new and original contributions with the understanding that, if accepted, they will not be published elsewhere. Papers reporting new theories, methodology, and/or important applications in quantum electronic structure, molecular dynamics, and statistical mechanics are appropriate for submission to this Journal. Specific topics include advances in or applications of ab initio quantum mechanics, density functional theory, design and properties of new materials, surface science, Monte Carlo simulations, solvation models, QM/MM calculations, biomolecular structure prediction, and molecular dynamics in the broadest sense including gas-phase dynamics, ab initio dynamics, biomolecular dynamics, and protein folding. The Journal does not consider papers that are straightforward applications of known methods including DFT and molecular dynamics. The Journal favors submissions that include advances in theory or methodology with applications to compelling problems.