Preparing ground states of correlated molecules on near-termquantumcomputers requires algorithms that are both accurate and resource-efficient.We introduce the qubit-adaptive variational quantum imaginary timeevolution (QAITE) algorithm, which synthesizes the systematic convergenceof imaginary-time evolution with hardware-efficient, adaptive ansatzconstruction. By integrating the linear-scaling qubit operator poolinto the adaptive variational quantum imaginary time evolution framework,QAITE deterministically constructs a compact ansatz without costlyclassical optimization loops. Numerical simulations for molecularsystems (H4, LiH, H2O, BeH2), benchmarkedagainst our own implementations of established adaptive algorithmsunder identical conditions, show that QAITE achieves chemical accuracywith a 15–45% reduction in CNOT gates compared to the standardadaptive variational quantum imaginary time evolution (AVQITE) method.For hydrogen chains (RHH = 1.5 Å, N = 6–16 qubits), QAITE’s circuit complexitygrows approximately quadratically and remains the lowest of the fourmethods at every system size, reaching 31% fewer CNOT gates than AVQITEat 16 qubits─a saving of 1322 gates. This efficiency extendsto heterogeneous (LiH)n and (HBe)n chains, where QAITE maintains a CNOT gateratio below 1 for all sizes studied (e.g., 0.81 for (LiH)2). We further show that the deterministic parameter update is numericallyrobust: the results are insensitive to the regularization of the quantumgeometric tensor over at least 4 orders of magnitude, and chemicalaccuracy is retained under realistic shot noise applied to both thequantum geometric tensor and the force vector. By outperforming establishedadaptive algorithms in both absolute gate count and scaling, QAITEestablishes a promising, scalable pathway for quantum molecular simulationson noisy intermediate-scale quantum devices.
在近期量子计算机上制备相关分子的基态需要精确和资源高效的算法。提出了一种量子比特自适应变分量子虚时间进化算法(QAITE),该算法将虚时间进化的系统收敛性与硬件高效、自适应的分析结构相结合。通过将线性标度量子比特算子池集成到自适应变分量子虚时间演化框架中,QAITE确定性地构建了一个不含昂贵经典优化循环的紧凑解集。分子系统(H4, LiH, H2O, BeH2)的数值模拟,以我们自己在相同条件下建立的自适应算法为基准,表明与标准自适应变分量子虚时间进化(AVQITE)方法相比,QAITE实现了化学精度,CNOT门减少了15-45%。对于氢链(RHH = 1.5 Å, N = 6-16量子位),QAITE的电路复杂性大约以二次增长,并且在每种系统尺寸下仍然是四种方法中最低的,在16量子位时比AVQITE少31%的CNOT门,节省了1322个门。这种效率扩展到非均相(LiH)n和(HBe)n链,其中QAITE在研究的所有尺寸(例如,(LiH)2的0.81)中保持CNOT栅比低于1。我们进一步证明了确定性参数更新具有数值鲁棒性:结果对量子几何张量的正则化不敏感至少超过4个数量级,并且在量子几何张量和力矢量同时施加的真实射击噪声下保持化学精度。通过在绝对门数和缩放方面优于现有的自适应算法,QAITE为嘈杂的中等规模量子器件上的量子分子模拟建立了一个有前途的、可扩展的途径。
{"title":"Qubit-Adaptive Variational Quantum Imaginary Time Evolution: A Resource-Efficient Algorithm for Ground-State Preparation of Correlated Molecules on Near-Term Quantum Computers","authors":"Thitiwuth Chaiyatho, Zhenyu Li, Jin-Shi Xu, Xiao-Ye Xu, Wiwittawin Sukmas","doi":"10.1021/acs.jctc.6c01171","DOIUrl":"10.1021/acs.jctc.6c01171","url":null,"abstract":"<p>Preparing ground states of correlated molecules on near-termquantumcomputers requires algorithms that are both accurate and resource-efficient.We introduce the qubit-adaptive variational quantum imaginary timeevolution (QAITE) algorithm, which synthesizes the systematic convergenceof imaginary-time evolution with hardware-efficient, adaptive ansatzconstruction. By integrating the linear-scaling qubit operator poolinto the adaptive variational quantum imaginary time evolution framework,QAITE deterministically constructs a compact ansatz without costlyclassical optimization loops. Numerical simulations for molecularsystems (H<sub>4</sub>, LiH, H<sub>2</sub>O, BeH<sub>2</sub>), benchmarkedagainst our own implementations of established adaptive algorithmsunder identical conditions, show that QAITE achieves chemical accuracywith a 15–45% reduction in CNOT gates compared to the standardadaptive variational quantum imaginary time evolution (AVQITE) method.For hydrogen chains (<em>R</em><sub>HH</sub> = 1.5 Å, <em>N</em> = 6–16 qubits), QAITE’s circuit complexitygrows approximately quadratically and remains the lowest of the fourmethods at every system size, reaching 31% fewer CNOT gates than AVQITEat 16 qubits─a saving of 1322 gates. This efficiency extendsto heterogeneous (LiH)<sub><em>n</em></sub> and (HBe)<sub><em>n</em></sub> chains, where QAITE maintains a CNOT gateratio below 1 for all sizes studied (e.g., 0.81 for (LiH)<sub>2</sub>). We further show that the deterministic parameter update is numericallyrobust: the results are insensitive to the regularization of the quantumgeometric tensor over at least 4 orders of magnitude, and chemicalaccuracy is retained under realistic shot noise applied to both thequantum geometric tensor and the force vector. By outperforming establishedadaptive algorithms in both absolute gate count and scaling, QAITEestablishes a promising, scalable pathway for quantum molecular simulationson noisy intermediate-scale quantum devices.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"22 19","pages":"10091–10100"},"PeriodicalIF":5.8,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-13Epub Date: 2026-09-25DOI: 10.1021/acs.jctc.6c01549
Saemee Song, Jae Woo Park
When a chemical system of interest contains heavy elements,itis important to obtain a balanced description of relativistic effectsand electron correlation. The exact two-component (X2C) Hamiltonianincludes both scalar-relativistic and spin–orbit effects witha reasonable computational cost. By using the spin–orbit X2CHamiltonian in state-averaged complete active space self-consistentfield (SA-CASSCF) calculations, it is possible to obtain equivalentdescriptions of the states with different spin characters. For moleculargeometry optimizations within this framework, the nuclear gradientsshould be efficiently evaluated. In this work, we describe a state-specificanalytical gradient algorithm for X2C-SA-CASSCF theory with the density-fittingapproximation. To realize such calculations, we formulate and implementthe response (Z-vector) equation for X2C-SA-CASSCFtheory. Using the obtained state-specific nuclear gradients, we optimizethe equilibrium geometries of metal porphyrins and the singlet–singletand singlet–triplet minimum energy crossing points or minimumenergy conical intersections of 2-thiouracil.
{"title":"State-Specific Analytical Nuclear Gradients for the Density-Fitted Exact Two-Component State-Averaged Complete Active Space Self-Consistent Field (X2C-SA-CASSCF) Theory","authors":"Saemee Song, Jae Woo Park","doi":"10.1021/acs.jctc.6c01549","DOIUrl":"10.1021/acs.jctc.6c01549","url":null,"abstract":"<p>When a chemical system of interest contains heavy elements,itis important to obtain a balanced description of relativistic effectsand electron correlation. The exact two-component (X2C) Hamiltonianincludes both scalar-relativistic and spin–orbit effects witha reasonable computational cost. By using the spin–orbit X2CHamiltonian in state-averaged complete active space self-consistentfield (SA-CASSCF) calculations, it is possible to obtain equivalentdescriptions of the states with different spin characters. For moleculargeometry optimizations within this framework, the nuclear gradientsshould be efficiently evaluated. In this work, we describe a state-specificanalytical gradient algorithm for X2C-SA-CASSCF theory with the density-fittingapproximation. To realize such calculations, we formulate and implementthe response (<em>Z</em>-vector) equation for X2C-SA-CASSCFtheory. Using the obtained state-specific nuclear gradients, we optimizethe equilibrium geometries of metal porphyrins and the singlet–singletand singlet–triplet minimum energy crossing points or minimumenergy conical intersections of 2-thiouracil.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"22 19","pages":"10203–10212"},"PeriodicalIF":5.8,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-13Epub Date: 2026-09-28DOI: 10.1021/acs.jctc.6c01161
Nithishwer Mouroug Anand, Antonia-Florina Panescu, Ronald M. A. Knegtel, Ewa I. Chudyk, Fabio Zuccotto, Philip C. Biggin
Free energy perturbation (FEP) methods provide a robustcomputationalframework for predicting protein-ligand binding affinities and haveseen increased adoption in drug discovery workflows. Among these,absolute binding free energy (ABFE) calculations are especially valuableas they enable affinity prediction for novel compounds without priorexperimental data. However, their broader adoption is limited by setupcomplexity, sampling challenges, and variable performance across systems.These challenges are particularly pronounced in therapeutically relevantcomplex membrane protein systems such as G protein-coupled receptors(GPCRs). This underscores the need to evaluate ABFE performance inGPCR systems and to develop strategies to mitigate these errors. Here,we evaluate ABFE calculations across three GPCR systems: the adenosineA2A receptor (A2AR), the dopamine D3 receptor(D3R), and the metabotropic glutamate receptor 5 (mGlu5). We focuson three sources of systematic error in these systems: (i) inadequateresolvation of the binding pocket in apo-like alchemical states, (ii)inconsistent treatment of metal ions, and (iii) insufficient samplingof receptor conformational transitions between holo-like and apo-likeensembles. To address these issues, we introduce two methodologicalimprovements: a biased grand-canonical-like water transport schemeto improve binding pocket resolvation, and a replica-exchange umbrellasampling (REUS)-based framework to quantify and correct the free energyassociated with receptor relaxation to apo-like conformations. Together,these approaches reduce the systematic overestimation of binding affinities,improving agreement with experimental data while maintaining rankingperformance. Overall, our results highlight the importance of accuratelyrepresenting the apo state in ABFE calculations and provide a practicalframework for applying high-accuracy free energy methods to membraneprotein targets.
{"title":"Improving ABFE Calculations for GPCRs by Addressing Errors in Apo-State Representation","authors":"Nithishwer Mouroug Anand, Antonia-Florina Panescu, Ronald M. A. Knegtel, Ewa I. Chudyk, Fabio Zuccotto, Philip C. Biggin","doi":"10.1021/acs.jctc.6c01161","DOIUrl":"10.1021/acs.jctc.6c01161","url":null,"abstract":"<p>Free energy perturbation (FEP) methods provide a robustcomputationalframework for predicting protein-ligand binding affinities and haveseen increased adoption in drug discovery workflows. Among these,absolute binding free energy (ABFE) calculations are especially valuableas they enable affinity prediction for novel compounds without priorexperimental data. However, their broader adoption is limited by setupcomplexity, sampling challenges, and variable performance across systems.These challenges are particularly pronounced in therapeutically relevantcomplex membrane protein systems such as G protein-coupled receptors(GPCRs). This underscores the need to evaluate ABFE performance inGPCR systems and to develop strategies to mitigate these errors. Here,we evaluate ABFE calculations across three GPCR systems: the adenosineA<sub>2A</sub> receptor (A<sub>2A</sub>R), the dopamine D3 receptor(D3R), and the metabotropic glutamate receptor 5 (mGlu5). We focuson three sources of systematic error in these systems: (i) inadequateresolvation of the binding pocket in apo-like alchemical states, (ii)inconsistent treatment of metal ions, and (iii) insufficient samplingof receptor conformational transitions between holo-like and apo-likeensembles. To address these issues, we introduce two methodologicalimprovements: a biased grand-canonical-like water transport schemeto improve binding pocket resolvation, and a replica-exchange umbrellasampling (REUS)-based framework to quantify and correct the free energyassociated with receptor relaxation to apo-like conformations. Together,these approaches reduce the systematic overestimation of binding affinities,improving agreement with experimental data while maintaining rankingperformance. Overall, our results highlight the importance of accuratelyrepresenting the apo state in ABFE calculations and provide a practicalframework for applying high-accuracy free energy methods to membraneprotein targets.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"22 19","pages":"10428–10444"},"PeriodicalIF":5.8,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149090897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Entanglementis a key bottleneck limiting the efficiency of tensor-networkand quantum simulations of molecular electronic structure. Here, wesystematically assess and extend Clifford disentanglers as a structure-preservingapproach to entanglement reduction: they can modify the entanglementstructure of qubit wave functions while retaining the Pauli-stringform of qubit Hamiltonians. To enable a practical search over Cliffordtransformations, we classify Clifford operators by their action onthe Schmidt spectrum across a bipartition, reducing the two- and four-qubitsearch spaces to 20 and 91392 representatives, respectively. Embeddedin an iterative Clifford-augmented matrix product state framework,these transformations reduce the energy errors at fixed bond dimensionfor the molecular test cases studied and mitigate the dependence onorbital ordering and Fermion-to-qubit mappings. We further show thatClifford disentanglers can also benefit quantum simulations such asshallow-circuit variational quantum eigensolver calculations. Together,these results establish Clifford disentanglers as a useful structure-preservingentanglement-engineering tool for tensor-network and quantum simulationsof molecular electronic structure, while also clarifying their dependenceon correlation and motivating future developments.
{"title":"Clifford Disentanglers for Entanglement Reduction in Molecular Electronic Structure Simulations","authors":"Longfei Chang, Zibo Wu, Yunzhi Li, Haiqi Liu, Jiajun Ren, Mingpu Qin, Zhendong Li, Wei-Hai Fang","doi":"10.1021/acs.jctc.6c01170","DOIUrl":"10.1021/acs.jctc.6c01170","url":null,"abstract":"<p>Entanglementis a key bottleneck limiting the efficiency of tensor-networkand quantum simulations of molecular electronic structure. Here, wesystematically assess and extend Clifford disentanglers as a structure-preservingapproach to entanglement reduction: they can modify the entanglementstructure of qubit wave functions while retaining the Pauli-stringform of qubit Hamiltonians. To enable a practical search over Cliffordtransformations, we classify Clifford operators by their action onthe Schmidt spectrum across a bipartition, reducing the two- and four-qubitsearch spaces to 20 and 91392 representatives, respectively. Embeddedin an iterative Clifford-augmented matrix product state framework,these transformations reduce the energy errors at fixed bond dimensionfor the molecular test cases studied and mitigate the dependence onorbital ordering and Fermion-to-qubit mappings. We further show thatClifford disentanglers can also benefit quantum simulations such asshallow-circuit variational quantum eigensolver calculations. Together,these results establish Clifford disentanglers as a useful structure-preservingentanglement-engineering tool for tensor-network and quantum simulationsof molecular electronic structure, while also clarifying their dependenceon correlation and motivating future developments.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"22 19","pages":"10113–10125"},"PeriodicalIF":5.8,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149091935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-13DOI: 10.1021/acs.jctc.6c01264
Stephen H. Yuwono,Katie A. Crouch,A. Eugene DePrince
Abstract Frequency-dependent linear and quadratic response functions are implemented for a cavity quantum electrodynamics (QED) generalization of Hartree–Fock (HF) theory. Dynamic electric dipole polarizability, optical rectification hyperpolarizability, and second harmonic generation hyperpolarizability tensors are evaluated for molecules strongly coupled to a single-mode optical cavity, and the results are benchmarked against the same tensors obtained from real-time time-dependent QED-HF simulations. Substantial cavity-induced changes to the frequency-dependent properties are observed for certain perturbing frequencies at large electron–photon coupling strengths. We also find special perturbing frequencies at which there is no cavity effect, regardless of the coupling strength.
{"title":"Dynamic Response Functions for Cavity Quantum Electrodynamics\u0000Hartree–Fock Theory","authors":"Stephen H. Yuwono,Katie A. Crouch,A. Eugene DePrince","doi":"10.1021/acs.jctc.6c01264","DOIUrl":"https://doi.org/10.1021/acs.jctc.6c01264","url":null,"abstract":"Abstract Frequency-dependent linear and quadratic response functions are implemented for a cavity quantum electrodynamics (QED) generalization of Hartree–Fock (HF) theory. Dynamic electric dipole polarizability, optical rectification hyperpolarizability, and second harmonic generation hyperpolarizability tensors are evaluated for molecules strongly coupled to a single-mode optical cavity, and the results are benchmarked against the same tensors obtained from real-time time-dependent QED-HF simulations. Substantial cavity-induced changes to the frequency-dependent properties are observed for certain perturbing frequencies at large electron–photon coupling strengths. We also find special perturbing frequencies at which there is no cavity effect, regardless of the coupling strength.","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":"24 1","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149209805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}