1
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Claudon B, Zylberman J, Feniou C, Debbasch F, Peruzzo A, Piquemal JP. Polylogarithmic-depth controlled-NOT gates without ancilla qubits. Nat Commun 2024; 15:5886. [PMID: 39003276 DOI: 10.1038/s41467-024-50065-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2024] [Accepted: 06/28/2024] [Indexed: 07/15/2024] Open
Abstract
Controlled operations are fundamental building blocks of quantum algorithms. Decomposing n-control-NOT gates (Cn(X)) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces Cn(X) circuits outperforming previous methods in the asymptotic and non-asymptotic regimes. Three distinct decompositions are presented: an exact one using one borrowed ancilla with a circuit depth Θ ( log ( n ) 3 ) , an approximating one without ancilla qubits with a circuit depth O ( log ( n ) 3 log ( 1 / ϵ ) ) and an exact one with an adjustable-depth circuit which decreases with the number m≤n of ancilla qubits available as O ( log ( n / ⌊ m / 2 ⌋ ) 3 + log ( ⌊ m / 2 ⌋ ) ) . The resulting exponential speedup is likely to have a substantial impact on fault-tolerant quantum computing by improving the complexities of countless quantum algorithms with applications ranging from quantum chemistry to physics, finance and quantum machine learning.
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Affiliation(s)
- Baptiste Claudon
- Qubit Pharmaceuticals, Advanced Research Department, Paris, France.
- Sorbonne Université, LCT, UMR 7616 CNRS, Paris, France.
| | - Julien Zylberman
- Sorbonne Université, Observatoire de Paris, Université PSL, CNRS, LERMA, Paris, France
| | - César Feniou
- Qubit Pharmaceuticals, Advanced Research Department, Paris, France
- Sorbonne Université, LCT, UMR 7616 CNRS, Paris, France
| | - Fabrice Debbasch
- Sorbonne Université, Observatoire de Paris, Université PSL, CNRS, LERMA, Paris, France
| | - Alberto Peruzzo
- Qubit Pharmaceuticals, Advanced Research Department, Paris, France
| | - Jean-Philip Piquemal
- Qubit Pharmaceuticals, Advanced Research Department, Paris, France.
- Sorbonne Université, LCT, UMR 7616 CNRS, Paris, France.
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2
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Rocca D, Cortes CL, Gonthier JF, Ollitrault PJ, Parrish RM, Anselmetti GL, Degroote M, Moll N, Santagati R, Streif M. Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization. J Chem Theory Comput 2024; 20:4639-4653. [PMID: 38788209 DOI: 10.1021/acs.jctc.4c00352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.
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Affiliation(s)
- Dario Rocca
- QC Ware Corporation, Palo Alto, California 94306, United States
| | | | | | | | | | | | - Matthias Degroote
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | - Nikolaj Moll
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | | | - Michael Streif
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
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3
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Jensen PWK, Kjellgren ER, Reinholdt P, Ziems KM, Coriani S, Kongsted J, Sauer SPA. Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing. J Chem Theory Comput 2024; 20:3613-3625. [PMID: 38701352 DOI: 10.1021/acs.jctc.4c00069] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/05/2024]
Abstract
Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH2 in the series of STO-3G/6-31G/6-31G* basis sets and of H4 and H2O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.
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Affiliation(s)
- Phillip W K Jensen
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Erik Rosendahl Kjellgren
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark
| | - Karl Michael Ziems
- Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Sonia Coriani
- Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen, Denmark
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4
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Ollitrault PJ, Loipersberger M, Parrish RM, Erhard A, Maier C, Sommer C, Ulmanis J, Monz T, Gogolin C, Tautermann CS, Anselmetti GLR, Degroote M, Moll N, Santagati R, Streif M. Estimation of Electrostatic Interaction Energies on a Trapped-Ion Quantum Computer. ACS CENTRAL SCIENCE 2024; 10:882-889. [PMID: 38680570 PMCID: PMC11046474 DOI: 10.1021/acscentsci.4c00058] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 03/11/2024] [Accepted: 03/12/2024] [Indexed: 05/01/2024]
Abstract
We present the first hardware implementation of electrostatic interaction energies by using a trapped-ion quantum computer. As test system for our computation, we focus on the reduction of NO to N2O catalyzed by a nitric oxide reductase (NOR). The quantum computer is used to generate an approximate ground state within the NOR active space. To efficiently measure the necessary one-particle density matrices, we incorporate fermionic basis rotations into the quantum circuit without extending the circuit length, laying the groundwork for further efficient measurement routines using factorizations. Measurements in the computational basis are then used as inputs for computing the electrostatic interaction energies on a classical computer. Our experimental results strongly agree with classical noise-less simulations of the same circuits, finding electrostatic interaction energies within chemical accuracy despite hardware noise. This work shows that algorithms tailored to specific observables of interest, such as interaction energies, may require significantly fewer quantum resources than individual ground state energies would require in the straightforward supermolecular approach.
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Affiliation(s)
- Pauline J. Ollitrault
- QC
Ware Corp., Palo Alto, California 94306, United States
- QC
Ware Corp., Paris 75003, France
| | - Matthias Loipersberger
- QC
Ware Corp., Palo Alto, California 94306, United States
- QC
Ware Corp., Paris 75003, France
| | - Robert M. Parrish
- QC
Ware Corp., Palo Alto, California 94306, United States
- QC
Ware Corp., Paris 75003, France
| | | | | | | | - Juris Ulmanis
- Alpine
Quantum Technologies GmbH, 6020 Innsbruck, Austria
| | - Thomas Monz
- Alpine
Quantum Technologies GmbH, 6020 Innsbruck, Austria
- Institut
für Experimentalphysik, Universität
Innsbruck, 6020 Innsbruck, Austria
| | | | - Christofer S. Tautermann
- Medicinal
Chemistry, Boehringer Ingelheim Pharma GmbH
& Co. KG, 88397 Biberach, Germany
- Department
of General, Inorganic and Theoretical Chemistry, University of Innsbruck, 6020 Innsbruck, Austria
| | | | - Matthias Degroote
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | - Nikolaj Moll
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | | | - Michael Streif
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
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5
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Fitzpatrick A, Nykänen A, Talarico NW, Lunghi A, Maniscalco S, García-Pérez G, Knecht S. Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive. J Phys Chem A 2024; 128:2843-2856. [PMID: 38547028 DOI: 10.1021/acs.jpca.3c05882] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.
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Affiliation(s)
- Aaron Fitzpatrick
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland
- Trinity Quantum Alliance, Unit 16, Trinity Technology and Enterprise Centre, Pearse Street, Dublin 2 D02 YN67, Ireland
| | - Anton Nykänen
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland
| | | | - Alessandro Lunghi
- School of Physics, AMBER and CRANN Institute, Trinity College, Dublin 2, Ireland
| | | | | | - Stefan Knecht
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences Vladimir-Prelog-Weg 1-5/10, Zürich 8093, Switzerland
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6
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Christopoulou G, Di Paola C, Elzinga FE, Jallat A, Muñoz Ramo D, Krompiec M. Quantum hardware calculations of the activation and dissociation of nitrogen on iron clusters and surfaces. Phys Chem Chem Phys 2024; 26:5895-5906. [PMID: 38315092 DOI: 10.1039/d3cp05167f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2024]
Abstract
Catalytic processes are the cornerstone of chemical industry, and catalytic conversion of nitrogen to ammonia remains one of the largest industrial processes implemented. Rational design of catalysts and catalytic reactions largely depends on approximate computational chemistry methods, such as density functional theory, which, however, suffer from limited accuracy, especially for strongly-correlated materials. Rigorous ab initio methods which account for static and dynamic electron correlation, while arbitrarily accurate for small systems, are generally too expensive to be applied to modelling of catalytic cycles, due to prohibitive time and space computational complexity with respect to the size of the active space. Recent advances in quantum computing give hope for enabling access to accurate ab initio methods at scale. Herein, we present a prototype hybrid quantum-classical workflow for modeling chemical reactions on surfaces, applied to proof-of-concept models of activation and dissociation of nitrogen on small Fe clusters and a single-layer (221) iron surface. First, we determined the structures of species present in the catalytic cycle at DFT level and studied their electronic structure using CASSCF. We show that it is possible to decouple the half-filled Fe-3d band from the Fe-N and N-N bond orbitals, thereby reducing the active space significantly. Subsequently, we translated the CASSCF wavefunctions into corresponding qubit quantum states, using the Adaptive Variational Quantum Eigensolver, and estimated their energies using a state vector simulator, H1-1E quantum emulator and (for selected systems) H1-1 quantum computer. We demonstrated that if a sufficiently small active orbital space is chosen, ground state energies obtained with classical methods and with the quantum computer are in reasonable agreement. We argue that once quantum computing methods are scaled up so that larger active spaces are accessible, they can offer a tremendous practical advantage to the computational catalysis community.
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Affiliation(s)
| | - Cono Di Paola
- Quantinuum, Terrington House, 13-15 Hills Road, CB2 1NL, Cambridge, UK.
| | | | | | - David Muñoz Ramo
- Quantinuum, Terrington House, 13-15 Hills Road, CB2 1NL, Cambridge, UK.
| | - Michal Krompiec
- Quantinuum, Terrington House, 13-15 Hills Road, CB2 1NL, Cambridge, UK.
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7
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Mazzola G. Quantum computing for chemistry and physics applications from a Monte Carlo perspective. J Chem Phys 2024; 160:010901. [PMID: 38165101 DOI: 10.1063/5.0173591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 10/18/2023] [Indexed: 01/03/2024] Open
Abstract
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo solutions into quantum algorithms. These include refined energy estimators, parameter optimization, real and imaginary-time dynamics, and variational circuits. Conversely, we will review new ideas for utilizing quantum hardware to accelerate the sampling in statistical classical models, with applications in physics, chemistry, optimization, and machine learning. This review aims to be accessible to both communities and intends to foster further algorithmic developments at the intersection of quantum computing and Monte Carlo methods. Most of the works discussed in this Perspective have emerged within the last two years, indicating a rapidly growing interest in this promising area of research.
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Affiliation(s)
- Guglielmo Mazzola
- Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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8
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Loaiza I, Izmaylov AF. Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries. J Chem Theory Comput 2023; 19:8201-8209. [PMID: 37939198 DOI: 10.1021/acs.jctc.3c00912] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2023]
Abstract
Computational cost of energy estimation for molecular electronic Hamiltonians via quantum phase estimation (QPE) grows with the difference between the largest and smallest eigenvalues of the Hamiltonian. In this work, we propose a preprocessing procedure that reduces the norm of the Hamiltonian without changing its eigenspectrum for the target states of a particular symmetry. The new procedure, block-invariant symmetry shift (BLISS), builds an operator T̂ such that the cost of implementing H ^ - T ^ is reduced compared to that of Ĥ, yet H ^ - T ^ acts on the subspaces of interest the same way as Ĥ does. BLISS performance is demonstrated for a linear combination of unitaries (LCU)-based QPE approaches on a set of small molecules. Using the number of electrons as the symmetry specifying the target set of states, BLISS provided a factor of 2 reduction of 1-norm for several LCU decompositions compared to their unshifted versions.
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Affiliation(s)
- Ignacio Loaiza
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto M5S 3H6, Canada
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto M1C 1A4, Canada
- Zapata Computing Canada Inc., Toronto M5E 1E5, Canada
| | - Artur F Izmaylov
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto M5S 3H6, Canada
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto M1C 1A4, Canada
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9
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Nishio S, Oba Y, Kurashige Y. Statistical errors in reduced density matrices sampled from quantum circuit simulation and the impact on multireference perturbation theory. Phys Chem Chem Phys 2023; 25:30525-30535. [PMID: 37927233 DOI: 10.1039/d3cp03520d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2023]
Abstract
In this work, we present a detailed analysis of statistical errors in reduced density matrices (RDMs) of active space wavefunctions sampled from quantum circuit simulation and the impact on results obtained by the multireference theories. From the sampling experiments, it is shown that the errors in sampled RDMs have a larger value for higher-order RDMs, and that the errors in sampled RDMs for excited states are larger than those for the ground state. We analytically derive the expected value of the sum of squared errors between the true distribution and sample distribution of weights of the electron configurations based on a multinomial distribution model, with which we present an assessment of the dependency of RDM errors on the number of shots for the observation (Nshot) and on the character of the target electronic state. With the benchmark calculations of short polyenes, C4H6 and C6H8, we report the statistical errors in CASCI and complete active space second-order perturbation theory (CASPT2) energies obtained with the sampled 1,2-RDMs and 1,2,3,4-RDMs, respectively. It was found that the standard deviation (SD) of the sampled CASCI energies is proportional to as predicted. It was also found that the dependence of the SD of the second-order correction energies are somewhat different but the errors in the reference CASCI energies are dominant as compared with the corrections and the SD of the resulting CASPT2 energies are proportional to . This suggests that the required Nshot for 3,4-RDMs used only in the second-order perturbative corrections is smaller than that for 1,2-RDM used to calculate the reference CASCI energies. It was also suggested from the analysis of the errors in the sampled energies that the required Nshot for 3-RDM, which is used to calculate the perturbative correction energies, can be smaller than that for 2-RDM to calculate the CASCI energies. In fact, it was shown that the potential energy curve along the isomerization reaction of the {[Cu(NH3)3]2O2}2+ complex as an archetype of metalloenzyme, in which static and dynamical electron correlations are both important, can be reasonably reproduced with Nshot = 106 for 1,2-RDMs but Nshot = 105 for 3-RDM by the sampling simulation.
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Affiliation(s)
- Soichiro Nishio
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto, 606-8502, Japan.
| | - Yuki Oba
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto, 606-8502, Japan.
| | - Yuki Kurashige
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto, 606-8502, Japan.
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10
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Yamaguchi K, Isobe H, Shoji M, Kawakami T, Miyagawa K. The Nature of the Chemical Bonds of High-Valent Transition-Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl-Radical Character by the Classical to Quantum Computations. Molecules 2023; 28:7119. [PMID: 37894598 PMCID: PMC10609222 DOI: 10.3390/molecules28207119] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Revised: 10/08/2023] [Accepted: 10/10/2023] [Indexed: 10/29/2023] Open
Abstract
This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).
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Affiliation(s)
- Kizashi Yamaguchi
- SANKEN, Osaka University, Ibaraki 567-0047, Osaka, Japan
- Center for Quantum Information and Quantum Biology (QIQB), Osaka University, Toyonaka 560-0043, Osaka, Japan
| | - Hiroshi Isobe
- Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Okayama, Japan;
| | - Mitsuo Shoji
- Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Ibaraki, Japan; (M.S.); (K.M.)
| | - Takashi Kawakami
- Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka 560-0043, Osaka, Japan;
| | - Koichi Miyagawa
- Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Ibaraki, Japan; (M.S.); (K.M.)
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11
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Babbush R, Huggins WJ, Berry DW, Ung SF, Zhao A, Reichman DR, Neven H, Baczewski AD, Lee J. Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods. Nat Commun 2023; 14:4058. [PMID: 37429883 DOI: 10.1038/s41467-023-39024-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2022] [Accepted: 05/26/2023] [Indexed: 07/12/2023] Open
Abstract
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.
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Affiliation(s)
| | | | - Dominic W Berry
- Department of Physics and Astronomy, Macquarie University, Sydney, NSW, Australia
| | - Shu Fay Ung
- Department of Chemistry, Columbia University, New York, NY, USA
| | - Andrew Zhao
- Google Quantum AI, Venice, CA, USA
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA
| | | | | | - Andrew D Baczewski
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, NM, USA
| | - Joonho Lee
- Google Quantum AI, Venice, CA, USA.
- Department of Chemistry, Columbia University, New York, NY, USA.
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, USA.
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12
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Pierce K, Valeev EF. Efficient Construction of Canonical Polyadic Approximations of Tensor Networks. J Chem Theory Comput 2023; 19:71-81. [PMID: 36484711 DOI: 10.1021/acs.jctc.2c00861] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
We consider the problem of constructing a canonical polyadic (CP) decomposition for a tensor network, rather than a single tensor. We illustrate how it is possible to reduce the complexity of constructing an approximate CP representation of the network by leveraging its structure in the course of the CP factor optimization. The utility of this technique is demonstrated for the order-4 Coulomb interaction tensor approximated by two order-3 tensors via an approximate generalized square-root (SQ) factorization, such as density fitting or (pivoted) Cholesky. The complexity of constructing a four-way CP decomposition is reduced from O(n4RCP) (for the nonapproximated Coulomb tensor) to O(n3RCP) (for the SQ-factorized Coulomb tensor), where n and RCP are the basis and CP ranks, respectively. This reduces the cost of constructing the CP approximation of two-body interaction tensors of relevance to accurate many-body electronic structure by up to 2 orders of magnitude for systems with up to 36 atoms studied here. The full four-way CP approximation of the Coulomb interaction tensor is shown to be more accurate than the known approaches which utilize CP-factorizations of the SQ factors (which are also constructed with an O(n3RCP) cost), such as the algebraic pseudospectral and tensor hypercontraction approaches. The CP-decomposed SQ factors can also serve as a robust initial guess for the four-way CP factors.
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Affiliation(s)
- Karl Pierce
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia24061, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia24061, United States
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