1
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Jensen RB, Christiansen O. Unitary vibrational coupled cluster: General theory and implementation. J Chem Phys 2025; 162:084112. [PMID: 40013890 DOI: 10.1063/5.0249469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2024] [Accepted: 01/31/2025] [Indexed: 02/28/2025] Open
Abstract
Along with the surge in interest in quantum computing, interest in the unitary coupled cluster (UCC) Ansatz has reemerged. Although extensively studied within electronic structure theory, the UCC Ansatz remains relatively unexplored for the problem of molecular vibrations. In this contribution, working equations for the unitary vibrational coupled cluster (UVCC) Ansatz are derived, implemented, and benchmarked. Accuracy and convergence of state-specific excitation energies toward the full vibrational configuration interaction (FVCI) limit are observed to be comparable to vibrational coupled cluster theory. In addition, the overlap of a truncated UVCC state with the FVCI state is shown to exhibit some interesting properties from the perspective of fault-tolerant quantum computing.
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Affiliation(s)
- Rasmus Berg Jensen
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
- Kvantify Aps, DK-2300 Copenhagen S, Denmark
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
- Kvantify Aps, DK-2300 Copenhagen S, Denmark
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2
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Malpathak S, Kallullathil SD, Izmaylov AF. Simulating Vibrational Dynamics on Bosonic Quantum Devices. J Phys Chem Lett 2025; 16:1855-1864. [PMID: 39950938 DOI: 10.1021/acs.jpclett.4c03480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/28/2025]
Abstract
Bosonic quantum devices, which utilize harmonic oscillator modes to encode information, are emerging as a promising alternative to conventional qubit-based quantum devices, especially for the simulation of vibrational dynamics and spectroscopy. We present a framework for digital quantum simulation of vibrational dynamics under anharmonic potentials on these bosonic devices. In our approach, the vibrational Hamiltonian is decomposed into solvable fragments that can be used for Hamiltonian simulation on currently available bosonic hardware. Specifically, we have extended the Cartan subalgebra approach [Yen, T.C.; Izmaylov, A. F. PRX Quantum 2, 2021; 040320]- a method for decomposing quantum Hamiltonians into solvable parts- to bosonic operators, enabling us to construct anharmonic Hamiltonian fragments that can be efficiently diagonalized using Bogoliubov transforms. The approach is tested using a simulation of tunneling dynamics in a model two-dimensional double-well potential and calculations of vibrational eigenenergies for small molecules. Our fragmentation scheme provides a new approach for digital quantum simulations on bosonic quantum hardware for multimode anharmonic vibrational dynamics.
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Affiliation(s)
- Shreyas Malpathak
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Sangeeth Das Kallullathil
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Artur F Izmaylov
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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3
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Olarte Hernandez R, Soldera A, Champagne B. Vibronic Structure of the UV/Visible Absorption Spectra of Phenol and Phenolate: A Hybrid Density Functional Theory─Doktorov's Quantum Algorithm Approach. J Phys Chem A 2025; 129:396-406. [PMID: 39718998 DOI: 10.1021/acs.jpca.4c06960] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2024]
Abstract
The Doktorov's quantum algorithm has been enacted in combination with time-dependent density functional theory (TD-DFT) to simulate the vibronic structure of the UV/visible absorption spectra of the phenol and phenolate molecules. On the one hand, DFT and TD-DFT are employed with classical algorithms to calculate the ground and excited-state electronic structures as well as their vibrational frequencies and normal modes, whereas, on the other hand, quantum algorithms are employed for evaluating the vibrational transition intensities. In comparison to a previous study, J. Phys. Chem. A 2024, 128, 4369-4377, which demonstrated Doktorov's quantum algorithm as a proof of concept to predict the vibronic structure of ionization spectra, it is applied here to medium-size molecules with more than 30 vibrational normal modes, without accounting for Duschinsky rotations due to software limitations. This application to simulate the vibronic structures of the spectra of phenol and phenolate also enables assessing the impact of the differences in vibrational frequencies between the ground and excited electronic states.
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Affiliation(s)
- Renato Olarte Hernandez
- Theoretical Chemistry Lab, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, Rue de Bruxelles, 61, Namur B-5000, Belgium
- Laboratory of Physical Chemistry of Matter, Department of Chemistry, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada
| | - Armand Soldera
- Laboratory of Physical Chemistry of Matter, Department of Chemistry, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada
| | - Benoît Champagne
- Theoretical Chemistry Lab, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, Rue de Bruxelles, 61, Namur B-5000, Belgium
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4
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Xu R, Jiang Z, Yang Q, Bloino J, Biczysko M. Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers. J Comput Chem 2024; 45:1846-1869. [PMID: 38682874 DOI: 10.1002/jcc.27377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2024] [Revised: 04/01/2024] [Accepted: 04/02/2024] [Indexed: 05/01/2024]
Abstract
Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.
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Affiliation(s)
- Ruiqin Xu
- Department of Physics, College of Sciences, Shanghai University, Shanghai, China
| | | | - Qin Yang
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Science, Prague, Czechia
| | - Julien Bloino
- Classe di Scienze, Scuola Normale Superiore, Pisa, Italy
| | - Malgorzata Biczysko
- Department of Physics, College of Sciences, Shanghai University, Shanghai, China
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5
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Majee K, Chakraborty S, Mukhopadhyay T, Nayak MK, Dutta AK. A reduced cost four-component relativistic unitary coupled cluster method for atoms and molecules. J Chem Phys 2024; 161:034101. [PMID: 39007370 DOI: 10.1063/5.0207091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Accepted: 06/12/2024] [Indexed: 07/16/2024] Open
Abstract
We present a four-component relativistic unitary coupled cluster method for atoms and molecules. We have used commutator-based non-perturbative approximation using the "Bernoulli expansion" to derive an approximation to the relativistic unitary coupled cluster method. The performance of the full quadratic unitary coupled-cluster singles and doubles method (qUCCSD), as well as a perturbative approximation variant (UCC3), has been reported for both energies and properties. It can be seen that both methods give results comparable to those of the standard relativistic coupled cluster method. The qUCCSD method shows better agreement with experimental results due to the better inclusion of relaxation effects. The relativistic UCC3 and qUCCSD methods can simulate the spin-forbidden transition with easy access to transition properties. A natural spinor-based scheme to reduce the computational cost of relativistic UCC3 and qUCCSD methods has been discussed.
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Affiliation(s)
- Kamal Majee
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Sudipta Chakraborty
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Tamoghna Mukhopadhyay
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Malaya K Nayak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
- Homi Bhabha National Institute, BARC Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Achintya Kumar Dutta
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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6
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Olarte Hernandez R, Champagne B, Soldera A. Simulating Vibronic Spectra by Direct Application of Doktorov Formulas on a Superconducting Quantum Simulator. J Phys Chem A 2024; 128:4369-4377. [PMID: 38751235 DOI: 10.1021/acs.jpca.4c01234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2024]
Abstract
In this work, a direct quantum implementation of the Doktorov formulas for calculating the vibronic spectrum of molecules under the harmonic approximation is presented. It is applied to the three-atom molecules H2O, SO2, ClO2, HS2, and ZnOH. The method solves the classically hard problem of estimating the Franck-Condon (FC) factors by using the Duschinsky matrices as the only input via the Doktorov quantum circuit. This has the advantage of avoiding basis changes, artificial squeezing parameters, and symmetry dependencies. In other words, it is a general method for three-atom molecules that can easily be generalized to bigger molecules. The results are compared with other quantum algorithms and classical anharmonic algorithms. Furthermore, the circuit requirements are studied in order to estimate its applicability on real superconducting quantum hardware.
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Affiliation(s)
- Renato Olarte Hernandez
- Theoretical Chemistry Lab, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, rue de Bruxelles 61, B-5000 Namur, Belgium
- Laboratory of Physical Chemistry of Matter, Department of Chemistry, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| | - Benoît Champagne
- Theoretical Chemistry Lab, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, rue de Bruxelles 61, B-5000 Namur, Belgium
| | - Armand Soldera
- Laboratory of Physical Chemistry of Matter, Department of Chemistry, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
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7
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Kale SS, Kais S. Simulation of Chemical Reactions on a Quantum Computer. J Phys Chem Lett 2024; 15:5633-5642. [PMID: 38759104 DOI: 10.1021/acs.jpclett.4c01100] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/19/2024]
Abstract
Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities. In this study, we develop and apply a quantum computing algorithm for the calculation of scattering matrix elements. In our approach, we employ the time-dependent method based on the Møller operator formulation where the S-matrix element between the respective reactant and product channels is determined through the time correlation function of the reactant and product Møller wavepackets. We successfully apply our quantum algorithm to calculate scattering matrix elements for 1D semi-infinite square well potential and on the colinear hydrogen exchange reaction. As we navigate the complexities of quantum interactions, this quantum algorithm is general and emerges as a promising avenue, shedding light on new possibilities for simulating chemical reactions on quantum computers.
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Affiliation(s)
- Sumit Suresh Kale
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Sabre Kais
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
- Department of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
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8
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Majland M, Ettenhuber P, Zinner NT, Christiansen O. Vibrational ADAPT-VQE: Critical points lead to problematic convergence. J Chem Phys 2024; 160:154109. [PMID: 38634491 DOI: 10.1063/5.0191074] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 04/02/2024] [Indexed: 04/19/2024] Open
Abstract
Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.
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Affiliation(s)
- Marco Majland
- Kvantify Aps, DK-2300 Copenhagen S, Denmark
- Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
| | | | - Nikolaj Thomas Zinner
- Kvantify Aps, DK-2300 Copenhagen S, Denmark
- Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark
| | - Ove Christiansen
- Kvantify Aps, DK-2300 Copenhagen S, Denmark
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
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9
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Gong Q, Man Q, Zhao J, Li Y, Dou M, Wang Q, Wu YC, Guo GP. Simulating chemical reaction dynamics on quantum computer. J Chem Phys 2024; 160:124103. [PMID: 38526102 DOI: 10.1063/5.0192036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 03/06/2024] [Indexed: 03/26/2024] Open
Abstract
The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.
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Affiliation(s)
- Qiankun Gong
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Qingmin Man
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Jianyu Zhao
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Ye Li
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Menghan Dou
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Qingchun Wang
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, Anhui 230088, China
| | - Yu-Chun Wu
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, Anhui 230088, China
- CAS Key Laboratory of Quantum Information, School of Physics, University of Science and Technology of China, Hefei 230026, China
| | - Guo-Ping Guo
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, Anhui 230088, China
- CAS Key Laboratory of Quantum Information, School of Physics, University of Science and Technology of China, Hefei 230026, China
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10
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Prasad VK, Cheng F, Fekl U, Jacobsen HA. Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry. Phys Chem Chem Phys 2024; 26:4071-4082. [PMID: 38225897 DOI: 10.1039/d3cp03523a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2024]
Abstract
The field of quantum computing has the potential to transform quantum chemistry. The variational quantum eigensolver (VQE) algorithm has allowed quantum computing to be applied to chemical problems in the noisy intermediate-scale quantum (NISQ) era. Applications of VQE have generally focused on predicting absolute energies instead of chemical properties that are relative energy differences and that are most interesting to chemists studying a chemical problem. We address this shortcoming by constructing a molecular benchmark data set in this work containing isomers of C10H16 and carbocationic rearrangements of C10H15+, calculated at a high-level of theory. Using the data set, we compared noiseless VQE simulations to conventionally performed density functional and wavefunction theory-based methods to understand the quality of results. We also investigated the effectiveness of a quantum state tomography-based error mitigation technique in applications of VQE under noise (simulated and real). Our findings reveal that the use of quantum error mitigation is crucial in the NISQ era and advantageous to yield almost noiseless quality results.
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Affiliation(s)
- Viki Kumar Prasad
- The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 Kings College Road, Toronto, Ontario, Canada, M5S 3G4. arno,
- Department of Chemical and Physical Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Mississauga, Ontario, Canada, L5L 1C6.
| | - Freeman Cheng
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada, M5S 2E4
| | - Ulrich Fekl
- Department of Chemical and Physical Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Mississauga, Ontario, Canada, L5L 1C6.
| | - Hans-Arno Jacobsen
- The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 Kings College Road, Toronto, Ontario, Canada, M5S 3G4. arno,
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada, M5S 2E4
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11
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Iyengar SS, Zhang JH, Saha D, Ricard TC. Graph-| Q⟩⟨ C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure. J Phys Chem A 2023; 127:9334-9345. [PMID: 37906738 DOI: 10.1021/acs.jpca.3c04261] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
The accurate determination of chemical properties is known to have a critical impact on multiple fundamental chemical problems but is deeply hindered by the steep algebraic scaling of electron correlation calculations and the exponential scaling of quantum nuclear dynamics. With the advent of new quantum computing hardware and associated developments in creating new paradigms for quantum software, this avenue has been recognized as perhaps one way to address exponentially complex challenges in quantum chemistry and molecular dynamics. In this paper, we discuss a new approach to drastically reduce the quantum circuit depth (by several orders of magnitude) and help improve the accuracy in the quantum computation of electron correlation energies for large molecular systems. The method is derived from a graph-theoretic approach to molecular fragmentation and enables us to create a family of projection operators that decompose quantum circuits into separate unitary processes. Some of these processes can be treated on quantum hardware and others on classical hardware in a completely asynchronous and parallel fashion. Numerical benchmarks are provided through the computation of unitary coupled-cluster singles and doubles (UCCSD) energies for medium-sized protonated and neutral water clusters using the new quantum algorithms presented here.
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Affiliation(s)
- Srinivasan S Iyengar
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Juncheng Harry Zhang
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Debadrita Saha
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Timothy C Ricard
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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12
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Schleich P, Boen J, Cincio L, Anand A, Kottmann JS, Tretiak S, Dub PA, Aspuru-Guzik A. Partitioning Quantum Chemistry Simulations with Clifford Circuits. J Chem Theory Comput 2023. [PMID: 37490516 DOI: 10.1021/acs.jctc.3c00335] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/27/2023]
Abstract
Current quantum computing hardware is restricted by the availability of only few, noisy qubits which limits the investigation of larger, more complex molecules in quantum chemistry calculations on quantum computers in the near term. In this work, we investigate the limits of their classical and near-classical treatment while staying within the framework of quantum circuits and the variational quantum eigensolver. To this end, we consider naive and physically motivated, classically efficient product ansatz for the parametrized wavefunction adapting the separable-pair ansatz form. We combine it with post-treatment to account for interactions between subsystems originating from this ansatz. The classical treatment is given by another quantum circuit that has support between the enforced subsystems and is folded into the Hamiltonian. To avoid an exponential increase in the number of Hamiltonian terms, the entangling operations are constructed from purely Clifford or near-Clifford circuits. While Clifford circuits can be simulated efficiently classically, they are not universal. In order to account for missing expressibility, near-Clifford circuits with only few, selected non-Clifford gates are employed. The exact circuit structure to achieve this objective is molecule-dependent and is constructed using simulated annealing and genetic algorithms. We demonstrate our approach on a set of molecules of interest and investigate the extent of our methodology's reach.
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Affiliation(s)
- Philipp Schleich
- Department of Computer Science, University of Toronto, Toronto M5S 1A1, Canada
- Vector Institute for Artificial Intelligence, Toronto M5G 1M1, Canada
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Joseph Boen
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Department of Applied Mathematics & Statistics, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Abhinav Anand
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto M5S 1A1, Canada
| | - Jakob S Kottmann
- Department of Computer Science, University of Augsburg, Augsburg 86159, Germany
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Alán Aspuru-Guzik
- Department of Computer Science, University of Toronto, Toronto M5S 1A1, Canada
- Vector Institute for Artificial Intelligence, Toronto M5G 1M1, Canada
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto M5S 1A1, Canada
- Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto M5S 1A1, Canada
- Department of Materials Science and Engineering, University of Toronto, Toronto M5S 1A1, Canada
- Canadian Institute for Advanced Research (CIFAR) Lebovic Fellow, Toronto M5S 1M1, Canada
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13
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Majland M, Berg Jensen R, Greisen Højlund M, Thomas Zinner N, Christiansen O. Optimizing the number of measurements for vibrational structure on quantum computers: coordinates and measurement schemes. Chem Sci 2023; 14:7733-7742. [PMID: 37476724 PMCID: PMC10355095 DOI: 10.1039/d3sc01984e] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 06/07/2023] [Indexed: 07/22/2023] Open
Abstract
One of the primary challenges prohibiting demonstrations of practical quantum advantages for near-term devices amounts to excessive measurement overheads for estimating relevant physical quantities such as ground state energies. However, with major differences between the electronic and vibrational structures of molecules, the question of how the resource requirements of computing anharmonic, vibrational states can be reduced remains relatively unexplored compared to its electronic counterpart. Importantly, bosonic commutation relations, distinguishable Hilbert spaces and vibrational coordinates allow manipulations of the vibrational system that can be exploited to minimize resource requirements. In this work, we investigate the impact of different coordinate systems and measurement schemes on the number of measurements needed to estimate anharmonic, vibrational states for a variety of three-mode (six-mode) molecules. We demonstrate an average of 3-fold (1.5-fold), with up to 7-fold (2.5-fold), reduction in the number of measurements required by employing appropriate coordinate transformations, based on an automized construction of qubit Hamiltonians from a conventional vibrational structure program.
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Affiliation(s)
- Marco Majland
- Kvantify Aps DK-2300 Copenhagen S Denmark
- Department of Physics and Astronomy, Aarhus University DK-8000 Aarhus C Denmark
- Department of Chemistry, Aarhus University DK-8000 Aarhus C Denmark
| | - Rasmus Berg Jensen
- Department of Physics and Astronomy, Aarhus University DK-8000 Aarhus C Denmark
- Department of Chemistry, Aarhus University DK-8000 Aarhus C Denmark
| | | | - Nikolaj Thomas Zinner
- Kvantify Aps DK-2300 Copenhagen S Denmark
- Department of Physics and Astronomy, Aarhus University DK-8000 Aarhus C Denmark
| | - Ove Christiansen
- Kvantify Aps DK-2300 Copenhagen S Denmark
- Department of Chemistry, Aarhus University DK-8000 Aarhus C Denmark
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14
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Li W, Allcock J, Cheng L, Zhang SX, Chen YQ, Mailoa JP, Shuai Z, Zhang S. TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era. J Chem Theory Comput 2023. [PMID: 37317520 DOI: 10.1021/acs.jctc.3c00319] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
TenCirChem is an open-source Python library for simulating variational quantum algorithms for quantum computational chemistry. TenCirChem shows high-performance in the simulation of unitary coupled-cluster circuits, using compact representations of quantum states and excitation operators. Additionally, TenCirChem supports noisy circuit simulation and provides algorithms for variational quantum dynamics. TenCirChem's capabilities are demonstrated through various examples, such as the calculation of the potential energy curve of H2O with a 6-31G(d) basis set using a 34-qubit quantum circuit, the examination of the impact of quantum gate errors on the variational energy of the H2 molecule, and the exploration of the Marcus inverted region for charge transfer rate based on variational quantum dynamics. Furthermore, TenCirChem is capable of running real quantum hardware experiments, making it a versatile tool for both simulation and experimentation in the field of quantum computational chemistry.
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Affiliation(s)
- Weitang Li
- Tencent Quantum Lab, Shenzhen 518057, China
| | | | | | | | | | | | - Zhigang Shuai
- Department of Chemistry, Tsinghua University, Beijing, 100084, China
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, China
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15
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Mátyus E, Martín Santa Daría A, Avila G. Exact quantum dynamics developments for floppy molecular systems and complexes. Chem Commun (Camb) 2023; 59:366-381. [PMID: 36519578 DOI: 10.1039/d2cc05123k] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Molecular rotation, vibration, internal rotation, isomerization, tunneling, intermolecular dynamics of weakly and strongly interacting systems, intra-to-inter-molecular energy transfer, hindered rotation and hindered translation over surfaces are important types of molecular motions. Their fundamentally correct and detailed description can be obtained by solving the nuclear Schrödinger equation on a potential energy surface. Many of the chemically interesting processes involve quantum nuclear motions which are 'delocalized' over multiple potential energy wells. These 'large-amplitude' motions in addition to the high dimensionality of the vibrational problem represent challenges to the current (ro)vibrational methodology. A review of the quantum nuclear motion methodology is provided, current bottlenecks of solving the nuclear Schrödinger equation are identified, and solution strategies are reviewed. Technical details, computational results, and analysis of these results in terms of limiting models and spectroscopically relevant concepts are highlighted for selected numerical examples.
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Affiliation(s)
- Edit Mátyus
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary.
| | - Alberto Martín Santa Daría
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary.
| | - Gustavo Avila
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary.
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16
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Miessen A, Ollitrault PJ, Tacchino F, Tavernelli I. Quantum algorithms for quantum dynamics. NATURE COMPUTATIONAL SCIENCE 2023; 3:25-37. [PMID: 38177956 DOI: 10.1038/s43588-022-00374-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2021] [Accepted: 11/12/2022] [Indexed: 01/06/2024]
Abstract
Among the many computational challenges faced across different disciplines, quantum-mechanical systems pose some of the hardest ones and offer a natural playground for the growing field of quantum technologies. In this Perspective, we discuss quantum algorithmic solutions for quantum dynamics, reporting on the latest developments and offering a viewpoint on their potential and current limitations. We present some of the most promising areas of application and identify possible research directions for the coming years.
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Affiliation(s)
| | - Pauline J Ollitrault
- IBM Quantum, IBM Research - Zurich, Rüschlikon, Switzerland
- QC Ware, Palo Alto, CA, USA
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17
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Kumar A, DeGregorio N, Ricard T, Iyengar SS. Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics. J Chem Theory Comput 2022; 18:7243-7259. [PMID: 36332133 DOI: 10.1021/acs.jctc.2c00484] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Molecular fragmentation methods have revolutionized quantum chemistry. Here, we use a graph-theoretically generated molecular fragmentation method, to obtain accurate and efficient representations for multidimensional potential energy surfaces and the quantum time-evolution operator, which plays a critical role in quantum chemical dynamics. In doing so, we find that the graph-theoretic fragmentation approach naturally reduces the potential portion of the time-evolution operator into a tensor network that contains a stream of coupled lower-dimensional propagation steps to potentially achieve quantum dynamics with reduced complexity. Furthermore, the fragmentation approach used here has previously been shown to allow accurate and efficient computation of post-Hartree-Fock electronic potential energy surfaces, which in many cases has been shown to be at density functional theory cost. Thus, by combining the advantages of molecular fragmentation with the tensor network formalism, the approach yields an on-the-fly quantum dynamics scheme where both the electronic potential calculation and nuclear propagation portion are enormously simplified through a single stroke. The method is demonstrated by computing approximations to the propagator and to potential surfaces for a set of coupled nuclear dimensions within a protonated water wire problem exhibiting the Grotthuss mechanism of proton transport. In all cases, our approach has been shown to reduce the complexity of representing the quantum propagator, and by extension action of the propagator on an initial wavepacket, by several orders, with minimal loss in accuracy.
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Affiliation(s)
- Anup Kumar
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Nicole DeGregorio
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Timothy Ricard
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
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18
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Zhang JH, Iyengar SS. Graph-| Q⟩⟨ C|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid Quantum/Classical Hardware Systems: Improved Quantum Circuit Depth Performance. J Chem Theory Comput 2022; 18:2885-2899. [PMID: 35412836 DOI: 10.1021/acs.jctc.1c01303] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a procedure to reduce the depth of quantum circuits and improve the accuracy of results in computing post-Hartree-Fock electronic structure energies in large molecular systems. The method is based on molecular fragmentation where a molecular system is divided into overlapping fragments through a graph-theoretic procedure. This allows us to create a set of projection operators that decompose the unitary evolution of the full system into separate sets of processes, some of which can be treated on quantum hardware and others on classical hardware. Thus, we develop a procedure for an electronic structure that can be asynchronously spawned onto a potentially large ensemble of classical and quantum hardware systems. We demonstrate this method by computing Unitary Coupled Cluster Singles and Doubles (UCCSD) energies for a set of [H2]n clusters, with n ranging from 4 to 128. We implement our methodology using quantum circuits, and when these quantum circuits are processed on a quantum simulator, we obtain energies in agreement with the UCCSD energies in the milli-hartree energy range. We also show that our circuit decomposition approach yields up to 9 orders of magnitude reduction in the number of CNOT gates and quantum circuit depth for the large-sized clusters when compared to a standard quantum circuit implementation available on IBM's Quantum Information Science kit, known as Qiskit.
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Affiliation(s)
- Juncheng Harry Zhang
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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19
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Bernal DE, Ajagekar A, Harwood SM, Stober ST, Trenev D, You F. Perspectives of Quantum Computing for Chemical Engineering. AIChE J 2022. [DOI: 10.1002/aic.17651] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- David E. Bernal
- Research Institute for Advanced Computer Science Universities Space Research Association Mountain View California USA
- Quantum Artificial Intelligence Laboratory (QuAIL) NASA Ames Research Center Moffett Field California USA
- Department of Chemical Engineering Carnegie Mellon University Pittsburgh Pennsylvania USA
| | | | - Stuart M. Harwood
- Corporate Strategic Research ExxonMobil Research and Engineering Clinton New Jersey USA
| | - Spencer T. Stober
- Corporate Strategic Research ExxonMobil Research and Engineering Clinton New Jersey USA
| | - Dimitar Trenev
- Corporate Strategic Research ExxonMobil Research and Engineering Clinton New Jersey USA
| | - Fengqi You
- Systems Engineering Cornell University New York USA
- Robert Frederick Smith School of Chemical and Biomolecular Engineering Cornell University New York USA
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20
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Anand A, Schleich P, Alperin-Lea S, Jensen PWK, Sim S, Díaz-Tinoco M, Kottmann JS, Degroote M, Izmaylov AF, Aspuru-Guzik A. A quantum computing view on unitary coupled cluster theory. Chem Soc Rev 2022; 51:1659-1684. [PMID: 35166276 DOI: 10.1039/d1cs00932j] [Citation(s) in RCA: 64] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided, followed by a broad discussion of the formulation of CC theory. This includes touching on the merits and difficulties of the method and several variants, UCC among them, in the classical context, to motivate their applications on quantum computers. In the core of the text, the UCC ansatz and its implementation on a quantum computer are discussed at length, in addition to a discussion on several derived and related ansätze specific to quantum computing. The review concludes with a unified perspective on the discussed ansätze, attempting to bring them under a common framework, as well as with a reflection upon open problems within the field.
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Affiliation(s)
- Abhinav Anand
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
| | - Philipp Schleich
- Department of Computer Science, University of Toronto, 214 College St, Toronto, ONM5T 3A1, Canada. .,Applied and Computational Mathematics, Department of Mathematics, RWTH Aachen University, Aachen, Germany.,Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, Ontario M5G 1M1, Canada
| | - Sumner Alperin-Lea
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
| | - Phillip W K Jensen
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
| | - Sukin Sim
- Department of Chemistry and Chemical Biology, Harvard University, USA
| | - Manuel Díaz-Tinoco
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Physical and Environmental Sciences, University of Toronto Scarborough, Canada
| | - Jakob S Kottmann
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Computer Science, University of Toronto, 214 College St, Toronto, ONM5T 3A1, Canada.
| | - Matthias Degroote
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Computer Science, University of Toronto, 214 College St, Toronto, ONM5T 3A1, Canada.
| | - Artur F Izmaylov
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Physical and Environmental Sciences, University of Toronto Scarborough, Canada
| | - Alán Aspuru-Guzik
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Computer Science, University of Toronto, 214 College St, Toronto, ONM5T 3A1, Canada. .,Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, Ontario M5G 1M1, Canada.,Lebovic Fellow, Canadian Institute for Advanced Research (CIFAR), 661 University Ave., Toronto, ON M5G 1M1, Canada
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21
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Ratini L, Capecci C, Benfenati F, Guidoni L. Wave Function Adapted Hamiltonians for Quantum Computing. J Chem Theory Comput 2022; 18:899-909. [PMID: 35041784 DOI: 10.1021/acs.jctc.1c01170] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
The use of the variational quantum eigensolver (VQE) for quantum chemistry is one of the most promising applications for noisy intermediate-scale quantum (NISQ) devices. A major limitation is represented by the need to build compact and shallow circuit ansatzes having the variational flexibility to catch the complexity of the electronic structure problem. To alleviate this drawback, we introduce a modified VQE scheme in which the form of the molecular Hamiltonian is adapted to the circuit ansatz through an optimization procedure. Exploiting the invariance of the Hamiltonian by molecular orbital rotations, we can optimize it using gradients that can be calculated without significant computational overload. The proposed method, named Wavefunction Adapted Hamiltonian Through Orbital Rotation (WAHTOR), has been applied to small molecules in numerical state vector simulations. The results demonstrate that, at variance with standard VQE, the method is less dependent on circuit topology and less prone to be trapped into high-energy local minima. It is able to recover a significant amount of electron correlation even with only empirical ansatzes with shallow circuit depth. Noisy calculations demonstrate the robustness and feasibility of the proposed methodology and indicate the hardware requirements to effectively apply the procedure using forthcoming NISQ devices.
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Affiliation(s)
- Leonardo Ratini
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, 67100 Coppito, L'Aquila, Italy
| | - Chiara Capecci
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, 67100 Coppito, L'Aquila, Italy
| | - Francesco Benfenati
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, 67100 Coppito, L'Aquila, Italy
| | - Leonardo Guidoni
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, 67100 Coppito, L'Aquila, Italy
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22
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Ollitrault PJ, Miessen A, Tavernelli I. Molecular Quantum Dynamics: A Quantum Computing Perspective. Acc Chem Res 2021; 54:4229-4238. [PMID: 34787398 DOI: 10.1021/acs.accounts.1c00514] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
ConspectusSimulating molecular dynamics (MD) within a comprehensive quantum framework has been a long-standing challenge in computational chemistry. An exponential scaling of computational cost renders solving the time dependent Schrödinger equation (TDSE) of a molecular Hamiltonian, including both electronic and nuclear degrees of freedom (DOFs), as well as their couplings, infeasible for more than a few DOFs. In the Born-Oppenheimer (BO), or adiabatic, picture, electronic and nuclear parts of the wave function are decoupled and treated separately. Within this framework, the nuclear wave function evolves along potential energy surfaces (PESs) computed as solutions to the electronic Schrödinger equation parametrized in the nuclear DOFs. This approximation, together with increasingly elaborate numerical approaches to solve the nuclear time dependent Schrödinger equation (TDSE), enabled the treatment of up to a few dozens of degrees of freedom (DOFs). However, for particular applications, such as photochemistry, the BO approximation breaks down. In this regime of non-adiabatic dynamics, solving the full molecular problem including electron-nuclear couplings becomes essential, further increasing the complexity of the numerical solution. Although valuable methods such as multiconfigurational time-dependent Hartree (MCTDH) have been proposed for the solution of the coupled electron-nuclear dynamics, they remain hampered by an exponential scaling in the number of nuclear DOFs and by the difficulty of finding universal variational forms.In this Account, we present a perspective on novel quantum computational algorithms, aiming to alleviate the exponential scaling inherent to the simulation of many-body quantum dynamics. In particular, we focus on the derivation and application of quantum algorithms for adiabatic and non-adiabatic quantum dynamics, which include efficient approaches for the calculation of the BO potential energy surfaces (PESs). Thereafter, we study the time-evolution of a model system consisting of two coupled PESs in first and second quantization. In a first application, we discuss a recently introduced quantum algorithm for the evolution of a wavepacket in first quantization and exploit the potential quantum advantage of mapping its spatial grid representation to logarithmically many qubits. For the second demonstration, we move to the second quantization framework and review the scaling properties of two alternative time-evolution algorithms, namely, a variational quantum algorithm (VQA) (based on the McLachlan variational principle) and conventional Trotter-type evolution (based on a Lie-Trotter-Suzuki formula). Both methods clearly demonstrate the potential of quantum algorithms and their favorable scaling compared to the available classical approaches. However, a clear demonstration of quantum advantage in the context of molecular quantum dynamics may require the implementation of these algorithms in fault-tolerant quantum computers, while their application in near-term, noisy quantum devices is still unclear and deserves further investigation.
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23
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Saha D, Iyengar SS, Richerme P, Smith JM, Sabry A. Mapping Quantum Chemical Dynamics Problems to Spin-Lattice Simulators. J Chem Theory Comput 2021; 17:6713-6732. [PMID: 34694820 DOI: 10.1021/acs.jctc.1c00688] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The accurate computational determination of chemical, materials, biological, and atmospheric properties has a critical impact on a wide range of health and environmental problems, but is deeply limited by the computational scaling of quantum mechanical methods. The complexity of quantum chemical studies arises from the steep algebraic scaling of electron correlation methods and the exponential scaling in studying nuclear dynamics and molecular flexibility. To date, efforts to apply quantum hardware to such quantum chemistry problems have focused primarily on electron correlation. Here, we provide a framework that allows for the solution of quantum chemical nuclear dynamics by mapping these to quantum spin-lattice simulators. Using the example case of a short-strong hydrogen-bonded system, we construct the Hamiltonian for the nuclear degrees of freedom on a single Born-Oppenheimer surface and show how it can be transformed to a generalized Ising model Hamiltonian. We then demonstrate a method to determine the local fields and spin-spin couplings needed to identically match the molecular and spin-lattice Hamiltonians. We describe a protocol to determine the on-site and intersite coupling parameters of this Ising Hamiltonian from the Born-Oppenheimer potential and nuclear kinetic energy operator. Our approach represents a paradigm shift in the methods used to study quantum nuclear dynamics, opening the possibility to solve both electronic structure and nuclear dynamics problems using quantum computing systems.
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Affiliation(s)
- Debadrita Saha
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Philip Richerme
- Department of Physics and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Jeremy M Smith
- Department of Chemistry, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Amr Sabry
- Department of Computer Science, School of Informatics, Computing, and Engineering, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
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24
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Chicco S, Chiesa A, Allodi G, Garlatti E, Atzori M, Sorace L, De Renzi R, Sessoli R, Carretta S. Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla. Chem Sci 2021; 12:12046-12055. [PMID: 34667570 PMCID: PMC8457369 DOI: 10.1039/d1sc01358k] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Accepted: 08/02/2021] [Indexed: 01/06/2023] Open
Abstract
We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds a nuclear spin 7/2 coupled to an electronic spin 1/2 by hyperfine interaction. This qubit-qudit unit can be exploited to implement quantum error correction and quantum simulation algorithms. Through a combined theoretical and broadband nuclear magnetic resonance study, we demonstrate that the elementary operations of such algorithms can be efficiently implemented on the nuclear spin qudit. Manipulation of the nuclear qudit can be achieved by resonant radio-frequency pulses, thanks to the remarkably long coherence times and the effective quadrupolar coupling induced by the strong hyperfine interaction. This approach may open new perspectives for developing new molecular qubit-qudit systems.
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Affiliation(s)
- Simone Chicco
- Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche I-43124 Parma Italy
- UdR Parma, INSTM I-43124 Parma Italy
| | - Alessandro Chiesa
- Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche I-43124 Parma Italy
- UdR Parma, INSTM I-43124 Parma Italy
| | - Giuseppe Allodi
- Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche I-43124 Parma Italy
| | - Elena Garlatti
- Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche I-43124 Parma Italy
- UdR Parma, INSTM I-43124 Parma Italy
| | - Matteo Atzori
- Dipartimento di Chimica "Ugo Schiff" & INSTM, Università Degli Studi di Firenze I-50019 Sesto Fiorentino Italy
- Laboratoire National des Champs Magnétiques Intenses (LNCMI), Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS F-38043 Grenoble France
| | - Lorenzo Sorace
- Dipartimento di Chimica "Ugo Schiff" & INSTM, Università Degli Studi di Firenze I-50019 Sesto Fiorentino Italy
| | - Roberto De Renzi
- Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche I-43124 Parma Italy
| | - Roberta Sessoli
- Dipartimento di Chimica "Ugo Schiff" & INSTM, Università Degli Studi di Firenze I-50019 Sesto Fiorentino Italy
| | - Stefano Carretta
- Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche I-43124 Parma Italy
- UdR Parma, INSTM I-43124 Parma Italy
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25
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Rice JE, Gujarati TP, Motta M, Takeshita TY, Lee E, Latone JA, Garcia JM. Quantum computation of dominant products in lithium-sulfur batteries. J Chem Phys 2021; 154:134115. [PMID: 33832277 DOI: 10.1063/5.0044068] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Quantum chemistry simulations of some industrially relevant molecules are reported, employing variational quantum algorithms for near-term quantum devices. The energies and dipole moments are calculated along the dissociation curves for lithium hydride (LiH), hydrogen sulfide, lithium hydrogen sulfide, and lithium sulfide. In all cases, we focus on the breaking of a single bond to obtain information about the stability of the molecular species being investigated. We calculate energies and a variety of electrostatic properties of these molecules using classical simulators of quantum devices, with up to 21 qubits for lithium sulfide. Moreover, we calculate the ground-state energy and dipole moment along the dissociation pathway of LiH using IBM quantum devices. This is the first example, to the best of our knowledge, of dipole moment calculations being performed on quantum hardware.
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Affiliation(s)
- Julia E Rice
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
| | - Tanvi P Gujarati
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
| | - Mario Motta
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
| | - Tyler Y Takeshita
- Mercedes Benz Research and Development North America, Sunnyvale, California 94085, USA
| | - Eunseok Lee
- Mercedes Benz Research and Development North America, Sunnyvale, California 94085, USA
| | - Joseph A Latone
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
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