1
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Chan A, Shi Z, Dellantonio L, Dür W, Muschik CA. Measurement-Based Infused Circuits for Variational Quantum Eigensolvers. PHYSICAL REVIEW LETTERS 2024; 132:240601. [PMID: 38949342 DOI: 10.1103/physrevlett.132.240601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 04/10/2024] [Accepted: 05/15/2024] [Indexed: 07/02/2024]
Abstract
Variational quantum eigensolvers (VQEs) are successful algorithms for studying physical systems on quantum computers. Recently, they were extended to the measurement-based model of quantum computing, bringing resource graph states and their advantages into the realm of quantum simulation. In this Letter, we incorporate such ideas into traditional VQE circuits. This enables novel problem-informed designs and versatile implementations of many-body Hamiltonians. We showcase our approach on real superconducting quantum computers by performing VQE simulations of testbed systems including the perturbed planar code, Z_{2} lattice gauge theory, 1D quantum chromodynamics, and the LiH molecule.
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Affiliation(s)
| | | | - Luca Dellantonio
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
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2
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Dhawan D, Zgid D, Motta M. Quantum Algorithm for Imaginary-Time Green's Functions. J Chem Theory Comput 2024; 20:4629-4638. [PMID: 38761142 DOI: 10.1021/acs.jctc.4c00241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/20/2024]
Abstract
Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green's function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines the variational quantum eigensolver and the quantum subspace expansion methods to calculate Green's function in Lehmann's representation. We demonstrate the validity of this algorithm by simulating H2 and H4 on quantum simulators and on IBM's quantum devices.
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Affiliation(s)
- Diksha Dhawan
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Mario Motta
- IBM Quantum, Almaden Research Center, San Jose, California 95120, United States
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3
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Sugisaki K, Nakano T, Mochizuki Y. Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme. J Comput Chem 2024. [PMID: 38795375 DOI: 10.1002/jcc.27438] [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: 03/15/2024] [Revised: 05/08/2024] [Accepted: 05/09/2024] [Indexed: 05/27/2024]
Abstract
The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH)3 $$ {}_3 $$ and (FH)2 $$ {}_2 $$ -H2 $$ {}_2 $$ O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH)2 $$ {}_2 $$ -H2 $$ {}_2 $$ O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.
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Affiliation(s)
- Kenji Sugisaki
- Graduate School of Science and Technology, Keio University, Kawasaki, Japan
- Quantum Computing Center, Keio University, Yokohama, Japan
- Centre for Quantum Engineering, Research and Education, TCG Centres for Research and Education in Science and Technology, Kolkata, India
| | - Tatsuya Nakano
- Division of Medicinal Safety Science, National Institute of Health Sciences, Kawasaki, Japan
| | - Yuji Mochizuki
- Department of Chemistry and Research Center for Smart Molecules, Faculty of Science, Rikkyo University, Toshima-ku, Japan
- Institute of Industrial Science, The University of Tokyo, Meguro-ku, Japan
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4
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Reinholdt P, Kjellgren ER, Fuglsbjerg JH, Ziems KM, Coriani S, Sauer SPA, Kongsted J. Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer. J Chem Theory Comput 2024; 20:3729-3740. [PMID: 38691524 DOI: 10.1021/acs.jctc.4c00211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2024]
Abstract
We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H10) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H2, LiH, H2O, OH-, and NH3, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the C6 coefficients of H2, LiH, H2O, OH-, and NH3.
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Affiliation(s)
- Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
| | - Erik Rosendahl Kjellgren
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, 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
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
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5
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Kjellgren ER, Reinholdt P, Fitzpatrick A, Talarico WN, Jensen PWK, Sauer SPA, Coriani S, Knecht S, Kongsted J. The variational quantum eigensolver self-consistent field method within a polarizable embedded framework. J Chem Phys 2024; 160:124114. [PMID: 38533884 DOI: 10.1063/5.0190594] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 03/10/2024] [Indexed: 03/28/2024] Open
Abstract
We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the computational stress on the quantum device is only slightly increased in terms of gate counts compared to regular VQE-SCF. On the other hand, no increase in shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling of real chemical systems using a simulation of the reaction barrier of the Diels-Alder reaction between furan and ethene as an example.
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Affiliation(s)
- Erik Rosendahl Kjellgren
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | | | - Walter N Talarico
- Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
- Department of Applied Physics, QTF Centre of Excellence, Center for Quantum Engineering, Aalto University School of Science, FIN-00076 AALTO Espoo, Finland
| | - Phillip W K Jensen
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Sonia Coriani
- DTU Chemistry - Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | - Stefan Knecht
- Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences, Vladimir-Prelog-Weg 1-5/10, CH-8093 Zürich, Switzerland
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
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6
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Liu S. Harvesting Chemical Understanding with Machine Learning and Quantum Computers. ACS PHYSICAL CHEMISTRY AU 2024; 4:135-142. [PMID: 38560751 PMCID: PMC10979482 DOI: 10.1021/acsphyschemau.3c00067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Revised: 12/29/2023] [Accepted: 01/02/2024] [Indexed: 04/04/2024]
Abstract
It is tenable to argue that nobody can predict the future with certainty, yet one can learn from the past and make informed projections for the years ahead. In this Perspective, we overview the status of how theory and computation can be exploited to obtain chemical understanding from wave function theory and density functional theory, and then outlook the likely impact of machine learning (ML) and quantum computers (QC) to appreciate traditional chemical concepts in decades to come. It is maintained that the development and maturation of ML and QC methods in theoretical and computational chemistry represent two paradigm shifts about how the Schrödinger equation can be solved. New chemical understanding can be harnessed in these two new paradigms by making respective use of ML features and QC qubits. Before that happens, however, we still have hurdles to face and obstacles to overcome in both ML and QC arenas. Possible pathways to tackle these challenges are proposed. We anticipate that hierarchical modeling, in contrast to multiscale modeling, will emerge and thrive, becoming the workhorse of in silico simulations in the next few decades.
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7
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Misiewicz J, Evangelista FA. Implementation of the Projective Quantum Eigensolver on a Quantum Computer. J Phys Chem A 2024; 128:2220-2235. [PMID: 38452262 PMCID: PMC10961848 DOI: 10.1021/acs.jpca.3c07429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Revised: 01/29/2024] [Accepted: 02/20/2024] [Indexed: 03/09/2024]
Abstract
We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.
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Affiliation(s)
| | - Francesco A. Evangelista
- Department of Chemistry and
Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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8
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Chae E, Choi J, Kim J. An elementary review on basic principles and developments of qubits for quantum computing. NANO CONVERGENCE 2024; 11:11. [PMID: 38498068 PMCID: PMC10948723 DOI: 10.1186/s40580-024-00418-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Accepted: 03/04/2024] [Indexed: 03/19/2024]
Abstract
An elementary review on principles of qubits and their prospects for quantum computing is provided. Due to its rapid development, quantum computing has attracted considerable attention as a core technology for the next generation and has demonstrated its potential in simulations of exotic materials, molecular structures, and theoretical computer science. To achieve fully error-corrected quantum computers, building a logical qubit from multiple physical qubits is crucial. The number of physical qubits needed depends on their error rates, making error reduction in physical qubits vital. Numerous efforts to reduce errors are ongoing in both existing and emerging quantum systems. Here, the principle and development of qubits, as well as the current status of the field, are reviewed to provide information to researchers from various fields and give insights into this promising technology.
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Affiliation(s)
- Eunmi Chae
- Department of Physics, Korea University, Seoul , 02841, Republic of Korea.
| | - Joonhee Choi
- Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA.
| | - Junki Kim
- SKKU Advanced Institute of Nanotechnology (SAINT) & Department of Nano Science and Technology, Sungkyunkwan University, Suwon, 16419, Republic of Korea.
- Department of Nano Engineering, Sungkyunkwan University, Suwon, 16419, Republic of Korea.
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9
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Matoušek M, Pernal K, Pavošević F, Veis L. Variational Quantum Eigensolver Boosted by Adiabatic Connection. J Phys Chem A 2024; 128:687-698. [PMID: 38214999 PMCID: PMC10823474 DOI: 10.1021/acs.jpca.3c07590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Revised: 12/28/2023] [Accepted: 12/29/2023] [Indexed: 01/14/2024]
Abstract
In this work, we integrate the variational quantum eigensolver (VQE) with the adiabatic connection (AC) method for efficient simulations of chemical problems on near-term quantum computers. Orbital-optimized VQE methods are employed to capture the strong correlation within an active space, and classical AC corrections recover the dynamical correlation effects comprising electrons outside of the active space. On two challenging strongly correlated problems, namely, the dissociation of N2 and the electronic structure of the tetramethyleneethane biradical, we show that the combined VQE-AC approach enhances the performance of VQE dramatically. Moreover, since the AC corrections do not bring any additional requirements on quantum resources or measurements, they can actually boost the VQE algorithms. Our work paves the way toward quantum simulations of real-life problems on near-term quantum computers.
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Affiliation(s)
- Mikuláš Matoušek
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
- Faculty
of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005 Lodz, Poland
| | | | - Libor Veis
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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10
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Sun J, Cheng L, Li W. Toward Chemical Accuracy with Shallow Quantum Circuits: A Clifford-Based Hamiltonian Engineering Approach. J Chem Theory Comput 2024; 20:695-707. [PMID: 38169365 DOI: 10.1021/acs.jctc.3c00886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2024]
Abstract
Achieving chemical accuracy with shallow quantum circuits is a significant challenge in quantum computational chemistry, particularly for near-term quantum devices. In this work, we present a Clifford-based Hamiltonian engineering algorithm, namely CHEM, that addresses the trade-off between circuit depth and accuracy. Based on a variational quantum eigensolver and hardware-efficient ansatz, our method designs the Clifford-based Hamiltonian transformation that (1) ensures a set of initial circuit parameters corresponding to the Hartree-Fock energy can be generated, (2) effectively maximizes the initial energy gradient with respect to circuit parameters, (3) imposes negligible overhead for classical processing and does not require additional quantum resources, and (4) is compatible with any circuit topology. We demonstrate the efficacy of our approach using a quantum hardware emulator, achieving chemical accuracy for systems as large as 12 qubits with fewer than 30 two-qubit gates. Our Clifford-based Hamiltonian engineering approach offers a promising avenue for practical quantum computational chemistry on near-term quantum devices.
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Affiliation(s)
- Jiace Sun
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Lixue Cheng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Weitang Li
- Tencent Quantum Lab, Shenzhen 518057, China
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11
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Lai J, Fan Y, Fu Q, Li Z, Yang J. Accurate and efficient calculations of Hellmann-Feynman forces for quantum computation. J Chem Phys 2023; 159:114113. [PMID: 37724727 DOI: 10.1063/5.0167444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 08/31/2023] [Indexed: 09/21/2023] Open
Abstract
First-order derivatives of energies with respect to atomic coordinates are widely computed and used in quantum chemistry simulations. The rapidly emerging technology of quantum computing offers a new paradigm for solving relevant quantum chemistry equations. In this work, we have achieved analytical calculations of atomic forces based on the Hellmann-Feynman theorem within the framework of the variational quantum eigensolver. The accuracy of the approach is demonstrated by calculating the atomic forces of H2, LiH, H2O, and NH3 molecules, which are in excellent agreement with values obtained from full configuration interaction calculations. In particular, for systems with degenerate molecular orbitals, the analytical approach has a significant accuracy advantage over finite-difference-based methods and will not involve additional computational effort on a quantum computer. The calculated forces are further used to optimize the geometries of NH3 and CH4 molecules and to perform ab initio molecular dynamics simulations for the umbrella inversion of NH3, demonstrating the feasibility of the approach in practical quantum chemistry simulations.
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Affiliation(s)
- Juntao Lai
- School of Future Technology, University of Science and Technology of China, Hefei 230026, China
| | - Yi Fan
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Qiang Fu
- School of Future Technology, University of Science and Technology of China, Hefei 230026, China
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Zhenyu Li
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jinlong Yang
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China
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12
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Winkler R, Ciria M, Ahmad M, Plank H, Marcuello C. A Review of the Current State of Magnetic Force Microscopy to Unravel the Magnetic Properties of Nanomaterials Applied in Biological Systems and Future Directions for Quantum Technologies. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:2585. [PMID: 37764614 PMCID: PMC10536909 DOI: 10.3390/nano13182585] [Citation(s) in RCA: 17] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Revised: 09/13/2023] [Accepted: 09/15/2023] [Indexed: 09/29/2023]
Abstract
Magnetism plays a pivotal role in many biological systems. However, the intensity of the magnetic forces exerted between magnetic bodies is usually low, which demands the development of ultra-sensitivity tools for proper sensing. In this framework, magnetic force microscopy (MFM) offers excellent lateral resolution and the possibility of conducting single-molecule studies like other single-probe microscopy (SPM) techniques. This comprehensive review attempts to describe the paramount importance of magnetic forces for biological applications by highlighting MFM's main advantages but also intrinsic limitations. While the working principles are described in depth, the article also focuses on novel micro- and nanofabrication procedures for MFM tips, which enhance the magnetic response signal of tested biomaterials compared to commercial nanoprobes. This work also depicts some relevant examples where MFM can quantitatively assess the magnetic performance of nanomaterials involved in biological systems, including magnetotactic bacteria, cryptochrome flavoproteins, and magnetic nanoparticles that can interact with animal tissues. Additionally, the most promising perspectives in this field are highlighted to make the reader aware of upcoming challenges when aiming toward quantum technologies.
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Affiliation(s)
- Robert Winkler
- Christian Doppler Laboratory—DEFINE, Graz University of Technology, 8010 Graz, Austria; (R.W.); (H.P.)
| | - Miguel Ciria
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain;
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - Margaret Ahmad
- Photobiology Research Group, IBPS, UMR8256 CNRS, Sorbonne Université, 75005 Paris, France;
| | - Harald Plank
- Christian Doppler Laboratory—DEFINE, Graz University of Technology, 8010 Graz, Austria; (R.W.); (H.P.)
- Graz Centre for Electron Microscopy, 8010 Graz, Austria
- Institute of Electron Microscopy, Graz University of Technology, 8010 Graz, Austria
| | - Carlos Marcuello
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain;
- Laboratorio de Microscopias Avanzadas (LMA), Universidad de Zaragoza, 50018 Zaragoza, Spain
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13
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Pyrkov A, Aliper A, Bezrukov D, Lin YC, Polykovskiy D, Kamya P, Ren F, Zhavoronkov A. Quantum computing for near-term applications in generative chemistry and drug discovery. Drug Discov Today 2023; 28:103675. [PMID: 37331692 DOI: 10.1016/j.drudis.2023.103675] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Revised: 05/22/2023] [Accepted: 06/13/2023] [Indexed: 06/20/2023]
Abstract
In recent years, drug discovery and life sciences have been revolutionized with machine learning and artificial intelligence (AI) methods. Quantum computing is touted to be the next most significant leap in technology; one of the main early practical applications for quantum computing solutions is predicted to be in quantum chemistry simulations. Here, we review the near-term applications of quantum computing and their advantages for generative chemistry and highlight the challenges that can be addressed with noisy intermediate-scale quantum (NISQ) devices. We also discuss the possible integration of generative systems running on quantum computers into established generative AI platforms.
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Affiliation(s)
- Alexey Pyrkov
- Insilico Medicine Hong Kong Ltd, Pak Shek Kok, New Territories, Hong Kong.
| | - Alex Aliper
- Insilico Medicine AI Ltd, Masdar City, Abu Dhabi, United Arab Emirates
| | - Dmitry Bezrukov
- Insilico Medicine Hong Kong Ltd, Pak Shek Kok, New Territories, Hong Kong
| | - Yen-Chu Lin
- Insilico Medicine Taiwan Ltd, Taipei, Taiwan
| | | | | | - Feng Ren
- Insilico Medicine Shanghai Ltd, Shanghai, China
| | - Alex Zhavoronkov
- Insilico Medicine Hong Kong Ltd, Pak Shek Kok, New Territories, Hong Kong
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14
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D'Cunha R, Crawford TD, Motta M, Rice JE. Challenges in the Use of Quantum Computing Hardware-Efficient Ansätze in Electronic Structure Theory. J Phys Chem A 2023; 127:3437-3448. [PMID: 37040444 DOI: 10.1021/acs.jpca.2c08430] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/13/2023]
Abstract
Advances in quantum computation for electronic structure, and particularly heuristic quantum algorithms, create an ongoing need to characterize the performance and limitations of these methods. Here we discuss some potential pitfalls connected with the use of hardware-efficient Ansätze in variational quantum simulations of electronic structure. We illustrate that hardware-efficient Ansätze may break Hamiltonian symmetries and yield nondifferentiable potential energy curves, in addition to the well-known difficulty of optimizing variational parameters. We discuss the interplay between these limitations by carrying out a comparative analysis of hardware-efficient Ansätze versus unitary coupled cluster and full configuration interaction, and of second- and first-quantization strategies to encode Fermionic degrees of freedom to qubits. Our analysis should be useful in understanding potential limitations and in identifying possible areas of improvement in hardware-efficient Ansätze.
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Affiliation(s)
- Ruhee D'Cunha
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - T Daniel Crawford
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Mario Motta
- IBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, California 95120, United States
| | - Julia E Rice
- IBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, California 95120, United States
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15
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Ryabinkin IG, Jena AJ, Genin SN. Efficient Construction of Involutory Linear Combinations of Anticommuting Pauli Generators for Large-Scale Iterative Qubit Coupled Cluster Calculations. J Chem Theory Comput 2023; 19:1722-1733. [PMID: 36820812 DOI: 10.1021/acs.jctc.2c01155] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
Abstract
We present an efficient method for construction of a fully anticommutative set of Pauli generators (elements of the Pauli group) from a commutative set of operators that are composed exclusively from Pauli x̂ operators (purely X generators) and sorted by an associated numerical measure, such as absolute energy gradients. Our approach uses the Gauss-Jordan elimination applied to a binary matrix that encodes the set of X generators to bring it to the reduced row-echelon form, followed by the construction of an anticommutative system in a standard basis by means of a modified Jordan-Wigner transformation and returning to the original basis. The algorithm complexity is linear in the size of the X set and quadratic in the number of qubits. The resulting anticommutative sets are used to construct the qubit coupled cluster Ansatz with involutory linear combinations of anticommuting Paulis (QCC-ILCAP) proposed in J. Chem. Theory Comput. 2021, 17 (1), 66-78. We applied the iterative qubit coupled cluster method with the QCC-ILCAP Ansatz to calculations of ground-state potential energy curves for symmetric stretching of the water molecule (36 qubits) and dissociation of N2 (56 qubits).
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Affiliation(s)
- Ilya G Ryabinkin
- OTI Lumionics Inc., 3415 American Drive Unit 1, Mississauga, Ontario L4V 1T4, Canada
| | - Andrew J Jena
- Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Scott N Genin
- OTI Lumionics Inc., 3415 American Drive Unit 1, Mississauga, Ontario L4V 1T4, Canada
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Tammaro A, Galli DE, Rice JE, Motta M. N-Electron Valence Perturbation Theory with Reference Wave Functions from Quantum Computing: Application to the Relative Stability of Hydroxide Anion and Hydroxyl Radical. J Phys Chem A 2023; 127:817-827. [PMID: 36638358 DOI: 10.1021/acs.jpca.2c07653] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
Quantum simulations of the hydroxide anion and hydroxyl radical are reported, employing variational quantum algorithms for near-term quantum devices. The energy of each species is calculated along the dissociation curve, to obtain information about the stability of the molecular species being investigated. It is shown that simulations restricted to valence spaces incorrectly predict the hydroxyl radical to be more stable than the hydroxide anion. Inclusion of dynamical electron correlation from nonvalence orbitals is demonstrated, through the integration of the variational quantum eigensolver and quantum subspace expansion methods in the workflow of N-electron valence perturbation theory, and shown to correctly predict the hydroxide anion to be more stable than the hydroxyl radical, provided that basis sets with diffuse orbitals are also employed. Finally, we calculate the electron affinity of the hydroxyl radical using an aug-cc-pVQZ basis on IBM's quantum devices.
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Affiliation(s)
- Alessandro Tammaro
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, via Celoria 16, I-20133Milano, Italy
| | - Davide E Galli
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, via Celoria 16, I-20133Milano, Italy
| | - Julia E Rice
- IBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, California95120, United States
| | - Mario Motta
- IBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, California95120, United States
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17
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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: 2] [Impact Index Per Article: 2.0] [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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18
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Huang K, Cai X, Li H, Ge ZY, Hou R, Li H, Liu T, Shi Y, Chen C, Zheng D, Xu K, Liu ZB, Li Z, Fan H, Fang WH. Variational Quantum Computation of Molecular Linear Response Properties on a Superconducting Quantum Processor. J Phys Chem Lett 2022; 13:9114-9121. [PMID: 36154018 DOI: 10.1021/acs.jpclett.2c02381] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Simulating response properties of molecules is crucial for interpreting experimental spectroscopies and accelerating materials design. However, it remains a long-standing computational challenge for electronic structure methods on classical computers. While quantum computers hold the promise of solving this problem more efficiently in the long run, existing quantum algorithms requiring deep quantum circuits are infeasible for near-term noisy quantum processors. Herein, we introduce a pragmatic variational quantum response (VQR) algorithm for response properties, which circumvents the need for deep quantum circuits. Using this algorithm, we report the first simulation of linear response properties of molecules including dynamic polarizabilities and absorption spectra on a superconducting quantum processor. Our results indicate that a large class of important dynamical properties, such as Green's functions, are within the reach of near-term quantum hardware using this algorithm in combination with suitable error mitigation techniques.
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Affiliation(s)
- Kaixuan Huang
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, Teda Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xiaoxia Cai
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Hao Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physics, Northwest University, Xi'an 710127, China
| | - Zi-Yong Ge
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Ruijuan Hou
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Hekang Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Tong Liu
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Yunhao Shi
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Chitong Chen
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Dongning Zheng
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Kai Xu
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Zhi-Bo Liu
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, Teda Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
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19
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Lan Z, Liang W. Amplitude Reordering Accelerates the Adaptive Variational Quantum Eigensolver Algorithms. J Chem Theory Comput 2022; 18:5267-5275. [PMID: 35971280 DOI: 10.1021/acs.jctc.2c00403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The variational quantum eigensolver (VQE) algorithm can simulate the chemical systems such as molecules in the noisy-intermediate-scale quantum devices and shows promising applications in quantum chemistry simulations. The accuracy and computational cost of the VQE simulations are determined by the underlying ansatz. Therefore, the most important issue is to generate a compact and accurate ansatz, which requires a shallower parametric quantum circuit and can achieve an acceptable accuracy. The newly developed adaptive algorithms (AAs) such as the adaptive derivative-assembled pseudo-Trotter VQE (ADAPT-VQE) can solve this issue via generating compact and accurate ansatzes. However, these AAs show very low computational efficiency because they require a large number of additional measurements. Here we propose an amplitude reordering (AR) strategy to accelerate the promising but expensive AAs by adding operators in a "batched" fashion in a way that their order is still quasi-optimal. We first introduce the AR method into ADAPT-VQE and build the AR-ADAPT-VQE algorithm. We then endow the energy-sorting VQE (ES-VQE) algorithm with the adaptive feature and introduce the AR into AES-VQE to form the AR-AES-VQE algorithm. To demonstrate the performance of these algorithms, we calculate the dissociation curves of three small molecules, LiH, linear BeH2, and linear H6, by using (AR-)ADAPT-VQE and (AR-)AES-VQE algorithms. It is found that all of the AR-equipped AAs (AR-AAs) can significantly reduce the number of iterations and subsequently accelerate the calculations with a speedup of up to more than ten times without the obvious loss of accuracy. The final ansatz generated by the AR-AAs not only avoids extra circuit depth but also maintains the computational accuracy; sometimes the AR-AAs even outperforms their original counterparts.
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Affiliation(s)
- Zhihao Lan
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, Fujian Province, Peoples' Republic of China
| | - WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, Fujian Province, Peoples' Republic of China
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20
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Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers. Symmetry (Basel) 2022. [DOI: 10.3390/sym14030624] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.
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