1
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Yoshida Y, Takemori N, Mizukami W. Ab initio extended Hubbard model of short polyenes for efficient quantum computing. J Chem Phys 2024; 161:084303. [PMID: 39193941 DOI: 10.1063/5.0213525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2024] [Accepted: 08/05/2024] [Indexed: 08/29/2024] Open
Abstract
We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, toward efficient quantum computing of molecular electronic structure calculations. By utilizing this method, the first-principles Hamiltonian of chemical systems can be coarse-grained by eliminating the electronic degrees of freedom in higher energy space and reducing the number of terms of electron repulsion integral from O(N4) to O(N2). Our approach is validated numerically on the vertical excitation energies and excitation characters of ethylene, butadiene, and hexatriene. The dynamical electron correlation is incorporated within the framework of the constrained random phase approximation in advance of quantum computations, and the constructed models capture the trend of experimental and high-level quantum chemical calculation results. As expected, the L1-norm of the fermion-to-qubit mapped model Hamiltonians is significantly lower than that of conventional ab initio Hamiltonians, suggesting improved scalability of quantum computing. Those numerical outcomes and the results of the simulation of excited-state sampling demonstrate that the ab initio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers.
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Affiliation(s)
- Yuichiro Yoshida
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
| | - Nayuta Takemori
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
| | - Wataru Mizukami
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
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2
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Scheurer M, Anselmetti GLR, Oumarou O, Gogolin C, Rubin NC. Tailored and Externally Corrected Coupled Cluster with Quantum Inputs. J Chem Theory Comput 2024; 20:5068-5093. [PMID: 38829984 DOI: 10.1021/acs.jctc.4c00037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2024]
Abstract
We propose to use wave function overlaps obtained from a quantum computer as inputs for the classical split-amplitude techniques, tailored and externally corrected coupled cluster, to achieve balanced treatment of static and dynamic correlation effects in molecular electronic structure simulations. By combining insights from statistical properties of matchgate shadows, which are used to measure quantum trial state overlaps, with classical correlation diagnostics, we can provide quantum resource estimates well into the classically no longer exactly solvable regime. We find that rather imperfect wave functions and remarkably low shot counts are sufficient to cure qualitative failures of plain coupled cluster singles doubles and to obtain chemically precise dynamic correlation energy corrections. We provide insights into which wave function preparation schemes have a chance of yielding quantum advantage, and we test our proposed method using overlaps measured on Google's Sycamore device.
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3
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Rocca D, Cortes CL, Gonthier JF, Ollitrault PJ, Parrish RM, Anselmetti GL, Degroote M, Moll N, Santagati R, Streif M. Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization. J Chem Theory Comput 2024; 20:4639-4653. [PMID: 38788209 DOI: 10.1021/acs.jctc.4c00352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.
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Affiliation(s)
- Dario Rocca
- QC Ware Corporation, Palo Alto, California 94306, United States
| | | | | | | | | | | | - Matthias Degroote
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | - Nikolaj Moll
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | | | - Michael Streif
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
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4
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Stenger JPT, Hellberg CS, Gunlycke D. Demonstration of the Effectiveness of the Cascaded Variational Quantum Eigensolver Using the Jastrow Ansatz for Molecular Calculations. ACS OMEGA 2024; 9:21353-21364. [PMID: 38764642 PMCID: PMC11097349 DOI: 10.1021/acsomega.4c01642] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/20/2024] [Revised: 04/08/2024] [Accepted: 04/10/2024] [Indexed: 05/21/2024]
Abstract
We demonstrate how the cascaded variational quantum eigensolver (CVQE) can be applied to study molecular systems for the family of Jastrow ansatzes. Specifically, we applied CVQE to the water molecule. We find that CVQE has a number of advantages. In particular, our results show that CVQE requires 2 to 3 orders of magnitude fewer quantum computing (QC) executions than VQE for the water molecule. Furthermore, our results indicate that CVQE might provide some robustness against two-qubit gate errors given that the number of CNOT gates used in our calculation was ∼300 and the errors in the QC calculations are still comparable to those obtained by VQE.
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Affiliation(s)
- John P. T. Stenger
- U.S. Naval Research Laboratory, Washington, District of
Columbia 20375, United States
| | - C. Stephen Hellberg
- U.S. Naval Research Laboratory, Washington, District of
Columbia 20375, United States
| | - Daniel Gunlycke
- U.S. Naval Research Laboratory, Washington, District of
Columbia 20375, United States
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5
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Xiao X, Zhao H, Ren J, Fang WH, Li Z. Physics-Constrained Hardware-Efficient Ansatz on Quantum Computers That Is Universal, Systematically Improvable, and Size-Consistent. J Chem Theory Comput 2024; 20:1912-1922. [PMID: 38354395 DOI: 10.1021/acs.jctc.3c00966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2024]
Abstract
Variational wave function ansätze are at the heart of solving quantum many-body problems in physics and chemistry. Previous designs of hardware-efficient ansatz (HEA) on quantum computers are largely based on heuristics and lack rigorous theoretical foundations. In this work, we introduce a physics-constrained approach for designing HEA with rigorous theoretical guarantees by imposing a few fundamental constraints. Specifically, we require that the target HEA to be universal, systematically improvable, and size-consistent, which is an important concept in quantum many-body theories for scalability but has been overlooked in previous designs of HEA. We extend the notion of size-consistency to HEA and present a concrete realization of HEA that satisfies all these fundamental constraints while only requiring linear qubit connectivity. The developed physics-constrained HEA is superior to other heuristically designed HEA in terms of both accuracy and scalability, as demonstrated numerically for the Heisenberg model and some typical molecules. In particular, we find that restoring size-consistency can significantly reduce the number of layers needed to reach a certain accuracy. In contrast, the failure of other HEA to satisfy these constraints severely limits their scalability to larger systems with more than 10 qubits. Our work highlights the importance of incorporating physical constraints into the design of HEA for efficiently solving many-body problems on quantum computers.
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Affiliation(s)
- Xiaoxiao Xiao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Hewang Zhao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Jiajun Ren
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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6
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Halder S, Dey A, Shrikhande C, Maitra R. Machine learning assisted construction of a shallow depth dynamic ansatz for noisy quantum hardware. Chem Sci 2024; 15:3279-3289. [PMID: 38425512 PMCID: PMC10901498 DOI: 10.1039/d3sc05807g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 01/16/2024] [Indexed: 03/02/2024] Open
Abstract
The development of various dynamic ansatz-constructing techniques has ushered in a new era, making the practical exploitation of Noisy Intermediate-Scale Quantum (NISQ) hardware for molecular simulations increasingly viable. However, such ansatz construction protocols incur substantial measurement costs during their execution. This work involves the development of a novel protocol that capitalizes on regenerative machine learning methodologies and many-body perturbation theoretical measures to construct a highly expressive and shallow ansatz within the variational quantum eigensolver (VQE) framework with limited measurement costs. The regenerative machine learning model used in our work is trained with the basis vectors of a low-rank expansion of the N-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This resource-efficient approach is quintessential for determining spectroscopic and other molecular properties, thereby facilitating the study of emerging chemical phenomena in the near-term quantum computing framework.
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Affiliation(s)
- Sonaldeep Halder
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
| | - Anish Dey
- Department of Chemical Sciences, Indian Institute of Science Education and Research Kolkata West Bengal 741246 India
| | - Chinmay Shrikhande
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
| | - Rahul Maitra
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
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7
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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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8
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Loaiza I, Izmaylov AF. Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries. J Chem Theory Comput 2023; 19:8201-8209. [PMID: 37939198 DOI: 10.1021/acs.jctc.3c00912] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2023]
Abstract
Computational cost of energy estimation for molecular electronic Hamiltonians via quantum phase estimation (QPE) grows with the difference between the largest and smallest eigenvalues of the Hamiltonian. In this work, we propose a preprocessing procedure that reduces the norm of the Hamiltonian without changing its eigenspectrum for the target states of a particular symmetry. The new procedure, block-invariant symmetry shift (BLISS), builds an operator T̂ such that the cost of implementing H ^ - T ^ is reduced compared to that of Ĥ, yet H ^ - T ^ acts on the subspaces of interest the same way as Ĥ does. BLISS performance is demonstrated for a linear combination of unitaries (LCU)-based QPE approaches on a set of small molecules. Using the number of electrons as the symmetry specifying the target set of states, BLISS provided a factor of 2 reduction of 1-norm for several LCU decompositions compared to their unshifted versions.
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Affiliation(s)
- Ignacio Loaiza
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto M5S 3H6, Canada
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto M1C 1A4, Canada
- Zapata Computing Canada Inc., Toronto M5E 1E5, Canada
| | - Artur F Izmaylov
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto M5S 3H6, Canada
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto M1C 1A4, Canada
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9
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Evangelista FA, Batista VS. Editorial: Quantum Computing for Chemistry. J Chem Theory Comput 2023; 19:7435-7436. [PMID: 37961754 DOI: 10.1021/acs.jctc.3c01043] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2023]
Affiliation(s)
- Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520-8107, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06520-8263, United States
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10
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Motta M, Sung KJ, Whaley KB, Head-Gordon M, Shee J. Bridging physical intuition and hardware efficiency for correlated electronic states: the local unitary cluster Jastrow ansatz for electronic structure. Chem Sci 2023; 14:11213-11227. [PMID: 37860666 PMCID: PMC10583744 DOI: 10.1039/d3sc02516k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 09/20/2023] [Indexed: 10/21/2023] Open
Abstract
A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than a unitary coupled cluster with single and double excitations (qUCCSD), with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. As in the case of qUCCSD, exactly computing the energy scales factorially with system size on classical computers but polynomially on quantum devices. The local unitary cluster Jastrow ansatz removes the need for SWAP gates, can be tailored to arbitrary qubit topologies (e.g., square, hex, and heavy-hex), and is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers. The proposed family of ansatzes demonstrates that hardware efficiency and physical transparency are not mutually exclusive; indeed, chemical and physical intuition regarding electron correlation can illuminate a useful path towards hardware-friendly quantum circuits.
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Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research - Almaden San Jose CA 95120 USA
| | - Kevin J Sung
- IBM Quantum, IBM T. J. Watson Research Center Yorktown Heights NY 10598 USA
| | - K Birgitta Whaley
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Berkeley Quantum Information and Computation Center, University of California Berkeley CA 94720 USA
- Challenge Institute for Quantum Computation, University of California Berkeley CA 94720 USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
| | - James Shee
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Department of Chemistry, Rice University Houston TX 77005 USA
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11
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Tabares C, Muñoz de Las Heras A, Tagliacozzo L, Porras D, González-Tudela A. Variational Quantum Simulators Based on Waveguide QED. PHYSICAL REVIEW LETTERS 2023; 131:073602. [PMID: 37656849 DOI: 10.1103/physrevlett.131.073602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Revised: 04/28/2023] [Accepted: 07/03/2023] [Indexed: 09/03/2023]
Abstract
Waveguide QED simulators are analog quantum simulators made by quantum emitters interacting with one-dimensional photonic band gap materials. One of their remarkable features is that they can be used to engineer tunable-range emitter interactions. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms for certain problems. In particular, we illustrate their power in creating wave function Ansätze that capture accurately the ground state of quantum critical spin models (XXZ and Ising) with fewer gates and optimization parameters than other variational Ansätze based on nearest-neighbor or infinite-range entangling gates. Finally, we study the potential advantages of these waveguide Ansätze in the presence of noise. Overall, these results evidence the potential of using the interaction range as a variational parameter and place waveguide QED simulators as a promising platform for variational quantum algorithms.
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Affiliation(s)
- C Tabares
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - A Muñoz de Las Heras
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - L Tagliacozzo
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - D Porras
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - A González-Tudela
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
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12
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Khamoshi A, Dutta R, Scuseria GE. State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection. J Phys Chem A 2023; 127:4005-4014. [PMID: 37129503 DOI: 10.1021/acs.jpca.3c00525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen-Cooper-Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. The method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree-Fock based electronic structure methods.
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Affiliation(s)
- Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
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13
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Rossmannek M, Pavošević F, Rubio A, Tavernelli I. Quantum Embedding Method for the Simulation of Strongly Correlated Systems on Quantum Computers. J Phys Chem Lett 2023; 14:3491-3497. [PMID: 37011400 DOI: 10.1021/acs.jpclett.3c00330] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Quantum computing has emerged as a promising platform for simulating strongly correlated systems in chemistry, for which the standard quantum chemistry methods are either qualitatively inaccurate or too expensive. However, due to the hardware limitations of the available noisy near-term quantum devices, their application is currently limited only to small chemical systems. One way for extending the range of applicability can be achieved within the quantum embedding approach. Herein, we employ the projection-based embedding method for combining the variational quantum eigensolver (VQE) algorithm, although not limited to, with density functional theory (DFT). The developed VQE-in-DFT method is then implemented efficiently on a real quantum device and employed for simulating the triple bond breaking process in butyronitrile. The results presented herein show that the developed method is a promising approach for simulating systems with a strongly correlated fragment on a quantum computer.
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Affiliation(s)
- Max Rossmannek
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
- IBM Quantum, IBM Research - Zürich, 8803 Rüschlikon, Switzerland
| | - Fabijan Pavošević
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, 10010 New York, United States
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco (UPV/EHU), Av. Tolosa 72, 20018 San Sebastian, Spain
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, 10010 New York, United States
| | - Ivano Tavernelli
- IBM Quantum, IBM Research - Zürich, 8803 Rüschlikon, Switzerland
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14
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Motta M, Rice JE. Emerging quantum computing algorithms for quantum chemistry. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1580] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research‐Almaden San Jose California USA
| | - Julia E. Rice
- IBM Quantum, IBM Research‐Almaden San Jose California USA
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15
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Liu J, Fan Y, Li Z, Yang J. Quantum algorithms for electronic structures: basis sets and boundary conditions. Chem Soc Rev 2022; 51:3263-3279. [PMID: 35352716 DOI: 10.1039/d1cs01184g] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The advantages of quantum computers are believed to significantly change the research paradigm of chemical and materials sciences, where computational characterization and theoretical design play an increasingly important role. It is especially desirable to solve the electronic structure problem, a central problem in chemistry and materials science, efficiently and accurately with well-designed quantum algorithms. Various quantum electronic-structure algorithms have been proposed in the literature. In this article, we briefly review recent progress in this direction with a special emphasis on the basis sets and boundary conditions. Compared to classical electronic structure calculations, there are new considerations in choosing a basis set in quantum algorithms. For example, the effect of the basis set on the circuit complexity is very important in quantum algorithm design. Electronic structure calculations should be performed with an appropriate boundary condition. Simply using a wave function ansatz designed for molecular systems in a material system with a periodic boundary condition may lead to significant errors. Artificial boundary conditions can be used to partition a large system into smaller fragments to save quantum resources. The basis sets and boundary conditions are expected to play a crucial role in electronic structure calculations on future quantum computers, especially for realistic systems.
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Affiliation(s)
- Jie Liu
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Yi Fan
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Zhenyu Li
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Jinlong Yang
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
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16
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Malone FD, Parrish RM, Welden AR, Fox T, Degroote M, Kyoseva E, Moll N, Santagati R, Streif M. Towards the simulation of large scale protein-ligand interactions on NISQ-era quantum computers. Chem Sci 2022; 13:3094-3108. [PMID: 35414867 PMCID: PMC8926290 DOI: 10.1039/d1sc05691c] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Accepted: 01/14/2022] [Indexed: 11/29/2022] Open
Abstract
We explore the use of symmetry-adapted perturbation theory (SAPT) as a simple and efficient means to compute interaction energies between large molecular systems with a hybrid method combining NISQ-era quantum and classical computers. From the one- and two-particle reduced density matrices of the monomer wavefunctions obtained by the variational quantum eigensolver (VQE), we compute SAPT contributions to the interaction energy [SAPT(VQE)]. At first order, this energy yields the electrostatic and exchange contributions for non-covalently bound systems. We empirically find from ideal statevector simulations that the SAPT(VQE) interaction energy components display orders of magnitude lower absolute errors than the corresponding VQE total energies. Therefore, even with coarsely optimized low-depth VQE wavefunctions, we still obtain sub kcal mol-1 accuracy in the SAPT interaction energies. In SAPT(VQE), the quantum requirements, such as qubit count and circuit depth, are lowered by performing computations on the separate molecular systems. Furthermore, active spaces allow for large systems containing thousands of orbitals to be reduced to a small enough orbital set to perform the quantum portions of the computations. We benchmark SAPT(VQE) (with the VQE component simulated by ideal statevector simulators) against a handful of small multi-reference dimer systems and the iron center containing human cancer-relevant protein lysine-specific demethylase 5 (KDM5A).
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Affiliation(s)
| | | | | | - Thomas Fox
- Medicinal Chemistry, Boehringer Ingelheim Pharma GmbH & Co. KG Birkendorfer Straße 65 88397 Biberach an der Riß Germany
| | | | - Elica Kyoseva
- Quantum Lab, Boehringer Ingelheim 55218 Ingelheim am Rhein Germany
| | - Nikolaj Moll
- Quantum Lab, Boehringer Ingelheim 55218 Ingelheim am Rhein Germany
| | | | - Michael Streif
- Quantum Lab, Boehringer Ingelheim 55218 Ingelheim am Rhein Germany
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17
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Rubin NC, Lee J, Babbush R. Compressing Many-Body Fermion Operators under Unitary Constraints. J Chem Theory Comput 2022; 18:1480-1488. [PMID: 35166529 DOI: 10.1021/acs.jctc.1c00912] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The most efficient known quantum circuits for preparing unitary coupled cluster states and applying Trotter steps of the arbitrary basis electronic structure Hamiltonian involve interleaved sequences of Fermionic Gaussian circuits and Ising interaction-type circuits. These circuits arise from factorizing the two-body operators generating those unitaries as a sum of squared one-body operators that are simulated using product formulas. We introduce a numerical algorithm for performing this factorization that has an iteration complexity no worse than single particle basis transformations of the two-body operators and often results in many times fewer squared one-body operators in the sum of squares, compared to the analytical decompositions. As an application of this numerical procedure, we demonstrate that our protocol can be used to approximate generic unitary coupled cluster operators and prepare the necessary high-quality initial states for techniques (like ADAPT-VQE) that iteratively construct approximations to the ground state.
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Affiliation(s)
- Nicholas C Rubin
- Google Quantum AI, San Francisco, California 94105, United States
| | - Joonho Lee
- Google Quantum AI, San Francisco, California 94105, United States.,Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Ryan Babbush
- Google Quantum AI, San Francisco, California 94105, United States
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18
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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: 47] [Impact Index Per Article: 23.5] [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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19
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Aroeira GJR, Davis MM, Turney JM, Schaefer HF. Fermi.jl: A Modern Design for Quantum Chemistry. J Chem Theory Comput 2022; 18:677-686. [PMID: 34978451 DOI: 10.1021/acs.jctc.1c00719] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Approximating molecular wave functions involves heavy numerical effort; therefore, codes for such tasks are written completely or partially in efficient languages such as C, C++, and Fortran. While these tools are dominant throughout quantum chemistry packages, the efficient development of new methods is often hindered by the complexity associated with code development. In order to ameliorate this scenario, some software packages take a dual approach where a simpler, higher-level language, such as Python, substitutes the traditional ones wherever performance is not critical. Julia is a novel, dynamically typed, programming language that aims to solve this two-language problem. It gained attention because of its modern and intuitive design, while still being highly optimized to compete with "low-level" languages. Recently, some chemistry-related projects have emerged exploring the capabilities of Julia. Herein, we introduce the quantum chemistry package Fermi.jl, which contains the first implementations of post-Hartree-Fock methods written in Julia. Its design makes use of many Julia core features, including multiple dispatch, metaprogramming, and interactive usage. Fermi.jl is a modular package, where new methods and implementations can be easily added to the existing code. Furthermore, it is designed to maximize code reusability by relying on general functions with specialized methods for particular cases. The feasibility of the project is explored through evaluating the performance of popular ab initio methods. It is our hope that this project motivates the usage of Julia within the community and brings new contributions into Fermi.jl.
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Affiliation(s)
- Gustavo J R Aroeira
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - Matthew M Davis
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - Justin M Turney
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - Henry F Schaefer
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
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20
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Sugisaki K, Kato T, Minato Y, Okuwaki K, Mochizuki Y. Variational quantum eigensolver simulations with the multireference unitary coupled cluster ansatz: a case study of the C2v quasi-reaction pathway of beryllium insertion to H 2 molecule. Phys Chem Chem Phys 2022; 24:8439-8452. [DOI: 10.1039/d1cp04318h] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Variational quantum eigensolver (VQE)-based quantum chemical calculations have been extensively studied as a computational model using noisy intermediate-scale quantum devices. VQE uses a parametrized quantum circuit defined through an “ansatz”...
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21
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Li W, Huang Z, Cao C, Huang Y, Shuai Z, Sun X, Sun J, Yuan X, Lv D. Toward practical quantum embedding simulation of realistic chemical systems on near-term quantum computers. Chem Sci 2022; 13:8953-8962. [PMID: 36091203 PMCID: PMC9365244 DOI: 10.1039/d2sc01492k] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 07/11/2022] [Indexed: 01/04/2023] Open
Abstract
Quantum computing has recently exhibited great potential in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such as LiH and hydrogen chains of up to 12 qubits, by using quantum algorithms such as variational quantum eigensolver (VQE). Yet, originating from the limitations of the size and the fidelity of near-term quantum hardware, the accurate simulation of large realistic molecules remains a challenge. Here, integrating an adaptive energy sorting strategy and a classical computational method—the density matrix embedding theory, which respectively reduces the circuit depth and the problem size, we present a means to circumvent the limitations and demonstrate the potential of near-term quantum computers toward solving real chemical problems. We numerically test the method for the hydrogenation reaction of C6H8 and the equilibrium geometry of the C18 molecule, using basis sets up to cc-pVDZ (at most 144 qubits). The simulation results show accuracies comparable to those of advanced quantum chemistry methods such as coupled-cluster or even full configuration interaction, while the number of qubits required is reduced by an order of magnitude (from 144 qubits to 16 qubits for the C18 molecule) compared to conventional VQE. Our work implies the possibility of solving industrial chemical problems on near-term quantum devices. Quantum embedding simulation greatly enhanced the capability of near-term quantum computers on realistic chemical systems and reach accuracy comparable to advanced quantum chemistry methods.![]()
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Affiliation(s)
- Weitang Li
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
- Department of Chemistry, Tsinghua University, Beijing 100084, China
| | - Zigeng Huang
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
| | - Changsu Cao
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
| | - Yifei Huang
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
| | - Zhigang Shuai
- Department of Chemistry, Tsinghua University, Beijing 100084, China
| | - Xiaoming Sun
- Institute of Computing Technology, Chinese Academy of Sciences, China
- University of Chinese Academy of Sciences, China
| | - Jinzhao Sun
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
| | - Xiao Yuan
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Dingshun Lv
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
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22
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Benfenati F, Mazzola G, Capecci C, Barkoutsos PK, Ollitrault PJ, Tavernelli I, Guidoni L. Improved Accuracy on Noisy Devices by Nonunitary Variational Quantum Eigensolver for Chemistry Applications. J Chem Theory Comput 2021; 17:3946-3954. [PMID: 34077220 DOI: 10.1021/acs.jctc.1c00091] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We propose a modification of the Variational Quantum Eigensolver algorithm for electronic structure optimization using quantum computers, named nonunitary Variational Quantum Eigensolver (nu-VQE), in which a nonunitary operator is combined with the original system Hamiltonian leading to a new variational problem with a simplified wave function ansatz. In the present work, as nonunitary operator, we use the Jastrow factor, inspired from classical Quantum Monte Carlo techniques for simulation of strongly correlated electrons. The method is applied to prototypical molecular Hamiltonians for which we obtain accurate ground-state energies with shallower circuits, at the cost of an increased number of measurements. Finally, we also show that this method achieves an important error mitigation effect that drastically improves the quality of the results for VQE optimizations on today's noisy quantum computers. The absolute error in the calculated energy within our scheme is 1 order of magnitude smaller than the corresponding result using traditional VQE methods, with the same circuit depth.
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Affiliation(s)
- Francesco Benfenati
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, Coppito, L'Aquila 67100, Italy.,Multiverse Computing, Donostia-San Sebastián 20014, Spain
| | | | - Chiara Capecci
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, Coppito, L'Aquila 67100, Italy.,Dipartimento di Fisica, Sapienza Università di Roma, Roma 00185, Italy
| | | | | | | | - Leonardo Guidoni
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, Coppito, L'Aquila 67100, Italy
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23
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Smart SE, Mazziotti DA. Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices. PHYSICAL REVIEW LETTERS 2021; 126:070504. [PMID: 33666467 DOI: 10.1103/physrevlett.126.070504] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2020] [Revised: 10/02/2020] [Accepted: 01/05/2021] [Indexed: 06/12/2023]
Abstract
The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or nontrivial high-dimensional classical optimization. Here, we introduce a quantum solver of contracted eigenvalue equations, the quantum analog of classical methods for the energies and reduced density matrices of ground and excited states. The solver does not require deep circuits or difficult classical optimization and achieves an exponential speed-up over its classical counterpart. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.
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Affiliation(s)
- Scott E Smart
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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24
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Urbanek M, Camps D, Van Beeumen R, de Jong WA. Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion. J Chem Theory Comput 2020; 16:5425-5431. [PMID: 32822184 DOI: 10.1021/acs.jctc.0c00447] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
Simulating chemical systems on quantum computers has been limited to a few electrons in a minimal basis. We demonstrate experimentally that the virtual quantum subspace expansion (Takeshita, T.; Phys. Rev. X 2020, 10, 011004, 10.1103/PhysRevX.10.011004) can achieve full basis accuracy for hydrogen and lithium dimers, comparable to simulations requiring 20 or more qubits. We developed an approach to minimize the impact of experimental noise on the stability of the generalized eigenvalue problem, a crucial component of the quantum algorithm. In addition, we were able to obtain an accurate potential energy curve for the nitrogen dimer in a quantum simulation on a classical computer.
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Affiliation(s)
- Miroslav Urbanek
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Daan Camps
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Roel Van Beeumen
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Wibe A de Jong
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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25
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Motta M, Gujarati TP, Rice JE, Kumar A, Masteran C, Latone JA, Lee E, Valeev EF, Takeshita TY. Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer. Phys Chem Chem Phys 2020; 22:24270-24281. [DOI: 10.1039/d0cp04106h] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Molecular quantum computing simulations are currently limited by the use of minimal Gaussian bases, a problem we overcome using a canonical transcorrelated Hamiltonian to accelerate basis convergence, with unitary coupled cluster as an example.
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Affiliation(s)
- Mario Motta
- IBM Quantum
- IBM Research – Almaden
- San Jose
- USA
| | | | | | | | | | | | - Eunseok Lee
- Mercedes-Benz Research and Development North America
- Sunnyvale
- USA
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