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Dobrautz W, Sokolov IO, Liao K, Ríos PL, Rahm M, Alavi A, Tavernelli I. Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method. J Chem Theory Comput 2024; 20:4146-4160. [PMID: 38723159 PMCID: PMC11137825 DOI: 10.1021/acs.jctc.4c00070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 04/15/2024] [Accepted: 04/16/2024] [Indexed: 05/29/2024]
Abstract
Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using two and four qubits, respectively. To demonstrate our approach's current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today's quantum hardware.
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Affiliation(s)
- Werner Dobrautz
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, 41296 Gothenburg, Sweden
| | - Igor O. Sokolov
- IBM
Quantum, IBM Research Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Ke Liao
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Pablo López Ríos
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Martin Rahm
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, 41296 Gothenburg, Sweden
| | - Ali Alavi
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield
Road, Cambridge CB2 1EW, U.K.
| | - Ivano Tavernelli
- IBM
Quantum, IBM Research Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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2
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Bierman J, Li Y, Lu J. Qubit Count Reduction by Orthogonally Constrained Orbital Optimization for Variational Quantum Excited-State Solvers. J Chem Theory Comput 2024; 20:3131-3143. [PMID: 38598683 DOI: 10.1021/acs.jctc.3c01297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
We propose a state-averaged orbital optimization scheme for improving the accuracy of excited states of the electronic structure Hamiltonian for use on near-term quantum computers. Instead of parameterizing the orbital rotation operator in the conventional fashion as an exponential of an antihermitian matrix, we parameterize the orbital rotation as a general partial unitary matrix. Whereas conventional orbital optimization methods minimize the state-averaged energy using successive Newton steps of the second-order Taylor expansion of the energy, the method presented here optimizes the state-averaged energy using an orthogonally constrained gradient projection method that does not require any expansion approximations. Through extensive benchmarking of the method on various small molecular systems, we find that the method is capable of producing more accurate results than fixed basis FCI while simultaneously using fewer qubits. In particular, we show that for H2, the method is capable of matching the accuracy of FCI in the cc-pVTZ basis (56 qubits) while only using 14 qubits.
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Affiliation(s)
- Joel Bierman
- Department of Physics, Duke University, Durham, North Carolina 27708, United States
| | - Yingzhou Li
- School of Mathematical Sciences, Fudan University, Shanghai 200433, China
- Shanghai Key Laboratory for Contemporary Applied Mathematics, Shanghai 200433, China
- Key Laboratory of Computational Physical Sciences (MOE), Shanghai 200433, China
| | - Jianfeng Lu
- Department of Physics, Duke University, Durham, North Carolina 27708, United States
- Department of Mathematics, Duke University, Durham, North Carolina 27708, United States
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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3
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Kowalski K. Sub-system self-consistency in coupled cluster theory. J Chem Phys 2023; 158:054101. [PMID: 36754799 DOI: 10.1063/5.0125696] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
In this article, we provide numerical evidence indicating that the single-reference coupled-cluster (CC) energies can be calculated alternatively to their copybook definition. We demonstrate that the CC energy can be reconstructed by diagonalizing the effective Hamiltonians describing correlated sub-systems of the many-body system. In the extreme case, we provide numerical evidence that the CC energy can be reproduced through the diagonalization of the effective Hamiltonian describing sub-system composed of a single electron. These properties of the CC formalism can be exploited to design protocols to define effective interactions in sub-systems used as probes to calculate the energy of the entire system and introduce a new type of self-consistency for approximate CC approaches.
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Affiliation(s)
- Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
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4
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Kumar A, Asthana A, Masteran C, Valeev EF, Zhang Y, Cincio L, Tretiak S, Dub PA. Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits. J Chem Theory Comput 2022; 18:5312-5324. [PMID: 35984716 DOI: 10.1021/acs.jctc.2c00520] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.
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Affiliation(s)
- Ashutosh Kumar
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ayush Asthana
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Conner Masteran
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States.,Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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5
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Liu J, Matthews DA, Cheng L. Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version. J Chem Theory Comput 2022; 18:2281-2291. [PMID: 35312299 DOI: 10.1021/acs.jctc.1c01210] [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
An efficient implementation of the quadratic unitary coupled-cluster singles and doubles (qUCCSD) scheme for calculations of electronic ground and excited states using an unrestricted molecular spin-orbital formulation and an efficient tensor contraction library is reported. The accuracy of the qUCCSD scheme and the efficiency of the present implementation are demonstrated using extensive benchmark calculations of excitation energies and an application to S0 → S1 vertical excitation energies for cis- and trans-4a,4b-dihydrotriphenylene. The qUCCSD scheme has been shown to provide improved excitation energies compared with the UCC3 scheme formulated based on perturbation theory. A UCC truncation scheme that can provide excitation energies correct through the fourth order is also presented to further improve the accuracy of the qUCCSD scheme.
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Affiliation(s)
- Junzi Liu
- School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing, 100083, China
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
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6
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Abstract
Quantum embedding schemes are a promising way to extend multireference computations to large molecules with strong correlation effects localized on a small number of atoms. This work introduces a second-order active-space embedding theory [ASET(2)] which improves upon mean-field frozen embedding by treating fragment-environment interactions via an approximate canonical transformation. The canonical transformation employed in ASET(2) is formulated using the driven similarity renormalization group. The ASET(2) scheme is benchmarked on the N═N bond dissociation in pentyldiazene, the S0 to S1 excitation in 1-octene, and the interaction energy of the O2-benzene complex. The ASET(2) explicit treatment of fragment-environment interactions beyond the mean-field level generally improves the accuracy of embedded computations, and it becomes necessary to achieve an accurate description of excitation energies of 1-octene and the singlet-triplet gap of the O2-benzene complex.
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Affiliation(s)
- Nan He
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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7
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Bauman NP, Kowalski K. Coupled Cluster Downfolding Methods: the effect of double commutator terms on the accuracy of ground-state energies. J Chem Phys 2022; 156:094106. [DOI: 10.1063/5.0076260] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Karol Kowalski
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, United States of America
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8
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Dhawan D, Metcalf M, Zgid D. Dynamical Self-energy Mapping (DSEM) for Creation of Sparse Hamiltonians Suitable for Quantum Computing. J Chem Theory Comput 2021; 17:7622-7631. [PMID: 34739754 DOI: 10.1021/acs.jctc.1c00931] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present a two-step procedure called the dynamical self-energy mapping (DSEM) that allows us to find a sparse Hamiltonian representation for molecular problems. In the first part of this procedure, the approximate self-energy of a molecular system is evaluated using a low-level method and subsequently a sparse Hamiltonian is found that best recovers this low-level dynamic self-energy. In the second step, such a sparse Hamiltonian is used by a high-level method that delivers a highly accurate dynamical part of the self-energy that is employed in later calculations. The tests conducted on small molecular problems show that the sparse Hamiltonian parameterizations lead to very good total energies. DSEM has the potential to be used as a classical-quantum hybrid algorithm for quantum computing where the sparse Hamiltonian containing only O(n2) terms on a Gaussian orbital basis, where n is the number of orbitals in the system, could reduce the depth of the quantum circuit by at least an order of magnitude when compared with simulations involving a full Hamiltonian.
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Affiliation(s)
- Diksha Dhawan
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Mekena Metcalf
- Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, 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
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9
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Chan HHS, Fitzpatrick N, Segarra-Martí J, Bearpark MJ, Tew DP. Molecular excited state calculations with adaptive wavefunctions on a quantum eigensolver emulation: reducing circuit depth and separating spin states. Phys Chem Chem Phys 2021; 23:26438-26450. [PMID: 34806097 DOI: 10.1039/d1cp02227j] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Ab initio electronic excited state calculations are necessary for the quantitative study of photochemical reactions, but their accurate computation on classical computers is plagued by prohibitive resource scaling. The Variational Quantum Deflation (VQD) is an extension of the quantum-classical Variational Quantum Eigensolver (VQE) algorithm for calculating electronic excited state energies, and has the potential to address some of these scaling challenges using quantum computers. However, quantum computers available in the near term can only support a limited number of quantum circuit operations, so reducing the quantum computational cost in VQD methods is critical to their realisation. In this work, we investigate the use of adaptive quantum circuit growth (ADAPT-VQE) in excited state VQD calculations, a strategy that has been successful previously in reducing the resources required for ground state energy VQE calculations. We also invoke spin restrictions to separate the recovery of eigenstates with different spin symmetry to reduce the number of calculations and accumulation of errors in computing excited states. We created a quantum eigensolver emulation package - Quantum Eigensolver Building on Achievements of Both quantum computing and quantum chemistry (QEBAB) - for testing the proposed adaptive procedure against two existing VQD methods that use fixed-length quantum circuits: UCCGSD-VQD and k-UpCCGSD-VQD. For a lithium hydride test case we found that the spin-restricted adaptive growth variant of VQD uses the most compact circuits out of the tested methods by far, consistently recovers adequate electron correlation energy for different nuclear geometries and eigenstates while isolating the singlet and triplet manifold. This work is a further step towards developing techniques which improve the efficiency of hybrid quantum algorithms for excited state quantum chemistry, opening up the possibility of exploiting real quantum computers for electronic excited state calculations sooner than previously anticipated.
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Affiliation(s)
- Hans Hon Sang Chan
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK.
| | - Nathan Fitzpatrick
- Cambridge Quantum Computing Ltd, 9a Bridge Street, Cambridge CB2 1UB, UK
| | - Javier Segarra-Martí
- Instituto de Ciencia Molecular, Universitat de Valencia, PO Box 22085, Valencia, Spain
| | - Michael J Bearpark
- Department of Chemistry, Imperial College London, Molecular Sciences Research Hub, White City Campus, 82 Wood Lane, London, W12 0BZ, UK
| | - David P Tew
- Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
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10
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Wang DZ, Gauthier AQ, Siegmund AE, Hunt KLC. Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers. Phys Chem Chem Phys 2021; 23:6370-6387. [PMID: 33538732 DOI: 10.1039/d0cp05444e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.
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Affiliation(s)
- David Z Wang
- Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA.
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11
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Bauman NP, Liu H, Bylaska EJ, Krishnamoorthy S, Low GH, Granade CE, Wiebe N, Baker NA, Peng B, Roetteler M, Troyer M, Kowalski K. Toward Quantum Computing for High-Energy Excited States in Molecular Systems: Quantum Phase Estimations of Core-Level States. J Chem Theory Comput 2021; 17:201-210. [PMID: 33332965 DOI: 10.1021/acs.jctc.0c00909] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
This paper explores the utility of the quantum phase estimation (QPE) algorithm in calculating high-energy excited states characterized by the promotion of electrons occupying core-level shells. These states have been intensively studied over the last few decades, especially in supporting the experimental effort at light sources. Results obtained with QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is discussed. We also demonstrate the utility of the QPE algorithm in targeting excitations from specific centers in a molecule. Lastly, we discuss how the lowest-order Trotter formula can be applied to reducing the complexity of the ansatz without affecting the error.
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Affiliation(s)
- Nicholas P Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Hongbin Liu
- Microsoft Quantum, Redmond, Washington 98052, United States
| | - Eric J Bylaska
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Sriram Krishnamoorthy
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Guang Hao Low
- Microsoft Quantum, Redmond, Washington 98052, United States
| | | | - Nathan Wiebe
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Nathan A Baker
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Bo Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | | | | | - Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
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12
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Metcalf M, Bauman NP, Kowalski K, de Jong WA. Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and the Double Unitary Coupled-Cluster Approach. J Chem Theory Comput 2020; 16:6165-6175. [PMID: 32915568 DOI: 10.1021/acs.jctc.0c00421] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of the molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding preprocessing technique with the variational quantum eigensolver, we solve for the ground-state energy of H2, Li2, and BeH2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.
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Affiliation(s)
- Mekena Metcalf
- Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, California 94720, United States
| | - Nicholas P Bauman
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Karol Kowalski
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Wibe A de Jong
- Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, California 94720, United States
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13
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Kowalski K, Bauman NP. Sub-system quantum dynamics using coupled cluster downfolding techniques. J Chem Phys 2020; 152:244127. [DOI: 10.1063/5.0008436] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
| | - Nicholas P. Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
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14
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Sokolov IO, Barkoutsos PK, Ollitrault PJ, Greenberg D, Rice J, Pistoia M, Tavernelli I. Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents? J Chem Phys 2020; 152:124107. [PMID: 32241157 DOI: 10.1063/1.5141835] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum unitary variant of CC (UCC) with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the variational quantum eigensolver algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular, for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems, such as H4, H2O, and N2 molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.
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Affiliation(s)
- Igor O Sokolov
- Zurich Research Laboratory, IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | | | - Pauline J Ollitrault
- Zurich Research Laboratory, IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Donny Greenberg
- IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Julia Rice
- IBM Almaden Research Center, San Jose, California 95120, USA
| | - Marco Pistoia
- IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Ivano Tavernelli
- Zurich Research Laboratory, IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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