Werner Dobrautz

2023

1. JCTC

   Reference-State Error Mitigation: A Strategy for High Accuracy Quantum Computation of Chemistry

   Phalgun Lolur, Mårten Skogh, Werner Dobrautz, Christopher Warren, Janka Biznárová, and 5 more authors

   Journal of Chemical Theory and Computation, Jan 2023

   Abs arXiv Bib HTML

   Decoherence and gate errors severely limit the capabilities of state-of-the-art quantum computers. This work introduces a strategy for reference-state error mitigation (REM) of quantum chemistry that can be straightforwardly implemented on current and near-term devices. REM can be applied alongside existing mitigation procedures, while requiring minimal postprocessing and only one or no additional measurements. The approach is agnostic to the underlying quantum mechanical ansatz and is designed for the variational quantum eigensolver. Up to two orders-of-magnitude improvement in the computational accuracy of ground state energies of small molecules (H2, HeH+, and LiH) is demonstrated on superconducting quantum hardware. Simulations of noisy circuits with a depth exceeding 1000 two-qubit gates are used to demonstrate the scalability of the method.

   @article{Lolur2023,
     doi = {10.1021/acs.jctc.2c00807},
     url = {https://doi.org/10.1021/acs.jctc.2c00807},
     year = {2023},
     month = jan,
     publisher = {American Chemical Society ({ACS})},
     volume = {19},
     number = {3},
     pages = {783--789},
     author = {Lolur, Phalgun and Skogh, M{\aa}rten and Dobrautz, Werner and Warren, Christopher and Bizn{\'{a}}rov{\'{a}}, Janka and Osman, Amr and Tancredi, Giovanna and Wendin, G\"{o}ran and Bylander, Jonas and Rahm, Martin},
     title = {Reference-State Error Mitigation: A Strategy for High Accuracy Quantum Computation of Chemistry},
     journal = {Journal of Chemical Theory and Computation},
     dimensions = {true},
     project_quantum = {true},
     project_mitigation = {true}
   }

2. PRResearch

   Orders of magnitude increased accuracy for quantum many-body problems on quantum computers via an exact transcorrelated method

   Igor O. Sokolov, Werner Dobrautz, Hongjun Luo, Ali Alavi, and Ivano Tavernelli

   Phys. Rev. Res., Jun 2023

   Abs arXiv Bib HTML

   Transcorrelated methods provide an efficient way of partially transferring the description of electronic correlations from the ground-state wave function directly into the underlying Hamiltonian. In particular, Dobrautz et al. [Phys. Rev. B 99, 075119 (2019)] have demonstrated that the use of momentum-space representation, combined with a nonunitary similarity transformation, results in a Hubbard Hamiltonian that possesses a significantly more “compact” ground-state wave function, dominated by a single Slater determinant. This compactness/single-reference character greatly facilitates electronic structure calculations. As a consequence, however, the Hamiltonian becomes non-Hermitian, posing problems for quantum algorithms based on the variational principle. We overcome these limitations with the Ansatz-based quantum imaginary-time evolution algorithm and apply the transcorrelated method in the context of digital quantum computing. We demonstrate that this approach enables up to four orders of magnitude more accurate and compact solutions in various instances of the Hubbard model at intermediate interaction strength (U/t=4), enabling the use of shallower quantum circuits for wave-function Ansätzes. In addition, we propose a more efficient implementation of the quantum imaginary-time evolution algorithm in quantum circuits that is tailored to non-Hermitian problems. To validate our approach, we perform hardware experiments on the ibmq_lima quantum computer. Our work paves the way for the use of exact transcorrelated methods for the simulations of ab initio systems on quantum computers.

   @article{PhysRevResearch.5.023174,
     title = {Orders of magnitude increased accuracy for quantum many-body problems on quantum computers via an exact transcorrelated method},
     author = {Sokolov, Igor O. and Dobrautz, Werner and Luo, Hongjun and Alavi, Ali and Tavernelli, Ivano},
     journal = {Phys. Rev. Res.},
     volume = {5},
     issue = {2},
     pages = {023174},
     numpages = {19},
     year = {2023},
     month = jun,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevResearch.5.023174},
     url = {https://link.aps.org/doi/10.1103/PhysRevResearch.5.023174},
     dimensions = {true},
     project_quantum = {true},
     project_tc = {true},
     project_hubbard = {true}
   }

3. arXiv

   Ab Initio Transcorrelated Method enabling accurate Quantum Chemistry on near-term Quantum Hardware

   Werner Dobrautz, Igor O. Sokolov, Ke Liao, Pablo López Ríos, Martin Rahm, and 2 more authors

   arXiv, Jun 2023

   Abs arXiv Bib

   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 limited connectivity) hamper the straightforward implementation of most quantum algorithms and call for more noise-resilient solutions. In quantum chemistry, the limited number of available qubits and gate operations is particularly restrictive since, for each molecular orbital, one needs, in general, two qubits. In this study, we propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach, which transfers – without any approximation – correlation from the wavefunction directly into the Hamiltonian, thus reducing the number of resources needed to achieve accurate results with noisy, near-term quantum devices. In particular, we show that the exact transcorrelated approach not only allows for more shallow circuits but also improves the convergence towards the so-called basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, therefore, 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 just 4 and 6 qubits, respectively. Conventional methods require at least ten times more qubits for the same accuracy.

   @article{2303.02007,
     author = {Dobrautz, Werner and Sokolov, Igor O. and Liao, Ke and Ríos, Pablo López and Rahm, Martin and Alavi, Ali and Tavernelli, Ivano},
     title = {Ab Initio Transcorrelated Method enabling accurate Quantum Chemistry on near-term Quantum Hardware},
     year = {2023},
     eprint = {arXiv:2303.02007},
     journal = {arXiv},
     project_tc = {true},
     project_quantum = {true}
   }

2021

1. JCTC

   Spin-Pure Stochastic-CASSCF via GUGA-FCIQMC Applied to Iron–Sulfur Clusters

   Werner Dobrautz, Oskar Weser, Nikolay A. Bogdanov, Ali Alavi, and Giovanni Li Manni

   Journal of Chemical Theory and Computation, Sep 2021

   Abs arXiv Bib HTML

   In this work, we demonstrate how to efficiently compute the one- and two-body reduced density matrices within the spin-adapted full configuration interaction quantum Monte Carlo (FCIQMC) method, which is based on the graphical unitary group approach (GUGA). This allows us to use GUGA-FCIQMC as a spin-pure configuration interaction (CI) eigensolver within the complete active space self-consistent field (CASSCF) procedure and hence to stochastically treat active spaces far larger than conventional CI solvers while variationally relaxing orbitals for specific spin-pure states. We apply the method to investigate the spin ladder in iron–sulfur dimer and tetramer model systems. We demonstrate the importance of the orbital relaxation by comparing the Heisenberg model magnetic coupling parameters from the CASSCF procedure to those from a CI-only (CASCI) procedure based on restricted open-shell Hartree–Fock orbitals. We show that the orbital relaxation differentially stabilizes the lower-spin states, thus enlarging the coupling parameters with respect to the values predicted by ignoring orbital relaxation effects. Moreover, we find that, while CASCI results are well fit by a simple bilinear Heisenberg Hamiltonian, the CASSCF eigenvalues exhibit deviations that necessitate the inclusion of biquadratic terms in the model Hamiltonian.

   @article{Dobrautz2021,
     doi = {10.1021/acs.jctc.1c00589},
     url = {https://doi.org/10.1021/acs.jctc.1c00589},
     year = {2021},
     month = sep,
     publisher = {American Chemical Society ({ACS})},
     volume = {17},
     number = {9},
     pages = {5684--5703},
     author = {Dobrautz, Werner and Weser, Oskar and Bogdanov, Nikolay A. and Alavi, Ali and Manni, Giovanni Li},
     title = {Spin-Pure Stochastic-{CASSCF} via {GUGA}-{FCIQMC} Applied to Iron{\textendash}Sulfur Clusters},
     journal = {Journal of Chemical Theory and Computation},
     dimensions = {true},
     project_guga = {true},
     project_devel = {true},
     project_tm = {true},
     project_fciqmc = {true}
   }

2019

1. PRB

   Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via nonunitary similarity transformations

   Werner Dobrautz, Hongjun Luo, and Ali Alavi

   Phys. Rev. B, Feb 2019

   Abs arXiv Bib HTML

   Similarity transformation of the Hubbard Hamiltonian using a Gutzwiller correlator leads to a non-Hermitian effective Hamiltonian, which can be expressed exactly in momentum-space representation and contains three-body interactions. We apply this methodology to study the two-dimensional Hubbard model with repulsive interactions near half filling in the intermediate interaction strength regime (U/t=4). We show that at optimal or near optimal strength of the Gutzwiller correlator, the similarity-transformed Hamiltonian has extremely compact right eigenvectors, which can be sampled to high accuracy using the full configuration interaction quantum Monte Carlo (FCIQMC) method and its initiator approximation. Near-optimal correlators can be obtained using a simple projective equation, thus obviating the need for a numerical optimization of the correlator. The FCIQMC method, as a projective technique, is well suited for such non-Hermitian problems, and its stochastic nature can handle the three-body interactions exactly without undue increase in computational cost. The highly compact nature of the right eigenvectors means that the initiator approximation in FCIQMC is not severe and that large lattices can be simulated, well beyond the reach of the method applied to the original Hubbard Hamiltonian. Results are provided in lattice sizes up to 50 sites and compared to auxiliary-field QMC. New benchmark results are provided in the off-half-filling regime, with no severe sign problem being encountered. In addition, we show that methodology can be used to calculate excited states of the Hubbard model and lay the groundwork for the calculation of observables other than the energy.

   @article{PhysRevB.99.075119,
     title = {Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via nonunitary similarity transformations},
     author = {Dobrautz, Werner and Luo, Hongjun and Alavi, Ali},
     journal = {Phys. Rev. B},
     volume = {99},
     issue = {7},
     pages = {075119},
     numpages = {20},
     year = {2019},
     month = feb,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevB.99.075119},
     url = {https://link.aps.org/doi/10.1103/PhysRevB.99.075119},
     dimensions = {true},
     project_tc = {true},
     project_hubbard = {true}
   }

2. JCP

   Efficient formulation of full configuration interaction quantum Monte Carlo in a spin eigenbasis via the graphical unitary group approach

   Werner Dobrautz, Simon D. Smart, and Ali Alavi

   The Journal of Chemical Physics, Sep 2019

   Abs arXiv Bib HTML

   We provide a spin-adapted formulation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, based on the Graphical Unitary Group Approach (GUGA), which enables the exploitation of SU(2) symmetry within this stochastic framework. Random excitation generation and matrix element calculation on the Shavitt graph of GUGA can be efficiently implemented via a biasing procedure on the branching diagram. The use of a spin-pure basis explicitly resolves the different spin-sectors and ensures that the stochastically sampled wavefunction is an eigenfunction of the total spin operator Ŝ 2⁠. The method allows for the calculation of states with low or intermediate spin in systems dominated by Hund’s first rule, which are otherwise generally inaccessible. Furthermore, in systems with small spin gaps, the new methodology enables much more rapid convergence with respect to walker number and simulation time. Some illustrative applications of the GUGA-FCIQMC method are provided: computation of the 2F − 4F spin gap of the cobalt atom in large basis sets, achieving chemical accuracy to experiment, and the Σg+1⁠, Σg+3⁠, Σg+5⁠, and Σg+7 spin-gaps of the stretched N2 molecule, an archetypal strongly correlated system.

   @article{Dobrautz2019,
     doi = {10.1063/1.5108908},
     url = {https://doi.org/10.1063/1.5108908},
     year = {2019},
     month = sep,
     publisher = {{AIP} Publishing},
     volume = {151},
     number = {9},
     author = {Dobrautz, Werner and Smart, Simon D. and Alavi, Ali},
     title = {Efficient formulation of full configuration interaction quantum Monte Carlo in a spin eigenbasis via the graphical unitary group approach},
     journal = {The Journal of Chemical Physics},
     dimensions = {true},
     project_guga = {true},
     project_devel = {true},
     project_fciqmc = {true}
   }