My research in the area of novel quantum computing approaches to solve the electronic structure problem
! UNDER CONSTRUCTION !
Due to the unfavorable scaling with system and basis set size, accurate computational approaches are practically limited to small problem sizes, even on high-performance computing (HPC) clusters. Quantum computing, on the other hand, harnesses quantum mechanical phenomena to allow a major leap in computation. By using quantum bits (qubits) as the basic unit of information and computation, quantum computers can encode an exponentially growing problem space with the superposition of n qubits. Specifically designed quantum algorithms are then able to utilize quantum wave interference and entanglement to find solutions to problems in this vast multidimensional space. Multiple research teams were able to show so-called quantum advantage, solving problems on a quantum computer orders of magnitude faster than the largest supercomputers -- albeit for highly constructed and practically irrelevant problems. The sizes of electronic structure problems treatable on current quantum hardware are far more modest and do not yet exceed the capability of conventional computing approaches. The main roadblocks are noise, the circuit depth, and the limited number of available qubits, as the number of qubits needed to encode a given problem is equal to the size of the utilized basis set.
Thus, quantum computing has the potential to provide a significant speedup compared to classical computers, but the practical implementation is still in its infancy. Two central questions are: (1) in which field the current NISQ hardware can provide benefits compared to classical computers and (2) which methods and algorithms enable this advantage? My research in quantum computing aims to answer these questions by developing hybrid digital quantum computing algorithms to enable accurate electronic structure calculations on current and near-term quantum hardware. My research in this area focuses on NISQ-friendly hybrid quantum-classical approaches, where the quantum processing unit (QPU) is used to efficiently prepare and store parametrized quantum states and measure expectation values of operators of interest, i.e., the system's Hamiltonian. The measured expected values are then used on a classical processing unit (CPU) to update the parameters of our quantum state to iteratively perform a desired computation, i.e., ground/excited state energy calculation, time-evolution, dynamic response functions, etc. A major roadblock toward realistic electronic structure calculations on NISQ devices is the above-mentioned necessary expansion of a problem in larger and larger number of basis functions. A large number of basis functions increases the required number of qubits to encode the system of interest on quantum hardware. The transcorrelated method reduces the necessary expansion size, allowing highly accurate electronic structure calculations for relevant, realistic systems on NISQ devices. This directly tackles two of the major problems of current quantum computing hardware: (1) the limited number of available qubits (circuit width) and (2) the restricted circuit depth due to qubit/gate noise and decoherence.
Related Publications:
2024
Quantum
Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
David Fitzek, Robert S. Jonsson, Werner Dobrautz, and Christian Schäfer
@article{Fitzek2024,title={Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes},volume={8},issn={2521-327X},url={http://dx.doi.org/10.22331/q-2024-04-09-1313},doi={10.22331/q-2024-04-09-1313},journal={Quantum},publisher={Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften},author={Fitzek, David and Jonsson, Robert S. and Dobrautz, Werner and Sch\"{a}fer, Christian},year={2024},month=apr,pages={1313},project_devel={true},project_quantum={true},dimensions={true},}
@article{Dobrautz2024,title={Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method},volume={20},issn={1549-9626},url={http://dx.doi.org/10.1021/acs.jctc.4c00070},doi={10.1021/acs.jctc.4c00070},number={10},journal={Journal of Chemical Theory and Computation},publisher={American Chemical Society (ACS)},author={Dobrautz, Werner and Sokolov, Igor O. and Liao, Ke and Ríos, Pablo López and Rahm, Martin and Alavi, Ali and Tavernelli, Ivano},year={2024},month=may,pages={4146–4160},project_tc={true},project_quantum={true},dimensions={true},}
Faraday Diss.
Towards efficient quantum computing for quantum chemistry: reducing circuit complexity with transcorrelated and adaptive ansatz techniques
Erika Magnusson, Aaron Fitzpatrick, Stefan Knecht, Martin Rahm, and Werner Dobrautz
@article{Magnusson2024,title={Towards efficient quantum computing for quantum chemistry: reducing circuit complexity with transcorrelated and adaptive ansatz techniques},volume={254},issn={1364-5498},url={http://dx.doi.org/10.1039/D4FD00039K},doi={10.1039/d4fd00039k},journal={Faraday Discussions},publisher={Royal Society of Chemistry (RSC)},author={Magnusson, Erika and Fitzpatrick, Aaron and Knecht, Stefan and Rahm, Martin and Dobrautz, Werner},year={2024},pages={402–428},project_tc={true},project_quantum={true},dimensions={true},}
Chem. Sci.
The electron density: a fidelity witness for quantum computation
Mårten Skogh, Werner Dobrautz, Phalgun Lolur, Christopher Warren, Janka Biznárová, and 4 more authors
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}}
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}}
