Hartree-Fock on a superconducting qubit quantum computer (2004.04174v4)

Abstract: As the search continues for useful applications of noisy intermediate scale quantum devices, variational simulations of fermionic systems remain one of the most promising directions. Here, we perform a series of quantum simulations of chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and 114 one-qubit gates. We model the binding energy of ${\rm H}6$, ${\rm H}_8$, ${\rm H}{10}$ and ${\rm H}_{12}$ chains as well as the isomerization of diazene. We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realize the Givens rotation approach to non-interacting fermion evolution, which we variationally optimize to prepare the Hartree-Fock wavefunction. This ubiquitous algorithmic primitive corresponds to a rotation of the orbital basis and is required by many proposals for correlated simulations of molecules and Hubbard models. Because non-interacting fermion evolutions are classically tractable to simulate, yet still generate highly entangled states over the computational basis, we use these experiments to benchmark the performance of our hardware while establishing a foundation for scaling up more complex correlated quantum simulations of chemistry.

• The paper extends quantum chemistry simulations by doubling qubit count and increasing gate operations over tenfold compared to prior experiments.
• The paper implements a variational Hartree-Fock approach using a parameterized ansatz with Givens rotations to simulate hydrogen chains and diazene isomerization.
• The paper employs advanced error mitigation strategies, reducing errors to chemical accuracy and benchmarking the performance of the Sycamore processor.

Hartree-Fock on a Superconducting Qubit Quantum Computer

The paper "Hartree-Fock on a Superconducting Qubit Quantum Computer" presents a significant advancement in the quantum simulation of molecular systems using noisy intermediate-scale quantum (NISQ) devices. The research employs the Google Sycamore quantum processor to conduct variational quantum eigensolver (VQE) simulations, which extend the boundaries of quantum chemistry experiments by increasing both the number of qubits and the quantum gate operations involved.

Key Contributions

1. Extension of Quantum Chemistry Simulations: The authors perform simulations that involve twice the number of qubits and over ten times the number of quantum gates compared to previous experiments. Specifically, they simulate hydrogen chains as large as $\text{H}_{12}$ and the isomerization of diazene, demonstrating a significant leap in the complexity of quantum simulations feasible on current hardware.
2. Implementation of Hartree-Fock via VQE: The paper details a variational approach using a parameterized ansatz circuit that realizes Givens rotations for noninteracting fermion evolution. This is variationally optimized to prepare the Hartree-Fock wavefunction, which is crucial for initializing more complex molecular simulations.
3. Error Mitigation Techniques: The paper develops and applies error-mitigation strategies based on $N$-representability, which notably enhance the fidelity of the quantum experiments. These strategies include post-selection and McWeeny purification tactics tailored to reduce systematic errors and improve the accuracy of quantum simulations.
4. Benchmarking and Architectural Validation: The research serves as a benchmark for the Sycamore processor by implementing large-scale simulations that are classically tractable, thus providing a means to gauge quantum hardware performance and refine simulation techniques.

Results

• For the hydrogen chains, post-selection, purification, and variational relaxation reduced errors to within chemical accuracy, achieving remarkable fidelity improvements with error-mitigation techniques.
• In simulating diazene isomerization pathways, the research accurately resolved transition states and energy differences, demonstrating the capability of current quantum computers to facilitate near-term quantum chemistry applications.

Implications and Future Directions

The work emphasizes the potential of quantum computers to tackle computational chemistry problems that are classically challenging. By advancing error mitigation strategies and enhancing the VQE framework, this research lays a foundation for scaling up quantum simulations in chemistry. The results provide insights into the capabilities and limitations of NISQ devices, highlighting areas requiring innovation to bridge the gap towards classically intractable simulations.

Future research could explore integrating these techniques into more general quantum algorithms and expanding the hardware to support larger systems. Additionally, the development of more sophisticated error-mitigation mechanisms and the design of optimized quantum circuits for fermionic systems remain crucial for advancing quantum simulations of electronic structures above current scales.