Challenges in the Use of Quantum Computing Hardware-Efficient Ansätze in Electronic Structure Theory

Abstract

Advances in quantum computation for electronic structure, and particularly heuristic quantum algorithms, create an ongoing need to characterize the performance and limitations of these methods. Here we discuss some potential pitfalls connected with the use of hardware-efficient Ansätze in variational quantum simulations of electronic structure. We illustrate that hardware-efficient Ansätze may break Hamiltonian symmetries and yield nondifferentiable potential energy curves, in addition to the well-known difficulty of optimizing variational parameters. We discuss the interplay between these limitations by carrying out a comparative analysis of hardware-efficient Ansätze versus unitary coupled cluster and full configuration interaction, and of second- and first-quantization strategies to encode Fermionic degrees of freedom to qubits. Our analysis should be useful in understanding potential limitations and in identifying possible areas of improvement in hardware-efficient Ansätze.

Physics-Constrained Hardware-Efficient Ansatz on Quantum Computers That Is Universal, Systematically Improvable, and Size-Consistent

“…Figure shows the comparison of different HEA for the convergence of ground-state energies as a function of the number of layers L for hydrogen chains (H 4 , H 6 , and H 8 ), LiH, H 2 O, and N 2 , which were commonly used to benchmark the performance of quantum computing techniques. ,,,, For the stretched hydrogen chains, the OAO were used due to the faster convergence and the reference state was a Néel state, e.g., |Φ 0 ⟩ = |10011001⟩ for H 4 . As the number of hydrogen increases, the number of Slater determinants with large coefficients in the expansion of the exact ground state increases significantly.…”

“…It is obvious that the R y ansatz can only represent real wave functions, whereas it is unclear whether the R y R z ansatz is universal. Recently, a “cascade” ansatz is developed to satisfy the condition U l ( θ⃗ l ) = I by adding the inverse of the CNOT gates in R y ansatz into the repeating unit . However, it fails to meet the constraints (3) and (4).…”

“…These problems severely limit the scalability of HEA beyond small systems. Therefore, it is highly desirable to design a variational ansatz with rigorous theoretical basis, while at the same time being hardware-efficient on near-term devices. , …”

MQM 2022: The 10th Triennial Conference on Molecular Quantum Mechanics

“…Quantum computing is also explored in the MQM VSI in work by D’Cunha and Crawford at Virginia Tech and Motta and Rice at IBM Almaden, who examined potential pitfalls of hardware-efficient Ansätze in variational quantum simulations of molecular electronic structure . They report that such methods can yield broken symmetry solutions as well as nondifferentiable potential surfaces, and they offer an analysis that may guide future developments.…”

Statistical errors in reduced density matrices sampled from quantum circuit simulation and the impact on multireference perturbation theory

“…Simulation of the Hamiltonian for strongly entangled quantum systems is widely regarded as a promising application 10–18 in both noisy intermediate-scale quantum (NISQ) devices 19–24 and fault-tolerant quantum computers (FTQC), 25–28 which has the potential to enable calculations for large CAS wavefunctions that are difficult to achieve with classical computers. By associating an electronic configuration in the active space with an eigenstate of qubits, it is possible to map a CAS wavefunction onto a superposition state of qubits; the required number of qubits is equal to the number of spin–orbitals in the active space.…”