Complete Active Space Methods for NISQ Devices: The Importance of Canonical Orbital Optimization for Accuracy and Noise Resilience

Abstract

To avoid the scaling of the number of qubits with the size of the basis set, one can divide the molecular space into active and inactive regions, which is also known as complete active space methods. However, selecting the active space alone is not enough to accurately describe quantum mechanical effects such as correlation. This study emphasizes the importance of optimizing the active space orbitals to describe correlation and improve the basis-dependent Hartree−Fock energies. We will explore classical and quantum computation methods for orbital optimization and compare the chemically inspired ansatz, UCCSD, with the classical full CI approach for describing the active space in both weakly and strongly correlated molecules. Finally, we will investigate the practical implementation of a quantum CASSCF, where hardware-efficient circuits must be used and noise can interfere with accuracy and convergence. Additionally, we will examine the impact of using canonical and noncanonical active orbitals on the convergence of the quantum CASSCF routine in the presence of noise.

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive

“…In this article, we have presented the framework and implementation for a SCF complete-AS orbital-optimization algorithm that exploits adaptively optimized quantum circuits for the variational quantum eigensolver, serving as an AS solver in place of a classical full CI solver. Although our orbital optimization algorithm for quantum-computing-driven quantum chemistry is by no means the first of its kind (see, for example, refs – , it is, to the best of our knowledge, the first one that exploits within the VQE solver framework quantum circuits based on the so-called ADAPT family of ansätze . Dubbed as ADAPT-VQE-SCF approach, we demonstrated its capabilities by considering various molecular quantum-chemical applications ranging from state-specific electronic ground-state optimizations to multiroot SA optimizations simultaneously targeting electronic states of differing spin multiplicity.…”

“…In this work, we will add a pivotal milestone to the aforementioned adaptive VQE algorithms by combining the adaptive expansion of the quantum circuit and ensuing optimization of its accompanying {θ i } parameter set with simultaneous optimization of the orbital rotation parameters κ in the variational energy minimization as outlined in eq . In contrast to related recent works within the framework of near-term quantum-computing-driven MCSCF-type approaches, − our adaptive, SCF VQE algorithm, denoted in the following as ADAPT-VQE-SCF, greatly benefits from a considerable reduction in the number of two-qubit gates in the final ansatz that are required to reach convergence with respect to chemical precision. Moreover, we not only provide a state-specific energy minimization (eq ) ADAPT-VQE-SCF algorithm but also a SA one that opens up for an optimization of a common set of MOs for a multitude of states i , that is where λ i is a preselected, fixed weighting factor for the i -th state |Φ i ⟩ that satisfy the constraint but are arbitrary otherwise.…”

Variational Quantum Eigensolver Boosted by Adiabatic Connection

“…The standard UCCSD-VQE method (or its adaptive improvements) does not fulfill this requirement. Nevertheless, orbital-optimized (OO) UCC-VQE, ,,− as well as ADAPT-VQE-SCF, has been developed recently.…”

A Simulation of Hydrazine Molecule’s Potential Energy Surface using Variational Quantum Eigensolver Algorithm

“…Consequently, the number of qubits required in quantum devices for larger molecules with extensive basis sets significantly increases, posing an intractable challenge within the current era of noisy intermediate-scale quantum (NISQ) devices. To reduce the qubit requirements and enable the use of larger basis sets without the need for additional qubits, we can employ the Active Space (AS) approximation [20], which divides the initial state into active (|Ψ A 0 ⟩) and inactive (|Ψ I 0 ⟩) orbitals.…”