Quantinuum’s scientific team has developed a new chemical hybrid classical-quantum solver, which will allow more effective and accurate modelling of complex molecules. As published on arXiv on October 13, 2022, they achieved this by creating a new multi-reference technique to help select the active space of the molecule, which describes strongly correlated electrons.
The key problem in computational quantum chemistry, the Hamiltonian simulation, has long been described as too complicated to be solved in most cases. Full Configuration Interaction (FCI), the exact solution to the molecular electrical structure issue (in a finite basis), increases combinatorially with basis size. As a result, even in its stochastic approximation implementations, FCI is limited to small systems.
Due to the exponential (or near-exponential) speedup of some quantum algorithms, such as Quantum Phase Estimation (QPE), compared to classical methods such as FCI, quantum computing has lately emerged as a potential option for large-scale precise electronic structure computations.
While the desire for an exact or quantum solution to the chemical Hamiltonian simulation problem appears to be the driving force behind the development of quantum algorithms for computational chemistry, exact diagonalization of the entire Hamiltonian of a chemical system is, in practice, hardly ever needed.
Coupled Cluster methods, such as CCSD(T), can be used to calculate the ground-state energies of “single-reference” molecular systems, i.e., exhibiting primarily weak correlations and having one dominant configuration in the Configuration Interaction expansion.
The remaining strongly correlated electronic systems are often represented using multi-reference or multi-configurational approaches, in which interactions within just a subspace of the Hilbert space are estimated with great precision.
In contrast, interactions with remaining orbitals are only considered roughly. As a result, the orbitals are separated into two distinct groups: active orbitals and inactive (core and virtual) orbitals.
A model Hamiltonian is created in the reference (or model) subspace defined by Slater determinants generated by active orbital permutations and accounts mostly for static electron correlation. An expansion of the model space that encompasses all potential electron distributions in the specified (active) orbitals is called Complete active space (CAS).
The cost of CASPT2 and NEVPT2 computations, that is, 2nd order Complete Active Space Perturbation Theory and n-electron valence state perturbation theory, respectively, for large active spaces, is driven by the solution of the CAS problem, which increases exponentially with the size of the active space due to an exponential scaling of the CI basis.
But, it is possible to express this large CI basis via the 2N basis states of N qubits by mapping the electronic occupation number vectors of length N to qubits; the same mapping applied to the electronic Hamiltonian provides the matching qubit Hamiltonian.
As a result, replacing the CAS-CI component of the computation with an efficient quantum method would allow these approaches to be applied to very large active spaces, increasing their applicability to extensive, complicated chemical systems and eliminating the requirement for active orbital selection.
The quantum algorithm they used in this phase was based on measuring reduced density matrices and feeding them into a multi-reference perturbation theory computation, which had never been done in this situation before. When the quantum electronic structure solver is applied to the active space and measured reduced density matrices are used, the problem becomes less computationally expensive, and the solution becomes more accurate.
Quantinuum’s scientists used IBM’s 27-qubit device and Quantinuum’s hybrid solver, which was integrated into the InQuanto quantum computational chemistry platform, to evaluate their process on the molecules H2 and Li2.
The team’s findings demonstrated a great correlation with earlier models. In addition, the technique has shown considerable potential for achieving new heights of efficiency and precision for bigger molecules. The future significance of this discovery might result in the developing of a new paradigm for quantum chemistry.