Quantum Computing in Pharma: A MultilayerEmbedding Approach for Near Future Applications

Simulating molecules or even interactions between molecules in chemistry is a task that requires the advanced computing power that only quantum computers can offer. The latest models, like the ones described by Wang et al. [1] and Babbush et al. [2], are able to estimate the quantum phase of fluorine in a specific orbital space. This leads to the challenge of carefully selecting orbital spaces to simulate. To tackle this challenge, the Quantum Phase Estimation (QPE) and Variational Quantum Eigensolver (VQE) algorithms are used to describe the simulated molecules.

The QPE algorithm aims to retrieve the phase from the eigenvalue of an eigenstate which a unitary operator has acted on. Meanwhile, the QVE algorithm provides a lower bound for the minimum eigenvalue of a Hermitian matrix. The Hermitian matrix’s eigenvalue is often solved using this algorithm because it can characterize a chemical molecule.

In a paper released this month, Róbert Izsák from Riverlane Research, Christoph Riplinger from FAccTs, et al. outlined a procedure to select orbital spaces automatically. The goal of the procedure is to facilitate the accurate simulation of the active space in a chemical system. While the paper acknowledges that the size of the active spaces is limited, the results demonstrated can be used to treat larger-scale problems if given increased computing resources.

The challenge remains in the scalability of the VQE and QPE algorithms on quantum computers with insufficient fidelity. Because current quantum computers cannot deal with large enough numbers of qubits, embedding techniques are employed to divide a system into subparts that are then reassembled to describe a property. Future research could look into optimizing this computation to facilitate orbital selection.

You can read the original publication here:

https://arxiv.org/pdf/2202.04460.pdf

Further readings :

[1] https://quantum-journal.org/papers/q-2021-07-26-509/pdf/

[2] https://arxiv.org/pdf/1410.8159.pdf

https://qiskit.org/textbook/ch-algorithms/quantum-phase-estimation.html

https://qiskit.org/textbook/ch-applications/vqe-molecules.html#Introduction