With the much anticipated paradigm shift from 'classical' to 'quantum', it becomes a subject of great interest to make the most of it. Our motivation for this project lies in the fact that "Quantum Chemistry" promises the ability to accurately predict chemical and physical properties of molecules and materials. Predicting chemical properties using a first principles approach at the atomic scale is a theoretical and computational challenge [1]. Even the most widely used classical simulation approaches like Hartree Fock (HF), Configuration Interaction Singles and Doubles (CISD), Coupled Cluster Singles and Doubles (CCSD), Full Configuration Interaction(FCI) fail to deliver chemical accuracy for larger systems and scale polynomially with larger systems.
To give an idea, that why are we placing our bets on quantum computers to do chemical simulation, let's consider something that impacts the world in a great manner. Chemists hope that understanding FeMoco could accelerate efforts to improve upon the artificial catalyst currently used in industrial fertilizer production—a process that accounts for several percent (atleast 2-4%) of the world’s energy consumption. Unfortunately, classical methods such as DFT struggle to resolve the many closely-spaced energy levels of the complex FeMoco molecule[2].
With several applications in drug design, material science, water treatment - awaiting compuatational abilities- hopes ride on quantum computers’ potential to exactly simulate chemicals’ and materials’ quantum structures and behaviors. Coming back to the example of FeMoco molecule, it's been estimated that simulation of FeMoco would need 200 perfectly-operating qubits and several weeks time[3]. However, qubits don’t operate perfectly, so thousands of additional qubits would likely be needed to stabilize the quantum states of the 200 “logical” qubits. With exciting possibilities and avenues to achieve greater computational powers and accuracies, scientists around the worls are striving to reach that goal. What do we have left to work upon if we need a large number of qubits to simulate molecules? IBM quantum roadmap promises 1000 qubits by 2023 so do we wait till then? No!
Even in this NISQ era, we have several variational algorithms that solve electronic structure problem on Noisy Intermediate Scale Quantum devices. Vaiational Quantum Eigensolver or VQE is one of the most feasible techniques yet. VQE can be used to generate ground state energies, excited state energies[4] and several properties like charge density, dipole moment etc. of the molecules[5]. Studying reactions dynamics maybe a long shot for now, but we can start somewhere and accurately establishing molecular properties is a great advance.
Keeping all this in mind, in this project, we have attempted to demonstrate such calculations for small molecules - believe me they are not at all small in terms of resources they need- using classical methods of Full Configuration Interaction(FCI) and Hartree fock(HF) method, as well as using variational algorithms. We carried out classical simulations for H2, H2O, N2, LiH, NH3 using FCI and HF in minimal sto-3g basis and a bigger 6-31g basis.
FCI is the simplest formalism of post-Hatree-Fock methods, which is directly derived from the variational principleis. On the other hand, FCI is combinatorially expensive to execute with respect to the number of one-electron orbitals. In this project we try to bring the simplicity of FCI method into the quantum computational chemistry by directly converting the matrix elements into Pauli strings (qubit operator). If we focus only on the nonzero matrix elements, the cost is dramatically reduced, because the CI matrix is very sparse. In addition, there have been many methods proposed for reducing the size of matrix and extract only the low-lying eigenstates. We design the formalism of quantum computational chemistry so that we can take advantage of this flexibility in the classical side. This method is more robust to noise, because of the canonical mapping qubits.
Then we simulated ground state energies for H2 and LiH using VQE on noisy simulator and tried to find hardware efficient ansatz. We try few standard ansatz like UCC and try other better ansatz and compare the results.
Within 24 hours, we couldn't try out other simulations for calculation of molecular properties, which now form basis for future work.
We intend to run these experiments on real hardware or various other noisy models, we avoided doing that during the hackathon due to time constraints. We intend to create several modules that enable to calculate excited state energies and molecular properties efficiently in Qiskit. Other than that intend to explore newer algorithms like Variational Fast Forwarding(VFF) to calculate eigenvalues on IBM Q devices and benchmark the results for the same[6]. We also intend to explore other methods for efficiently simulating strongly correlated systems.