🔍 Research Project under Prof. Mathew Otten @ UW-Madison
This research focuses on finding quantum resource estimates to determine the ground state energy of the FeMoco molecule using quantum algorithms. I used the Li[2] FeMoco Hamiltonian, which consists of 76 orbitals and 113 electrons. I leveraged both Q# and Qualtran to build and test algorithms, utilizing the Q# estimator framework to find and compare resource estimates—such as Logical Qubits, Logical T Gates, Total Logical Gates, and Runtime—across three approaches: First-Order Trotterized QPE, Double-Factorized (DF) Qubitized QPE, and Tensor-Hypercontraction (THC) Qubitized QPE. The performance ranking emerged as THC > DF > Trotter.
I began by implementing a first-order Trotterized Quantum Phase Estimation (QPE) algorithm using Q#, Microsoft's quantum programming language. This approach was tested on several small molecules to estimate their ground state energies, and I used Q#’s built-in resource estimator to determine key metrics like the number of logical qubits, logical T-gates, total logical gates, and runtime.
Below are the ground state energy estimation results for He2 and Helium Hydrate molecule using first order trotterization algorithm
| Helium Dimer (He₂) | Helium Hydrate (HeH) |
|---|---|
However, when I attempted to estimate resources for the FeMoco Hamiltonian with nearly 8 million pauli terms—the method ran into significant issues. Q# requires that the Hamiltonian be passed as a single large string from Python, and encoding/decoding such a massive string proved to be both computationally expensive and inefficient. Splitting the Hamiltonian into smaller chunks was also attempted, but this approach resulted in slow and inaccurate estimates
To address the challenges faced with Q#, I moved to using Qualtran, a Python-based resource estimation framework developed by Google. I reimplemented the first-order Trotterized QPE algorithm in Qualtran, estimating the FeMoco resources by considering just the first 100k Hamiltonian terms to keep the problem tractable.
Next, By using existing double-factorized walk operator within the Qualtran framework built a quibitzed qpe version and estimated the resource of femoco molecule.
Finally, Qualtran have pre computed resource estimates for Li femoco hamiltonian. To compare with previous methods i applied a Tensor-Hypercontraction (THC) method in combination with qubitized QPE.
❗️ yet to post results
| Algorithm | Logical Qubits | Logical T-Gates | Total Logical Gates | Runtime |
|---|---|---|---|---|
| Trotterized QPE(100k terms) | 86 | 15.5 Trillion | 16.4 Trillion | 4 years |
| DF Qubitized QPE | 2.05 k | 2.1 Trillion | 2.2 Trillion | 67 days |
| THC Qubitized QPE | -- | -- | -- | -- |
✴️ Looking ahead, I'm interested in exploring Quantum Signal Processing (QSP) algorithms. Although QSP holds theoretical promise for even greater efficiency, its implementation poses significant challenges. Additionally, refining these methods for handling even larger Hamiltonians remains an important goal.
Currently, Qualtran’s THC Qubitized QPE implementation is not functioning. We have raised an issue with the maintainers and are awaiting their fix; alternatively, we may develop our own version. Once that is resolved, we will proceed to test multiple FCIDump files using the Trotterized QPE, DF Qubitized QPE, and THC Qubitized QPE algorithms.
- QREChem: Quantum Resource Estimation Software for Chemistry Applications
- Z. Li, J. Li, N. S. Dattani, C. J. Umrigar, and G. K.-L. Chan, The Journal of Chemical Physics, 150, 024302 (2019).
- Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction
- Qualtran: A Python-Based Resource Estimation Framework
- Q# (Microsoft Quantum Development Kit)