Variational Quantum Eigensolver
A quantum-classical hybrid algorithm for eigenvalue optimization
Project Overview
At MIT Beaverworks, I implemented the variational quantum eigensolver (VQE), a quantum algorithm that iteratively seeks the ground state configuration of molecules, with applications in material science and medicine. I implemented the qubit-efficient VQE as described in the 2019 Beijing Institute of Physics paper, computing the ground state by iteratively manipulating quantum parameters encoded in our quantum "ansatz" circuit.
Each molecule is represented by a set of Pauli gates, taking in the Jordan-Wigner encoding of a molecule, and is converted to its Hamiltonian matrix representation, which then undergoes gradient descent to optimize the eigenvalue of the Hamiltonian. The outcome is an eigenvalue that represents the final ground state energy of the system (in Hartrees).
Our demonstration was on di-hydrogen (H2), yielding an error within billionths of a Hartree within 200 iterations. My implementation used 4 qubits rather than the standard 16-qubit implementations, achieved by qubit recycling, and demonstrating quantum advantage over the classical counterpart to VQE utilizing quantum phase estimation (QPE).
MIT Beaverworks VQE Implementation Demo
Algorithm Overview
The VQE algorithm combines quantum and classical computation to find ground state energies of molecular systems. The quantum computer prepares trial wavefunctions using a parametrized quantum circuit (ansatz), while a classical optimizer adjusts the parameters to minimize the energy expectation value.
Research Paper Reference
Qubit-efficient VQE ImplementationKey Achievements
Successfully reduced qubit requirements from 16 to 4 qubits through innovative qubit recycling techniques. Achieved convergence within 200 iterations with sub-Hartree precision for H2 molecule ground state energy calculation. Demonstrated clear quantum advantage over classical quantum phase estimation methods.
Skills & Technologies
Project Info
June 2023 - July 2023
Completed