Ansatz significance in sample-based quantum diagonalization
By Olivia
EXTERNAL MENTOR: Dr. Jason Saroni, Virginia Tech
Introduction
The proposed research aims to answer a key quantum chemistry question in finding ground states of many-body systems. Sample-based quantum diagonalization (SQD) methods are an alternative approach to traditional Variational Quantum Eigensolvers (VQEs) for approximating ground states by projecting the Hamiltonian into a sampled subspace. As VQE is an iterative process, it can be computationally expensive as opposed to SQD. However, a requirement of SQD is that the circuit from which the subspace is created must be able to sample the ground-state wave function. We will explore the guidelines of such a circuit in hopes of making SQD a more efficient solution to finding the ground state of molecular systems.
Intellectual Merit
The intellectual merit of this experiment rests on choosing an appropriate ansatz such that sampling circuit electronic configurations creates a subspace that contains the Hamiltonian's ground state. This will allow us to diagonalize the Hamiltonian. There is already research on neural network-enhanced SQD approaches, sampling with time-evolution circuits, and on extending the use of SQD to find excited states rather than ground states of electronic systems, but this research will focus solely on SQD itself and sampling driven by variational ansatz.
Broader Impact
So far, scientists have shown that SQD succeeds in approximating ground states in active spaces of up to 36 orbitals and 77 qubits. By improving SQD, we can use this algorithm on more complex systems that take up more orbitals and qubits. SQD is critical to solvation modeling efforts, in which solutes and solvents are considered together in the same system. Ultimately, research on SQD can make leaps in efficiently solving for ground states of many-body systems, aiding in drug discovery and modern electronics development.