Self-consistent Quantum Iteratively Sparsified Hamiltonian method (SQuISH): A new algorithm for efficient Hamiltonian simulation and compression

TL;DR

SQuISH is a novel quantum algorithm that iteratively creates a resource-efficient, truncated Hamiltonian using both the Hamiltonian and an approximate ground state, significantly reducing quantum resource requirements.

Contribution

The paper introduces SQuISH, a new iterative method combining Hamiltonian and wavefunction information to efficiently simulate quantum systems with reduced resource needs.

Findings

Successfully applied to small molecules and larger systems

Reduces gate complexity for ground state calculations

Handles systems requiring over 200 qubits on quantum hardware

Abstract

It is crucial to reduce the resources required to run quantum algorithms and simulate physical systems on quantum computers due to coherence time limitations. With regards to Hamiltonian simulation, a significant effort has focused on building efficient algorithms using various factorizations and truncations, typically derived from the Hamiltonian alone. We introduce a new paradigm for improving Hamiltonian simulation and reducing the cost of ground state problems based on ideas recently developed for classical chemistry simulations. The key idea is that one can find efficient ways to reduce resources needed by quantum algorithms by making use of two key pieces of information: the Hamiltonian operator and an approximate ground state wavefunction. We refer to our algorithm as the $\textit{Self-consistent Quantum Iteratively Sparsified Hamiltonian}$ (SQuISH). By performing our scheme iteratively, one can drive SQuISH to create an accurate wavefunction using a truncated, resource-efficient Hamiltonian. Utilizing this truncated Hamiltonian provides an approach to reduce the gate complexity of ground state calculations on quantum hardware. As proof of principle, we implement SQuISH using configuration interaction for small molecules and coupled cluster for larger systems. Through our combination of approaches, we demonstrate how SQuISH performs on a range of systems, the largest of which would require more than 200 qubits to run on quantum hardware. Though our demonstrations are on a series of electronic structure problems, our approach is relatively generic and hence likely to benefit additional applications where the size of the problem Hamiltonian creates a computational bottleneck.