Ground State Preparation via Dynamical Cooling

TL;DR

This paper introduces a novel quantum algorithm for preparing ground states by transforming the Hamiltonian with quantum signal processing and simulating dynamics, avoiding the need for prior energy gap knowledge.

Contribution

It presents a new dynamical cooling method that uses Hamiltonian transformation and quantum signal processing for efficient ground-state preparation without extra qubits or gap knowledge.

Findings

Requires $ ilde{O}(d^{3/2}/)$ queries to the evolution operator

Does not rely on prior knowledge of energy gaps

Provides a framework combining quantum signal processing with Hamiltonian simulation

Abstract

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which can be challenging for large, strongly-correlated systems. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping eigenvalues into positive and negative subspaces separated by a large gap. This automatically ensures that all states within each subspace conserve energy with respect to the transformed Hamiltonian. Subsequent time-evolution with a perturbed Hamiltonian induces transitions to lower-energy states while preventing unwanted jumps to higher energy states. The approach does not rely on a priori knowledge of energy gaps and requires no additional qubits to model a bath. Furthermore, it makes $\tilde{\mathcal{O}}(d^{\,3/2}/\epsilon)$ queries to the time-evolution operator of the system and $\tilde{\mathcal{O}}(d^{\,3/2})$ queries to a block-encoding of the perturbation, for $d$ cooling steps and an $\epsilon$-accurate energy resolution. Our results provide a framework for combining quantum signal processing and Hamiltonian simulation to design heuristic quantum algorithms for ground-state preparation.