# Expanding Hardware-Efficiently Manipulable Hilbert Space via Hamiltonian Embedding

arXiv: https://arxiv.org/abs/2401.08550 · HTML: https://mlsanity.com/paper/2401.08550/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2024.

## Built on by (most cited first, 2 of 2)

- [Scalable Community Detection Using Quantum Hamiltonian Descent and QUBO Formulation](https://mlsanity.com/paper/2411.14696/) (2024)
- [Quantum Optimization via Gradient-Based Hamiltonian Descent](https://mlsanity.com/paper/2505.14670/) (2025)

## Abstract (arXiv)

Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although several theoretically appealing quantum algorithms have been proposed for this task, they typically require a black-box query model of the sparse Hamiltonian, rendering them impractical for near-term implementation on quantum devices. In this paper, we propose a technique named Hamiltonian embedding. This technique simulates a desired sparse Hamiltonian by embedding it into the evolution of a larger and more structured quantum system, allowing for more efficient simulation through hardware-efficient operations. We conduct a systematic study of this new technique and demonstrate significant savings in computational resources for implementing prominent quantum applications. As a result, we can now experimentally realize quantum walks on complicated graphs (e.g., binary trees, glued-tree graphs), quantum spatial search, and the simulation of real-space Schr"odinger equations on current trapped-ion and neutral-atom platforms. Given the fundamental role of Hamiltonian evolution in the design of quantum algorithms, our technique markedly expands the horizon of implementable quantum advantages in the NISQ era.