Expanding Hardware-Efficiently Manipulable Hilbert Space via Hamiltonian Embedding

• URL: http://arxiv.org/abs/2401.08550v1
• Date: Tue, 16 Jan 2024 18:19:29 GMT
• Title: Expanding Hardware-Efficiently Manipulable Hilbert Space via Hamiltonian Embedding
• Authors: Jiaqi Leng, Joseph Li, Yuxiang Peng, Xiaodi Wu
• Abstract summary: Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian. 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.
• Score: 9.219297088819634
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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