Single-ancilla ground state preparation via Lindbladians

• URL: http://arxiv.org/abs/2308.15676v4
• Date: Fri, 2 Aug 2024 22:55:27 GMT
• Title: Single-ancilla ground state preparation via Lindbladians
• Authors: Zhiyan Ding, Chi-Fang Chen, Lin Lin,
• Abstract summary: We design a quantum algorithm for ground state preparation in the early fault tolerant regime. As a Monte Carlo-style quantum algorithm, our method features a Lindbladian where the target state is stationary. Our algorithm can be implemented using just one ancilla qubit and efficiently simulated on a quantum computer.
• Score: 4.328210085579236
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We design a quantum algorithm for ground state preparation in the early fault tolerant regime. As a Monte Carlo-style quantum algorithm, our method features a Lindbladian where the target state is stationary. The construction of this Lindbladian is algorithmic and should not be seen as a specific approximation to some weakly coupled system-bath dynamics in nature. Our algorithm can be implemented using just one ancilla qubit and efficiently simulated on a quantum computer. It can prepare the ground state even when the initial state has zero overlap with the ground state, bypassing the most significant limitation of methods like quantum phase estimation. As a variant, we also propose a discrete-time algorithm, demonstrating even better efficiency and providing a near-optimal simulation cost depending on the desired evolution time and precision. Numerical simulation using Ising and Hubbard models demonstrates the efficacy and applicability of our method.

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