论文标题
用于各种吉布斯状态准备的热多尺度纠缠重归其化ansatz
Thermal Multi-scale Entanglement Renormalization Ansatz for Variational Gibbs State Preparation
论文作者
论文摘要
许多仿真任务要求一个首先准备系统的吉布斯状态。我们提出了一个量子电路家族，用于在量子计算机上进行热吉布斯态的变异制备；我们称它们为热多尺度纠缠重新归一化ANSATZ（TMERA）。 TMERA电路将输入Qubits转换为局部到不同长度尺度的波袋模式，并将系统gibbs状态近似为这些模式的混合状态。 TMERA是基于深的多尺度纠缠重新归一化Ansatz（DMera）； TMERA通过准备每个输入量子位作为混合状态来修改地面DMERA电路。输入Qubits的激发概率用作用于针对特定温度Gibbs状态的变异参数。由于TMERA是用于热态的产品光谱ANSATZ的特殊情况，因此准备，分析和优化非常简单。我们在一个维度上基准在横向字段ISING模型上基准测试TMERA，并发现对于$ d = 6 $，它会在所有温度下为512个站点系统产生全局保真度$ \ Mathcal f> 0.4 $。
Many simulation tasks require that one first prepare a system's Gibbs state. We present a family of quantum circuits for variational preparation of thermal Gibbs states on a quantum computer; we call them the thermal multi-scale entanglement renormalization ansatz (TMERA). TMERA circuits transform input qubits to wavepacket modes localized to varying length scales and approximate a systems Gibbs state as a mixed state of these modes. The TMERA is a based on the deep multi-scale entanglement renormalization ansatz (DMERA); a TMERA modifies a ground-state DMERA circuit by preparing each input qubit as a mixed state. The excitation probabilities for input qubits serve as variational parameters used to target particular temperature Gibbs states. Since a TMERA is a special case of the product spectrum ansatz for thermal states, it is simple to prepare, analyze, and optimize. We benchmark the TMERA on the transverse field Ising model in one dimension and find that for $D=6$ it produces global fidelities $\mathcal F > 0.4$ for 512-site systems across all temperatures.
