论文标题
与对称平均的关键ISING模型的变分量子模拟
Variational quantum simulation of critical Ising model with symmetry averaging
论文作者
论文摘要
在这里，我们研究了深层多尺度纠缠重新规范化（DMERA）电路作为无间隙系统基态的变异ansatz。我们将可辨别的一维临界横向视野模型用作测试床。在这种情况下，可以通过利用有效的经典算法来模拟匹配电路电路来对ANSATZ进行数值精确的模拟。我们发现，对于此系统，DMERA强烈胜过标准的QAOA风格的ANSATZ，并且使用DMERA近似的相关函数中系统误差的主要来源是破坏了转换和KRAMERS-WANNIER对称性模型的横向和KRAMERS-WANNIER对称性。通过对称平均，我们最多可以减少四个数量级，而不会产生Qubits或电路深度的额外成本。我们建议将这种缓解系统误差的技术应用于具有其他对称性的物理系统的NISQ模拟。
Here, we investigate the use of deep multi-scale entanglement renormalization (DMERA) circuits as a variational ansatz for ground states of gapless systems. We use the exactly-solvable one-dimensional critical transverse-field Ising model as a testbed. Numerically exact simulation of the ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, DMERA strongly outperforms a standard QAOA-style ansatz, and that a major source of systematic error in correlation functions approximated using DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. We propose that this technique for mitigating systematic error could be applied to NISQ simulations of physical systems with other symmetries.
