An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum information. Despite advances in numerical methods to simulate the spectral properties of multi-element superconducting circuits (Yurke B and Denker J S 1984 Phys. Rev. A 29 1419, Reiter F and Sorensen A S 2012 Phys. Rev. A 85 032111 and Amin M H et al 2012 Phys. Rev. A 86 052314), the literature lacks a consistent and effective method of determining the effective qubit Hamiltonian. Here we address this problem by introducing a novel local basis reduction method. This method does not require any ad hoc assumption on the structure of the Hamiltonian such as its linear response to applied fields. We numerically benchmark the local basis reduction method against other Hamiltonian reduction methods in the literature and report specific examples of superconducting qubits, including the capacitively-shunted flux qubit, where the standard reduction approaches fail. By combining the local basis reduction method with the Schrieffer–Wolff transformation we further extend its applicability to systems of interacting qubits and use it to extract both non-stoquastic two-qubit Hamiltonians and three-local interaction terms in three-qubit Hamiltonians.

中文翻译：

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相互作用超导量子位的有效哈密顿量：局部基约简和施里弗-沃尔夫变换

设计超导量子电路的一个悬而未决的问题是如何最好地将描述其动力学的全电路哈密顿量减少为适用于操纵量子信息的有效两级量子比特哈密顿量。尽管模拟多元素超导电路光谱特性的数值方法取得了进步（Yurke B 和 Denker JS 1984 Phys. Rev. A 29 1419、Reiter F 和 Sorensen AS 2012 Phys. Rev. A 85 032111 和 Amin MH et al 2012） Phys. Rev. A 86 052314），文献缺乏确定有效量子位哈密顿量的一致且有效的方法。在这里，我们通过引入一种新的局部基约简方法来解决这个问题。这种方法不需要对哈密顿量的结构进行任何特别假设，例如它对应用场的线性响应。我们将局部基约简方法与文献中的其他哈密顿约简方法进行了数值对比，并报告了超导量子位的具体示例，包括电容分流通量量子位，其中标准减少方法失败。通过将局部基约简方法与 Schrieffer-Wolff 变换相结合，我们进一步将其适用于相互作用的量子比特系统，并使用它来提取非稳态双量子比特哈密顿量和三量子比特哈密顿量中的三局部相互作用项。