Table 2 Interactions between jth qubit and \((j+1)\)th qubit produced by different choice of the phases \(\tilde{\varphi }^{(j)}_{1}\) and \(\tilde{\varphi }^{(j)}_{1}\), where we take odd j and even j both into account
From: Superconducting circuit architecture for digital-analog quantum computing
Operator | \(\tilde{\varphi }^{(j)}_{1}\) | \(\tilde{\varphi }^{(j)}_{2}\) |
|---|---|---|
\(\sigma ^{y}_{j} \sigma ^{y}_{j+1}\) | 2π | 2π |
\(-\sigma ^{y}_{j} \sigma ^{y}_{j+1}\) | π | π |
\(\sigma ^{x}_{j} \sigma ^{x}_{j+1}\) | 2π | π |
\(-\sigma ^{x}_{j} \sigma ^{x}_{j+1}\) | π | 2π |
\(\sigma ^{y}_{j} \sigma ^{x}_{j+1}\) | \((1+(-1)^{j}/2)\pi \) | 3/2π |
\(-\sigma ^{y}_{j} \sigma ^{x}_{j+1}\) | \((1+(-1)^{j+1}/2)\pi \) | 1/2π |
\(\sigma ^{x}_{j} \sigma ^{y}_{j+1}\) | \((1+(-1)^{j+1}/2)\pi \) | 3/2π |
\(-\sigma ^{x}_{j} \sigma ^{y}_{j+1}\) | \((1+(-1)^{j}/2)\pi \) | 1/2π |