Day 789: Logical Operators on the Torus

Learning Objectives

• •**Identify** non-contractible loops on the torus
• •**Construct** logical Z operators $\bar{Z}_1$ and $\bar{Z}_2$ as loop operators
• •**Construct** logical X operators $\bar{X}_1$ and $\bar{X}_2$ on dual cycles
• •**Verify** commutation relations: $[\bar{X}_i, \bar{Z}_j] = 0$ for $i \neq j$
• •**Verify** anti-commutation: $\{\bar{X}_i, \bar{Z}_i\} = 0$ for same index
• •**Explain** why logical operators cannot be local (weight < L)

Today's Schedule (7 hours)