Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power

Understand

We present a new framework for assessing the power of measurement-based quantum computation (MBQC) on short-range entangled symmetric resource states, in spatial dimension one.

• It requires fewer assumptions than previously known.
• The formalism can handle finitely extended systems (as opposed to the thermodynamic limit), and does not require translation-invariance.
• Further, we strengthen the connection between MBQC computational power and string order.