Magic of Random Matrix Product States

Understand

Magic, or nonstabilizerness, characterizes how far away a state is from the stabilizer states, making it an important resource in quantum computing, under the formalism of the Gotteman-Knill theorem.

• In this paper, we study the magic of the $1$-dimensional Random Matrix Product States (RMPSs) using the $L_{1}$-norm measure.
• We firstly relate the $L_{1}$-norm to the $L_{4}$-norm.
• We then employ a unitary $4$-design to map the $L_{4}$-norm to a $24$-component statistical physics model.