Quantifying magic for multi-qubit operations

Understand

The development of a framework for quantifying "non-stabiliserness" of quantum operations is motivated by the magic state model of fault-tolerant quantum computation, and by the need to estimate classical simulation cost for noisy intermediate-scale quantum (NISQ) devices.

• The robustness of magic was recently proposed as a well-behaved magic monotone for multi-qubit states and quantifies the simulation overhead of circuits composed of Clifford+T gates, or circuits using other gates from the Clifford hierarchy.
• Here we present a general theory of the "non-stabiliserness" of quantum operations rather than states, which are useful for classical simulation of more general circuits.
• We introduce two magic monotones, called channel robustness and magic capacity, which are well-defined for general n-qubit channels and treat all stabiliser-preserving CPTP maps as free operations.