Quantifying dynamical magic with completely stabilizer preserving operations as free

Abstract

In this paper, we extend the resource theory of magic to the channel case by considering completely stabilizer preserving operations (CSPOs) as free. We introduce and characterize the set of CSPO preserving and completely CSPO preserving superchannels. We quantify the magic of quantum channels by extending the generalized robustness and the min relative entropy of magic from the state to the channel domain and show that they bound the single-shot dynamical magic cost and distillation. We also provide analytical conditions for qubit interconversion under CSPOs and show that it is a linear programming feasibility problem and hence can be efficiently solved. Lastly, we give a classical simulation algorithm whose runtime is related to the generalized robustness of magic for channels. Our algorithm depends on some pre-defined precision, and if there is no bound on the desired precision then it achieves a constant runtime.

Scalable measures of magic resource for quantum computers

“…Magic are measures of distance to the set of stabiliz- ers states or unitaries [5,8,[17][18][19][20][21][22][23]. Most schemes to run fault-tolerant quantum computers rely on stabilizers [13],…”

“…To characterize magic, various measures have been proposed [5,8,[17][18][19][20][21][22][23]. However, most measures require solving an optimization program and access to the amplitudes of the quantum state.…”

Nonstabilizerness determining the hardness of direct fidelity estimation

“…In this letter, we show that the sample complexity of a direct fidelity estimation protocol, conducted via Monte Carlo sampling, is exactly quantified by the amount of magic in the state. Magic is an expensive, but fundamental fuel for quantum computation [69][70][71][72][73][74][75][76][77][78]: without magic, a quantum computer can do nothing more than a classical computer. While simulations of stabilizer states (free resources) and Clifford circuits (free operations) are efficient on classical computers, the injection of t non-Clifford gates makes the simulation exponentially harder in t, in fact unlocking quantum advantage.…”