Measuring magic on a quantum processor

Abstract

Magic states are the resource that allows quantum computers to attain an advantage over classical computers. This resource consists in the deviation from a property called stabilizerness which in turn implies that stabilizer circuits can be efficiently simulated on a classical computer. Without magic, no quantum computer can do anything that a classical computer cannot do. Given the importance of magic for quantum computation, it would be useful to have a method for measuring the amount of magic in a quantum state. In this work, we propose and experimentally demonstrate a protocol for measuring magic based on randomized measurements. Our experiments are carried out on two IBM Quantum Falcon processors. This protocol can provide a characterization of the effectiveness of a quantum hardware in producing states that cannot be effectively simulated on a classical computer. We show how from these measurements one can construct realistic noise models affecting the hardware.

Resource theory of quantum scrambling

“…Such protocols allow one to measure the OTOC by circumventing measurement techniques such as time reversal ( 97 – 99 ). Other magic monotones ( 100 – 102 ) have also been theoretically related to OTOCs.…”

Non-stabilizerness and entanglement from cat-state injection

“…The complexity gap between the efficient classical simulation of Clifford unitary circuits, and that of generic unitaries suggests it may be instructive to study the controlled introduction of non-Clifford gates into structured circuits. To that end, a framework known as doped random circuits proved to be useful in gradually obtaining unitary designs via magic doping [45,46], and in capturing the role of magic in quantum chaos [44,[47][48][49][50][51] and many-body entanglement spectrum statistics [52,53].…”

Two entangled and scientifically impactful lives: Jiří Patera, Pavel Winternitz and the Montréal school of mathematical physics

“…This would launch four decades of pioneering research by the two of them of which I will only give a succinct overview. 1 From the late 80's, with several collaborators Jiří developed the profound theory of Lie gradings that he had initiated with Zassenhaus [17]. Joris Van der Jeugt who had collaborated with Bob Sharp held a NSERC Visiting Researcher position at the CRM in that period and got involved in those studies.…”

“…Like quantum interacting particles that become entangled and yield "magic" [1], through the vicissitudes of History, these brilliant individuals were set on a colliding course which they steered to have profound influences on various fronts. This is the story that I will try to tell as a tribute to their accomplishments.…”