Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout an entire system. This concept accompanies the dynamics of thermalization in closed quantum systems, and has recently emerged as a powerful tool for characterizing chaos in black holes1,2,3,4. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, because scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process5,6. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous test for whether scrambling has occurred, while simultaneously measuring an OTOC. We engineer quantum scrambling processes through a tunable three-qubit unitary operation as part of a seven-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically about 80 per cent, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.
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We gratefully acknowledge discussions with R. Bousso, D. Harlow, F. Machado, I. Siddiqi, L. Susskind and Q. Zhuang. Additionally, we thank E. Edwards for the development of Fig. 1. This work is supported in part by the ARO through the IARPA LogiQ programme, the AFOSR MURI on Quantum Measurement and Verification, the ARO MURI on Modular Quantum Circuits, the DOE ASCR Program, and the NSF Physics Frontier Center at JQI. T.S. and N.Y.Y. acknowledge support from the Office of Science, Office of High Energy Physics of the US Department of Energy under contract number DE-AC02-05CH11231 through the COMPHEP pilot “Probing information scrambling via quantum teleportation” and the Office of Advanced Scientific Computing Research, Quantum Algorithm Teams Program. Research at the Perimeter Institute is supported by the Government of Canada through Innovation, Science and Economic Development Canada and by the province of Ontario through the Ministry of Economic Development, Job Creation and Trade. T.S. acknowledges support from the National Science Foundation Graduate Research Fellowship Program under grant number DGE 1752814.
Nature thanks Daniel Harlow and the other anonymous reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
Extended Data Fig. 6 Circuit representation of the scrambling unitary from equation (7), used for the data in Fig. 4.
Extended Data Fig. 7 The scrambling unitary from equation (7) compiled into native gates.