Resonant longitudinalZitterbewegungin zigzag graphene nanoribbons

Abstract

The Zitterbewegung of a wave packet in a zigzag graphene nanoribbon is theoretically investigated. The coupling between edge states and bulk states results in intriguing properties. Apart from the oscillation in position perpendicular to the direction of motion, we also observe an oscillation along the direction of propagation which is not present in semiconductor nanowires or infinite graphene sheets. We also observe a resonance of its amplitude with respect to the central momentum of the wave packet. We show here that this longitudinal Zitterbewegung is caused by the interplay between bulk and edge states, which is a unique property of a zigzag nanoribbon.

Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements

“…This is essential for accurate decoding of stabilizer measurements made during QEC. Furthermore, this idea can be combined with proposals for leakage reduction [12][13][14][15] to target such efforts, reducing unnecessary overhead. As leakage does not spread in superconducting qubits (to lowest order), and gives only local error signals [14], such a scheme would require a single HMM per (data and ancilla) qubit.…”

“…Furthermore, this idea can be combined with proposals for leakage reduction [12][13][14][15] to target such efforts, reducing unnecessary overhead. As leakage does not spread in superconducting qubits (to lowest order), and gives only local error signals [14], such a scheme would require a single HMM per (data and ancilla) qubit. Each individual HMM needs only to process the local error syndrome, and as demonstrated in this work, completely independent HMMs may be used for the detection of nearby data qubit and ancilla leakage.…”

“…This is due to the prevalent use of many-level systems as effective qubits, such as hyperfine levels in ions and weakly anharmonic transmons in superconducting circuits, making leakage from the twodimensional computational space of effective qubits a threatening error source. Although typically less frequent than qubit errors [2,4,11], if ignored, leakage can produce the dominant damage to encoded logical information [12][13][14][15]. Recent experiments have demonstrated single-and multi-round parity measurements to correct qubit errors in superconducting circuits with up to 9 physical qubits [16][17][18][19].…”

“…This HMM demonstration provides exciting prospects for leakage detection and correction. In larger systems, independent HMMs can be dedicated to each qubit because leakage produces local error signals [14]. An HMM for an ancilla only needs its measurement outcomes while a data-qubit HMM only needs the outcomes of the nearest-neighbour ancillas [details in [24]].…”

“…HMM outputs could be used as inputs to MWPM, allowing MWPM to dynamically adjust its weights. The outputs could also be used to trigger leakage reduction units [12][13][14][15] or qubit resets [29].…”