Abstract: Methods and systems are disclosed for restoring a state of a qubit transformed by a weak measurement to its original state. Unlike traditional methods, in which, the restoration was carried out by way of another weak measurement, the disclosed method uses an additional qubit, referred to as the ancillary qubit, and appropriate Hadamard and CNOT transformation for restoring the original state. Because the disclosed method avoids a second weak measurement, the time for restoration of the original state is considerably reduced.

Abstract: A laser pulse from an ultrashort pulse laser (USPL) is fired into the atmosphere. The USPL pulse is configured to generate a plasma filament at a predefined target in the atmosphere, in which free, or “seed,” electrons are generated by multi-photon or tunneling ionization of the air molecules in the filament. A second pulse is fired into the atmosphere to form a heater beam that impinges on the plasma filament and thermalizes the seed electrons within the plasma filament, leading to the collisional excitation of the electrons in the filament. The excited electrons collisionally excite various electronic and vibrational states of the air molecules in the filament, causing population inversions and lasing, e.g., exciting the C3?u?B3?g(v=0?0) transition of the N2 in the atmosphere to cause lasing at 337 nm.

Abstract: Methods and systems are disclosed for restoring a state of a qubit transformed by a weak measurement to its original state. Unlike traditional methods, in which, the restoration was carried out by way of another weak measurement, the disclosed method uses an additional qubit, referred to as the ancillary qubit, and appropriate Hadamard and CNOT transformation for restoring the original state. Because the disclosed method avoids a second weak measurement, the time for restoration of the original state is considerably reduced.