Dynamics Under Superposition of Unitary Operators: Robustness against Decoherence and Stronger Temporal Correlations

Abstract

Quantum theory contravenes classical macrorealism by allowing a system to be in a superposition of two or more physically distinct states, producing physical consequences radically different from that of classical physics. Motivated by this, we construct superpositions between time evolution unitaries and study the dynamics of a qubit under such superposed unitary operators. We find that the superposition of unitaries significantly affects the trajectory of the qubit in the Bloch sphere by shifting the path of evolution and making the speed of evolution non-linear in time. The qubit spends more time near the poles of the Bloch sphere and passes through the equator rather quickly. This  remarkably enhances the endurance against dephasing noise, making the superposed unitaries suitable for robust quantum control tasks. Moreover, we observe an extreme violation of Leggett-Garg inequalities beyond the temporal Tsirelson's bound, which increases with increasing superposition between the unitaries. This shows stronger temporal correlations achieved by the superposed unitares. Using an NMR quantum register, we experimentally demonstrate the superposition of unitaries with the help of an ancillary qubit and verify our theoretical predictions.