Mapping the optimal route between two quantum states

Abstract

A central feature of quantum mechanics is that a measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system in the presence of these fluctuations is of increasing importance in quantum information processing and finds application in fields ranging from nuclear magnetic resonance to chemical synthesis. A detailed understanding of this stochastic evolution is essential for the development of optimized control methods. Here we reconstruct the individual quantum trajectories of a superconducting circuit that evolves in competition between continuous weak measurement and driven unitary evolution. By tracking individual trajectories that evolve between an arbitrary choice of initial and final states we can deduce the most probable path through quantum state space. These pre- and post-selected quantum trajectories also reveal the optimal detector signal in the form of a smooth time-continuous function that connects the desired boundary conditions. Our investigation reveals the rich interplay between measurement dynamics, typically associated with wave function collapse, and unitary evolution of the quantum state as described by the Schrodinger equation. These results and the underlying theory, based on a principle of least action, reveal the optimal route from initial to final states, and may enable new quantum control methods for state steering and information processing.

12 pages, 9 figures

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Cited by in corpus (9)

• Weak Values are Interference Phenomena
• Prediction and retrodiction for a continuously monitored superconducting qubit
• Efficient Quantum Filtering for Quantum Feedback Control
• Heisenberg scaling with weak measurement: A quantum state discrimination point of view
• Robust quantum state transfer using tunable couplers
• Computing the Rates of Measurement-Induced Quantum Jumps
• Single Shot Quantum State Estimation via a Continuous Measurement in the Strong Backaction Regime
• Landau-Zener evolution under weak measurement: Manifestation of the Zeno effect under diabatic and adiabatic measurement protocols
• Violating the Modified Helstrom Bound with Nonprojective Measurements