Abstract
Making a system state follow a prescribed trajectory despite fluctuations and errors commonly consists of monitoring an observable (temperature, blood-glucose level, etc.) and reacting on its controllers (heater power, insulin amount, etc.). In the quantum domain, there is a change of paradigm in feedback, since measurements modify the state of the system, most dramatically when the trajectory goes through superpositions of measurement eigenstates. Here, we demonstrate the stabilization of an arbitrary trajectory of a superconducting qubit by measurement-based feedback. The protocol benefits from the long coherence time () of the 3D transmon qubit, the high efficiency () of the phase-preserving Josephson amplifier, and fast electronics that ensure less than 500 ns total delay. At discrete time intervals, the state of the qubit is measured and corrected in case an error is detected. For Rabi oscillations, where the discrete measurements occur when the qubit is supposed to be in the measurement pointer states, we demonstrate an average fidelity of to the targeted trajectory. For Ramsey oscillations, which do not go through pointer states, the average fidelity reaches . Incidentally, we demonstrate a fast reset protocol that allows us to cool a 3D transmon qubit down to in the excited state.
- Received 14 February 2013
DOI:https://doi.org/10.1103/PhysRevX.3.021008
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Published by the American Physical Society
Popular Summary
One of the basic requirements of quantum machines is to make the state of a quantum system follow a desired trajectory in time. But, the state of a quantum system is easily perturbed and changed by noise in its environment. To stabilize it against noise, feedback control, the time-tested concept consisting of sensing (or measurement) and controlling, seems to be the natural way to go. The catch lies, however, in one of the fundamental “quirks” of quantum phenomena: A measurement of a quantum system by a sensor can change randomly the state of the system. This happens when the measurement catches the system at a “bad time”—when it is not in a so-called eigenstate of the measurement device. The timing of the sensing measurements is then very important. Indeed, in this article, we experimentally show for the first time that by measuring a single qubit at optimal times we can stabilize any trajectory that we want the qubit to follow.
The qubit we use is of a superconducting variety. It has a long intrinsic coherence time; in other words, it can remain stable against noise relatively long on its own. We have made the technical advance by exploiting this quality in combination both with a nearly noiseless amplifier as a sensor that provides high detection efficiency and with a digital electronic board that offers unprecedented rapidity for feedback control. With physical insights into the backaction of the system to measurements made along a planned trajectory, we can identify the optimal times for making measurements so that the backaction is minimized and then measure the qubit at such times and correct the error if there is one. With this protocol, we have succeeded in maintaining two prototypical quantum trajectories, the so-called Rabi and Ramsey oscillations, with an average fidelity of and , respectively. Such fidelities are 2–3 times better than what has been achieved for single-state stabilization.
The quantum feedback control protocol demonstrated in our work is a timely development in quantum control. It could be extended to more complex quantum systems, and eventually to complete quantum machines performing computations or communications.
