Continuous feedback control — monitoring a system and adjusting its dynamics — is widely used to keep systems 'on track'. This approach has now been used to maintain the cycling of a quantum bit almost indefinitely. See Letter p.77
Imagine you have to test-drive a car on a smallish circular racetrack, making exactly one circuit every minute. There is a big clock on a tower by the start/finish line. What strategy do you adopt? An obvious one is to keep comparing your position around the track with the position of the second hand around the clock. If your circular position lags that of the second hand, then step on the accelerator; if it leads, then ease off (Fig. 1). This illustrates three typical features of a process known as continuous feedback control: monitoring, comparison with a goal and dynamical adjustment1. On page 77 of this issue, Vijay et al.2 apply this type of control to the most basic quantum system: a two-state system called a quantum bit (qubit). By monitoring the excitation of their qubit with quite high efficiency, inferring its lag or lead relative to a radio-frequency field (their clock), and modulating the power applied to their qubit, they maintain a regular cycling between the qubit's excited and ground states almost indefinitely.
In an ideal world, when the power supplied by a car's engine equals the power dissipated (for example, by air resistance and friction), the car's speed will remain steady. But in the real world, unpredictable fluctuations in the car and its environment (such as variations in wind speed, air pressure, tyre pressure, oil temperature, road surface and other variables) will cause the speed to vary even with constant power. With no feedback control, the position of the car around the track would, within an hour, become completely unrelated to the position of the second hand on the reference clock. In most modern cars, cruise control can do a good job of keeping the speed within a narrow range around a set value. But for the task in hand, a more sophisticated cruise-control mechanism would be needed, which compares the position of the car with the position of the second hand, as described above.
In their experiment, Vijay et al.2 use a transmon3, a tiny superconducting device that can be restricted (at ultra-low temperatures) to just two quantum states: its ground state and its first excited state. These two states define the qubit. The qubit dynamics in this experiment is in many ways analogous to that of the car on the circular track. If the start/finish line is like the ground state of the qubit, the point diametrically opposite is the excited state. The other points around the track are analogous to superpositions of the excited and ground states — they are still definite ('pure') states of the qubit, but, unlike the ground and excited states, they do not have a definite energy value.
By applying a microwave driving field, the qubit can be made to cycle around the 'superposition track' at a particular frequency, clockwise from ground state to excited state and back again. But like a car, the qubit also suffers from power dissipation. In the quantum world, this necessarily gives rise to fluctuations, even at zero temperature1. As a consequence, after several microseconds the state of the qubit on its cycle will be completely unpredictable.
It is not obvious a priori that using continuous measurement and feedback control to lock the qubit cycling to that of an external clock will work, because in the quantum regime monitoring induces fluctuations too1. However, as the original theoretical proposal for this quantum feedback protocol showed4, the process should work well for strong and efficient monitoring.
To monitor their transmon qubit, Vijay et al. coupled the qubit to a microwave probe field in a superconducting resonator that has a higher frequency than the driving field. The probe field continuously leaks out of the resonator, and is amplified into a macroscopic current. The authors used a simple feedback-control algorithm to modulate the driving field in proportion to the deviation of the observed current from an ideal sinusoidal current generated by the radio-frequency field acting as the external clock.
So how well does it work? Although the monitoring was strong (compared with the dissipation), its efficiency was less than 50%. As a result, the feedback control could not do better than to keep the qubit state more or less in the correct half (as defined by the external clock) of the superposition track at any given time. Moreover, for about 10% of the time the transmon was found in a higher excited state than its first excited state, outside the qubit's two states altogether. But compared with the no-feedback result of complete unpredictability within several microseconds, the observed stabilization of the qubit's cycling is a big step forward in the feedback control of an individual qubit.
This work paves the way to many more experiments on qubit feedback measurement and control, which would be enabled by more efficient monitoring than that achieved here. These experiments include rapid purification of a qubit5, tests of quantum-jump theory6, feedback control based on measurement back-action7 and feedback control based on the quantum Zeno effect8. In the longer term, continuous feedback control of multi-qubit systems is one path to correcting quantum errors in a quantum computer. With Vijay and colleagues' experiment, solid-state physics joins quantum optics at the forefront of quantum feedback-control investigations.
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Applied Physics Letters (2013)