Quantum trajectories from weak measurements of superconducting qubits

Short answer: A weak measurement extracts only a little information at a time, so a qubit's state can be followed as it drifts towards a measurement outcome instead of jumping to it. Two superconducting-circuit experiments report tracking these quantum trajectories: a 2013 Nature paper that tracked individual trajectories with tomography, and a 2018 preprint that observed the whole trajectory distribution. These are laboratory experiments.

What is a quantum trajectory?

The 2018 arXiv abstract says textbooks describe quantum measurements as instantaneous projections, but weak measurements stretch them out in time, letting one observe the evolution of a state as it heads towards one of the eigenstates of the measured operator. The authors describe this as a continuous nonlinear stochastic process generating an ensemble of quantum trajectories, made of noisy fluctuations on top of geodesics that attract the state towards the eigenstates. The rate of evolution is specific to each system and apparatus, and the Born rule requires the noise and the attraction to be precisely related.

What did the 2013 experiment do?

The 2013 Nature abstract starts from decoherence: the time a system stays in superposition depends on how strongly it interacts with its environment, and if the environment's fluctuations are not measured it acts as a source of noise that turns a pure state into a statistical mixture. By accurately measuring the environment in real time, the authors say, the system can be kept in a pure state and its evolution described by a quantum trajectory set by the measurement outcome. They use weak measurements to monitor a microwave cavity containing a superconducting qubit and track individual trajectories. The environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. With a near-quantum-limited parametric amplifier, they selectively measure either the phase or the amplitude of the cavity field, and so confine trajectories to the equator or a meridian of the Bloch sphere. They perform quantum state tomography at discrete times along the trajectory to verify the outcome. The remainder of the abstract was cut off in the page text, so no further claim is made.

What did the 2018 preprint add?

The preprint, which may not have been peer reviewed, reports that the authors experimentally observe the entire quantum trajectory distribution for weak measurements of a superconducting qubit in a circuit quantum electrodynamics architecture. They quantify it, and say it agrees very well with the predictions of a single-parameter white-noise stochastic process. They describe this as a powerful clue for unravelling the dynamics of quantum measurement beyond conventional axiomatic quantum theory, which is their interpretation.

What about the third source?

An escholarship.org page was also listed. Its text was not read, so nothing in this post comes from it.

How to read this

The 2013 paper tracks individual trajectories and the 2018 preprint characterises their statistics, so they answer different questions. Both are about physics of measurement and do not claim an advantage in computing or sensing. This post is based on abstracts, and full texts were not checked. It makes no claim about products.

FAQ

What is a weak measurement?

A measurement that gains only partial information and disturbs the state only slightly, so evolution can be watched, as the 2018 abstract describes.

What is a Bloch sphere trajectory?

The path of the qubit state on the Bloch sphere. In 2013 trajectories were confined to the equator or a meridian.

Which model fit the 2018 data?

A single-parameter white-noise stochastic process, per the authors.

Is this used for error correction?

Neither abstract claims it.