Quantum error correction with an ion trap quantum processor

Published in Nature a few days ago: Fault-tolerant control of an error-corrected qubit

This study by Christopher Monroe's team at the University of Maryland demonstrates error-corrected single qubit operations using an ion trap quantum processor. The publication is quite timely, given that the group's spin-off IonQ just became a publicly-traded company.

This is a milestone achievement. For a long time, quantum computing skeptics pointed to the lack of any demonstration of even a single logical qubit protected against native errors as evidence that large scale quantum computing is infeasible. Here, the authors demonstrate logical operations with error probability less than that of its constituent qubits. In theory, by increasing the number of physical qubits used per logical qubit one can exponentially suppress errors and build a fault-tolerant quantum computer.

In practice, it's not that simple and there are still significant hurdles to overcome. The present study has demonstrated fault-tolerant single qubit operations. Next steps will be to demonstrate error-corrected two-qubit gates and multiple rounds of error correction, requiring improvements to the native gate fidelities and the ability to perform mid-circuit measurements on ancilla qubits. And while ion trap quantum processors have very low gate errors (making this demonstration possible), their main drawback is that the gates are very slow (e.g. 0.2 ms for a native two-qubit gate). So even when large scale error-correction is achieved, you might be waiting a while for the calculation to run!

More on the physics: the error correction scheme used is based on products of 3-qubit entangled GHZ states. Since the GHZ states are decoupled from one another, a local error in one GHZ state can be detected (leading to a cubic suppression of the logical error-rate via post-selection) and/or corrected (giving a quadratic error suppression). The measured error rates (compared against a non-fault-tolerant circuit in which there is entanglement between the different GHZ steps) agree with this predicted scaling.