Decoherence-free subspaces in three experiments

Short answer: A decoherence-free subspace (DFS) is a way of encoding quantum information so that a particular kind of noise acts the same on every part of the encoding and cancels out. Experiments from 2001, 2003 and 2011 used it in trapped ions, an optical algorithm and a neutron interferometer. Reported gains include up to an order of magnitude in storage time and a drop in algorithm error rate from 35 to 7 percent.

What is a decoherence-free subspace?

The 2011 Physical Review Letters abstract calls a DFS an important class of quantum error-correcting codes proposed for fault-tolerant quantum computation. The idea is that information is encoded across several physical systems so that noise affecting all of them in the same way leaves the encoded state unchanged. The 2003 abstract frames it as a technique for managing decoherence in a practical quantum computer.

What did the trapped-ion experiment show?

The 2001 Science paper demonstrates a decoherence-free quantum memory of one qubit. The qubit is encoded into the DFS of a pair of trapped beryllium-9 ions, which protects it from environment-induced dephasing that limits the storage time of a qubit in a single ion. The authors measured storage time under ambient conditions and under an engineered noisy environment, and observed that encoding into the DFS increases storage time by up to an order of magnitude. The encoding reversibly transfers an arbitrary qubit stored in a single ion to the DFS of two ions.

What did the algorithm experiment show?

The 2003 Physical Review Letters paper reports the first use of DFSs to improve the performance of a quantum algorithm. An optical implementation of the Deutsch-Jozsa algorithm can be made insensitive to a particular class of phase noise by encoding information in the appropriate subspaces. The authors observe a reduction in error rate from 35 percent to 7 percent, which they describe as essentially the value without noise.

What about measurement devices?

The 2011 paper argues that error-correcting codes can improve the design of quantum devices beyond computing. Using neutron interferometry as a test bed, the authors built a five-blade neutron interferometer that includes both a standard Mach-Zehnder configuration and one based on a DFS. Experiments verify that the DFS interferometer is protected against low-frequency mechanical vibrations. They anticipate that the improvement will increase the range of applications for matter-wave interferometry, which is their expectation.

How to read this

A DFS protects against a specific noise class, such as collective dephasing, and not against all errors, which the abstracts imply by naming particular noise types. The three experiments are in different physical systems, so the gains are not comparable. This post is based on abstracts and visible summary text and full texts were not checked. It makes no claim about products.

FAQ

What noise does a DFS protect against?

Noise that affects all encoded parts equally, such as the phase noise in the 2003 experiment or dephasing in the 2001 ion experiment.

How much did it help the ion memory?

It increased storage time by up to an order of magnitude, per the 2001 abstract.

What happened to the algorithm error rate?

It fell from 35 percent to 7 percent in the 2003 optical Deutsch-Jozsa experiment.

Can DFS ideas help sensors?

The 2011 neutron interferometer protected against low-frequency mechanical vibrations.