A Mere Five Orders of Magnitude

After the cool PRL describing high visibility for a superconducting qubit, today I find in Physical Review Letters the article “Long-Lived Qubit Memory Using Atomic Ions” by Langer et al (volume 95, page 060502). This paper describes work at NIST (Boulder) with trapped Beryllium ions. This is a cool paper where they achieve coherence lifetimes for their qubit in excess of 10 seconds using two techniques: one involving tuning of an external magnetic field to obtain a sweet spot in the energy levels of their qubit and the other using a decoherence-free subspace encoding of the quantum information (this latter actually leads to slightly less than 10 seconds of coherence)
One of the main sources causing decoherence for ionic qubits comes from ambient fluctuating magnetic fields. In many implementations of qubits in ions, the energy levels used for the qubit are sensitive to magnetic fields. Stray magnetic fields cause these energy levels to fluctuate and this causes phase decoherence of the qubit. The trick which this paper reports on is to tune an external magnetic field to a percise point (0.01194 Tesla, the Earth’s magnetic field on the surface of the earth, for comparison is around 50 microTesla) where the energy difference the two energy levels used for the qubit have no first order dependence on the magnetic field (but do have a higher, second order dependence on the magnetic field.) Similar tricks have been used in neutral atom systems, in particular in Rubidium. But there these manipulations where done by microwaves and with large numbers of atoms. Further there are other problems (perhaps not killer, but they are there) for using these qubits in quantum computers. One problem is that using microwaves may eventually not be a practical way to build a quantum computer because they are hard to focus and other suggested techniques, like apply a magnetic field gradient to distinguish between qubits, may have other destructive overheads . For these reasons, this technique with a Berrylium ion qubit are very cool. What is really nice is that the authors obtain an increase in five orders of magntiude for the lifetime of this qubit over their previous experiments with this qubit. Nothing like a good five orders of magntidue to make my day. (Oh, and for those of you who care about these things, they quote this as a memory error rate per detection rate as around 10^(-5), below some of the good old fault-tolerant thresholds for quantum computation.)
The other technique the authors use to obtain long lifetimes is to encode their qubit into a decoherence-free subspace (DFS). Here the idea is to encode into one qubit into two qubits such that these logical qubits are effected equally by uniform (over the physical qubits) magnetic fields. Using DFSs to protect quantum information in the ion traps had previously been reported. In fact it helped me get my Ph.D. When I was giving my qualifying examine and explaining what a a DFS was, one unnamed experimentalist asked (roughly) “This is all good and fine, in theory, but does it correspond to the real world?” Luckily my next slide was a slide on the DFS demonstrated in ion traps by Kielpenski et. al. Booyah! In this paper the authors encode information into the DFS and then cause oscillations between the two levels of the qubit by applying a magentic field gradient. Since the DFS states are |01> and |10> this basically means that the system is almost always in an entangled state. The lifetime for this entangled state oscillation is measured to be around seven seconds!
Update: Right after I posted this, I read quant-ph and found, quant-p/ 0508021 “Robust Entanglement” by H. Haeffner et al. which reports on ion trap experiments in Innsbruck. Here they demonstrate lifetimes for entangled quantum states that are twenty seconds long in their Calcium ions. How cool is that!
Update update: Some press here