Trapped Ions Used in High-Fidelity Quantum Gate

A practical quantum computer is probably decades away, but it got a step closer with the recent demonstration of a high-fidelity, two-ion quantum bit phase gate by a team of researchers from the National Institute of Standards and Technology (NIST, Gaithersburg, Md.), University of Colorado (Boulder, Colo.), University of Oxford (Oxford, UK) and Institute of Physics (Belgrade, Serbia-Montenegro). As reported in the March 27 issue of Nature, the properties of the gate make it attractive for a multiplexed array of quantum bits — called "qubits" in quantum lingo — that could enable scaling to large numbers of qubits.

The advantages that quantum computing has over classical computing as it is performed today are mainly in the areas of memory storage and parallel computing. To do this, quantum computing takes advantage of the "superposition" phenomenon that tells us that something can actually exist in two different states at the same time. "In the quantum world, we're able to do something which is very non-classical. We can put the atoms in so-called superposition states where they're both zero and one simultaneously," said David Wineland of NIST's Time and Frequency Division (Boulder). "If you will accept the idea that we can put things into these superposition states, the idea in terms of memory for computer is that you get an enhancement in storage. Where the power potentially comes in is that there are 2ⁿ possible states for n bits and, in fact, we can store them in 2ⁿ states at once. A dramatic number is that, if we have 300 bits, which may store a line of text in a classical computer — in 300 quantum bits there are 2³⁰⁰ numbers we can store at once. If you take all the matter in the universe, you couldn't make a classical computer that could store that much information."

Not only can this much information be stored all at one time, but it's possible to perform mathematical functions on the data, using logic gates. "We operate on all 2ⁿ inputs at once so there's this potential for massive parallelism on a computer," Wineland said. There is a big caveat, however. "When we finally do a measurement on the system, we only get one of all possible 2ⁿ numbers." This means that quantum computers have to rely on algorithms that take advantage of the parallel computing power, yet, in the end deliver only one or a very small number of possible outcomes. To date, few of such algorithms have been developed; therefore, it remains unknown how many classes of problems will ultimately benefit from quantum computing.

Qubits are able to store superpositions of 0 and 1, denoted by α|0> + β|1>, where α and β give the weights of the superposition. In this notation, |x> signifies a quantum state and the plus sign (+) indicates a superposition. The states |0> and |1> may represent, for example, horizontal and vertical polarization of a single photon, or two particular energy levels within a single atom. The rules of quantum mechanics dictate that: (a) the evolution of α and β is described by the Schrödinger wave equation; and (b) when the above quantum bit is measured, it yields either |0> or |1> with probabilities related to α and β, respectively. In practice, internal states of an ion are derived from the lower and upper energy orientation of the ion's spin (labeled |Q> and |q>) with respect to a background uniform magnetic field. The ion's spin state can be altered by applying an oscillating magnetic field. Not only can the state be flipped from |Q> to |q>, but arbitrary superposition states |Q> R α|Q> + β|q> can be made by applying the oscillating field for particular times.

Phase space representation of the stretch-mode amplitude of two trapped ions. The displacement drive moves the motional state components associated with the |Qq> and |qQ> internal states around circular trajectories in phase space as indicated. Both components acquire the same phase because the enclosed area and sense of rotation are equal. (Source: Nature)

"The flag we're waving in this report is that this gate in the quantum world produces the highest-fidelity quantum entangled states compared to anything that's been demonstrated so far," Wineland said. The gate has 97% fidelity, but it needs to be 99.99% or better to be useful. "It's in the cards, but it's a big technical challenge to realize that."

For additional information on emerging technologies, go to www.semiconductor.net/emerging.