Physicists show how to encode three quantum bits using just two.
Without algorithms that compress data to encode information into fewer bits, hard drives would clog up and Internet traffic would slow to a snail's pace. Now, a group of physicists in Canada has shown for the first time that it is possible to compress the kind of data that might be used in the computers of tomorrow — known as quantum bits, or qubits.
Quantum computers promise to perform certain tasks, such as cracking encryption keys or searching databases, exponentially faster than conventional computers can. Such pace is possible in part because while in a classical computer a bit of information can be either a 0 or a 1, a quantum computer can store the information as both values simultaneously, so that qubits can exist in a wide range of 'superpositions' of the two states.
The quantum technology is still in its infancy, and many processes that are common in classical computers have yet to be demonstrated in quantum computers, including data compression. Aephraim Steinberg, a quantum physicist at the University of Toronto, and his colleagues set out to perform what would seem like a simple task: to compress the information contained in a number of identical qubits.
Classically, they point out, such an operation would be trivial, because a series of any number of identical bits encodes essentially the same information as just one bit. For quantum objects, however, this is not the case. The probabilistic nature of quantum mechanics means that the same measurement made on distinct, but identically prepared, qubits will yield a range values. As such, accurately recording the quantum state of just one qubit involves taking measurements of multiple identical copies and averaging the results.
The importance of order
Steinberg and his co-workers have shown how to reduce the proliferation of qubits by exploiting the fact that most of the information encoded by such objects relates to their ordering, rather than to their quantum state.
For example, if three qubits can each be in a superposition of 0 and 1, measuring them would yield eight possible outcomes: 000, 001, 010, 011, 100, 101, 110 or 111. But for the averaged measurements there are just four options: 0, 1/3, 2/3 or 1. For instance, 001 yields (0+0+1)/3 = 1/3, as do 010 and 100 (the same digits, but in a different order); 110 yields (1+1+0)/3 = 2/3, just as 101 and 011 do.
Because the qubits are identical, the extra information in the ordering can be simply discarded, say the researchers. To make the point, Steinberg draws a classical-physics analogy. "Keeping all of the information," he says, "is like storing the complete works of Shakespeare just to find out the average rates at which letters are used in the English language." The results are due to appear in Physical Review Letters1.
The research builds on the work of a group of theoretical physicists led by Isaac Chuang of the Massachusetts Institute of Technology in Cambridge, which in 2006 showed mathematically that it is possible to build a circuit that can separate qubits' permutation and state information into separate registers2. Steinberg and colleagues have now experimentally demonstrated a practical three-qubit version of that idea, using a laser and other optical components.
Normally each qubit gets encoded in one photon, but the authors did better, using only two photons to encode three qubits. They encoded the first two qubits using the polarization and path information of one photon, and the third qubit using the polarization of a second photon.
Way to go
Compressing the data from three qubits into two may seem like small fry, but the team says that this ratio will rise exponentially as the number of qubits goes up, with the state information from 1,000 qubits represented by just 10, and that from 1 million qubits squeezed into 20.
However, Alexander Korotkov, a quantum physicist at the University of California, Riverside, who was not involved in the latest work, points out that the authors' compression scheme is unsuited to general-purpose quantum computers, which use qubits that are highly correlated or 'entangled'. For example, two qubits could each be in a superposition of 1 and 0, but when measured they might always be found in opposite states, 10 or 01.
In addition, Martin Plesch, a theoretical physicist at the Slovak Academy of Sciences in Bratislava, says that scaling the approach up to larger numbers of photons could be difficult.
Steinberg acknowledges the difficulties, suggesting that it could help to compress qubits using trapped ions or superconductors rather than photons. "The problems we face are exactly those of building a larger quantum computer," he says.
Rozema, L. A., Mahler, D. H., Hayat, A., Turner, P. S. & Steinberg, A. M. Phys. Rev. Lett. (in the press).
Bacon, D. et al. Phys. Rev. Lett. 97, 170502 (2006).
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Cartlidge, E. Quantum bits get their first compression. Nature (2014). https://doi.org/10.1038/nature.2014.15961