Decoherence-free Subspaces and Quantum Computation

Quantum computation holds the promise of greatly enhanced speeds for solving certain problems, including factoring, simulation of quantum systems, and database mining. One main obstacle to quantum computation is the problem of decoherence—fragile quantum superpositions are destroyed by unwanted coupling to the environment. In particular, it is the entangling of the quantum system to unobserved degrees of freedom that leads to a loss of coherence.

Three basic theoretical strategies have emerged to cope with decoherence in quantum computation. The first, quantum error correcting codes, relies on trying to detect errors using ancillary quantum bits (qubits) and actively manipulating the interactions to correct these errors. The second strategy employs dynamical decoupling, in which rapid switching is used to average out the effects of a relatively slowly decohering environment. The final approach attempts to embed the logical qubits into a part of the overall Hilbert space (which describes all the states a system can possibly be in) that is inherently immune to noise, a "decoherence-free subspace" (DFS). Bardeen Professor of Physics Paul G. Kwiat and his colleagues recently demonstrated experimentally the existence of a DFS, using entangled photons as their qubits.

Correlated photons are produced via the process of spontaneous parametric down-conversion, in which a nonlinear optical crystal is used to split a parent ultraviolet photon into two correlated infrared daughter photons. In one implementation, these photons are emitted on opposite sides of the pump beam, along two cones, one of which has horizontal polarization, the other of which has vertical polarization. Photon pairs emitted along the intersections of the cones are entangled in polarization—each photon is individually unpolarized, and yet the photons necessarily have perpendicular polarizations, no matter how far apart they are. The figure shown above is a colorized infrared photograph of the downconversion output. The green rings correspond to photons with roughly equal energies (half that of the parent pump photon). Photons emitted along the bright spots are entangled.

Further information about quantum information, including quantum computing and quantum cryptography, is available from Professor Kwiat.

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