Quantum error correction of a qubit loss in an addressable atomic system

We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum nondemolition measurement and then transformed into a standard qubit error by inserting a new atom in the vacated lattice site. The logical qubit, encoded here into four physical qubits with the Grassl-Beth-Pellizzari code, is reconstructed via a sequence of one projective measurement, two single-qubit gates, and three controlled-NOT operations. No ancillary qubits are required. Both quantum nondemolition and projective measurements are implemented using a cavity quantum electrodynamics system which can also detect a general leakage error and thus allow qubit loss to be corrected within the same framework. The scheme can also be applied in quantum computation with trapped ions or with photons.

Figure 1

Qubit loss error correction circuit. In this example, the first qubit of the GBP code is lost to the environment. Quantum nondemolition measurements (QND) indicate the location of the error and trigger the conditional source (CS) to inject a new atom in state $\mid 0⟩$ into the optical lattice site. A projective measurement (PM) purifies the mixed state resulting from tracing out the lost qubit. Subsequent single qubit and two qubit operations reconstruct the encoded logical qubit.

Figure 2

(Color online) Scheme illustrating the implementation of the quantum nondemolition measurement using the cavity QED system.

Figure 3

(Color online) Scheme illustrating the projective measurement of a qubit encoded in the hyperfine structure of the Rb electronic ground state manifold.