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arXiv:quant-ph/0207063 · Physical Review A

Error-prevention scheme with two pairs of qubits

Chui‐Ping Yang, Shih‐I Chu, Siyuan Han

Published Sep 4, 2002• 7 citations
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Abstract

A scheme is presented for protecting one-qubit quantum information against decoherence due to a general environment and local exchange interactions. The scheme operates essentially by distributing information over two pairs of qubits and through error-prevention procedures. In the scheme, quantum information is encoded through a decoherence-free subspace for collective phase errors and exchange errors affecting the qubits in pairs; leakage out of the encoding space due to amplitude damping is reduced by quantum Zeno effect. In addition, how to construct decoherence-free states for n-qubit information against phase and exchange errors is discussed.

DOI
10.1103/physreva.66.034301

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A scheme is presented for protecting one-qubit quantum information against decoherence due to a general environment and local exchange interactions. The scheme operates essentially by distributing information over two pairs of qubits and through error-prevention procedures. In the scheme, quantum information is encoded through a decoherence-free subspace for collective phase errors and exchange errors affecting the qubits in pairs; leakage out of the encoding space due to amplitude damping is reduced by quantum Zeno effect. In addition, how to construct decoherence-free states for n-qubit information against phase and exchange errors is discussed.
We propose schemes that are efficient when each pair of qubits undergoes some imperfect collective decoherence with different baths. In the proposed scheme, each pair of qubits is first encoded in a decoherence-free subspace composed of two qubits. Leakage out of the encoding space generated by the imperfection is reduced by the quantum Zeno effect. Phase errors in the encoded bits generated by the imperfection are reduced by concatenation of the decoherence-free subspace with either a three-qubit quantum error correcting code that corrects only phase errors or a two-qubit quantum error detecting code that detects only phase errors connected with the quantum Zeno effect again.
The exchange interaction between identical qubits in a quantum-information processor gives rise to unitary two-qubit errors. It is shown here that decoherence-free subspaces (DFSs) for collective decoherence undergo Pauli errors under exchange, which, however, do not take the decoherence-free states outside of the DFS. In order to protect DFSs against these errors it is sufficient to employ a recently proposed concatenated DFS quantum-error-correcting code scheme [D. A. Lidar, D. Bacon, and K.B. Whaley, Phys. Rev. Lett. 82, 4556 (1999)].
A scheme for protecting quantum states from both independent and cooperative decoherence is proposed. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into corresponding coherence-preserving states of qubit pairs. In this scheme, amplitude damping (loss of energy) as well as phase damping (dephasing) is prevented by a strategy called ``free-Hamiltonian elimination.'' We further extend the scheme to include quantum gate operations and show that loss and decoherence during such operations can also be prevented.
In order to reduce errors, error correction codes need to be implemented fast. They can correct the errors corresponding to the first few orders in the Taylor expansion of the time evolution operator corresponding to the Hamiltonian of the interaction with the environment. If implemented fast enough, the zeroth order error predominates and the dominant effect is of error prevention by measurement (Zeno effect) rather than correction. In this ``Zeno regime,'' codes with less redundancy are sufficient for protection. We describe such a simple scheme, which uses two ``noiseless'' qubits to protect a large number, nnn, of information qubits from noise from the environment. The ``noisless qubits'' can be realized by treating them as logical qubits to be encoded by one of the previously introduced encoding schemes.