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Quantum Information Processing

Robust preparation of four-qubit decoherence-free states for superconducting quantum interference devices against collective amplitude damping

Xiao‐Qiang Shao, Tai-Yu Zheng, Shou Zhang

Published Jun 27, 2013• 2 citations
Publisher
DOI
10.1007/s11128-013-0604-y

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Physical Review A•Oct 17, 2012•6 citations
Enlightened by the idea of purification through Zeno-like measurements (Nakazato et al 2003 Phys. Rev. Lett. 90 060401), we propose a scheme for generating three- and four-qubit decoherence-free states with respect to collective amplitude damping. The whole system is in a star configuration of a spin network and the outer spin qubits construct the decoherence-free state via measuring the state of central spin qubit at intervals of τ repeatedly. An interesting feature is found: namely, that in order to prepare the three-qubit decoherence-free state successfully, the value of τ for the projected time-evolution operator must be set definitely, while this restrictive condition is relaxed for achieving the four-qubit decoherence-free state. The simulation results reveal that the fidelity approaches one asymptotically, and the corresponding success probability reaches a stable value by increasing the number of measurements N.
We propose an encoding scheme to fight against ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$-type local collective noise. In our scheme, a logical qubit consists of two charge qubits coupled by a variable capacitance, and different logical qubits are coupled by a common inductance. A logical qubit provides a decoherence-free subspace (DFS) immune to the ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$-type collective noise. We show how to realize universal quantum computation in the DFS. Any two logical qubits can be selectively and controllably coupled by adjusting fluxes through the common inductance and superconducting-quantum-interference-device loops, which makes it possible to scale our scheme up to a large number of logical qubits. Finally, we show how to prepare a logical qubit in the DFS.