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arXiv:quant-ph/0608134 · Journal of the Physical Society of Japan

Generation and Suppression of Decoherence in Artificial Environment for Qubit System

Yasushi Kondo, Mikio Nakahara, Shogo Tanimura, Sachiko Kitajima, Chikako Uchiyama, Fumiaki Shibata

Published Jun 25, 2007• 13 citations

Abstract

It is known that a quantum system with finite degrees of freedom can simulate a composite of a system and an environment if the state of the hypothetical environment is randomized by external manipulation. We show theoretically that any phase decoherence phenomena of a single qubit can be simulated with a two-qubit system and demonstrate experimentally two examples: one is phase decoherence of a single qubit in a transmission line, and the other is that in a quantum memory. We perform NMR experiments employing a two-spin molecule and clearly measure decoherence for both cases. We also prove experimentally that the bang-bang control efficiently suppresses decoherence.

DOI: 10.1143/jpsj.76.074002

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It is known that a quantum system with finite degrees of freedom can simulate a composite of a system and an environment if the state of the hypothetical environment is randomized by external manipulation. We show theoretically that any phase decoherence phenomena of a single qubit can be simulated with a two-qubit system and demonstrate experimentally two examples: one is phase decoherence of a single qubit in a transmission line, and the other is that in a quantum memory. We perform NMR experiments employing a two-spin molecule and clearly measure decoherence for both cases. We also prove experimentally that the bang-bang control efficiently suppresses decoherence.

To suppress the decoherence, in addition to error-correcting codes and the error-avoiding codes, bang-bang control has also been introduced. Here in this work, we discuss how to suppress decoherence in quantum systems using bang-bang control, two cases have been discussed, adiabatic decoherence alone, and decoherence with both phase and amplitude damping. We also discussed the different cases when the system is made up of one atom or multi-atom and when such atom with two level or multi-level. It is found that in all the above cases, bang-bang control can suppress decoherence effectively.

We present an open-loop (bang-bang) scheme to control decoherence in a generic one-qubit quantum gate and implement it in a realistic simulation. The system is consistently described within the spin-boson model, with interactions accounting for both adiabatic and thermal decoherence. The external control is included from the beginning in the Hamiltonian as an independent interaction term. After tracing out the environment modes, reduced equations are obtained for the two-level system in which the effects of both decoherence and external control appear explicitly. The controls are determined exactly from the condition to eliminate decoherence, i.e. to restore unitarity. Numerical simulations show excellent performance and robustness of the proposed control scheme.

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In this paper, we have detailedly studied the dynamical suppression of the phase damping for the two-qubit quantum memory of Ising model by the quantum ``bang-bang" technique. We find the sequence of periodic radio-frequency pulses repetitively to flip the state of the two-qubit system and quantitatively find that these pulses can be used to effectively suppress the phase damping decoherence of the quantum memory and freeze the system state into its initial state. The general sequence of periodic radio-frequency pulses to suppress the phase damping of multi-qubit of Ising model is also given.