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arXiv:quant-ph/0609203 · Physical Review Letters

Keeping a Quantum Bit Alive by Optimized π -Pulse Sequences

Götz Silvester Uhrig

Published Mar 9, 2007• 715 citations
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Abstract

A general strategy to maintain the coherence of a quantum bit is proposed. The analytical result is derived rigorously including all memory and backaction effects. It is based on an optimized pi-pulse sequence for dynamic decoupling extending the Carr-Purcell-Meiboom-Gill cycle. The optimized sequence is very efficient, in particular, for strong couplings to the environment.

DOI
10.1103/physrevlett.98.100504

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A general strategy to maintain the coherence of a quantum bit is proposed. The analytical result is derived rigorously including all memory and backaction effects. It is based on an optimized pi-pulse sequence for dynamic decoupling extending the Carr-Purcell-Meiboom-Gill cycle. The optimized sequence is very efficient, in particular, for strong couplings to the environment.
We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of π-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and Carr–Purcell–Meiboom–Gill (CPMG) sequences applied to a single 43 Ca + trapped-ion qubit and find that they afford comparable protection in our ambient noise environment.
In quantum information processing, it is vital to protect the coherence of qubits in noisy environments. Dynamical decoupling (DD), which applies a sequence of flips on qubits and averages the qubit-environment coupling to zero, is a promising strategy compatible with other desired functionalities, such as quantum gates. Here, we review the recent progresses in theories of dynamical decoupling and experimental demonstrations. We give both semiclassical and quantum descriptions of the qubit decoherence due to coupling to noisy environments. Based on the quantum picture, a geometrical interpretation of DD is presented. The periodic Carr-Purcell-Meiboom-Gill DD and the concatenated DD are reviewed, followed by a detailed exploration of the recently developed Uhrig DD, which employs the least number of pulses in an unequally spaced sequence to suppress the qubit-environment coupling to a given order of the evolution time. Some new developments and perspectives are also discussed.
The aim of dynamical decoupling consists in the suppression of decoherence by appropriate coherent control of a quantum register. Effectively, the interaction with the environment is reduced. In particular, a sequence of π pulses is considered. Here we present exact results on the suppression of the coupling of a quantum bit to its environment by optimized sequences of π pulses. The effect of various cut-offs of the spectral density of the environment is investigated. As a result we show that the harder the cut-off is, the better an optimized pulse sequence can deal with it. For cut-offs which are neither completely hard nor very soft we advocate iterated optimized sequences.
Reliable long-time storage of arbitrary quantum states is a key element of quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment by non-instantaneous pulses, we introduce an optimized sequence of N control π pulses that are realistic in the sense that they have a finite duration and a finite amplitude. We show that optimized dynamical decoupling is still applicable and that higher-order decoupling can be reached if shaped pulses are implemented. The sequence suppresses decoherence up to the order , with T being the total duration of the sequence and τ mx the maximum length of the pulses. The exponent depends on the shape of the pulse. Based on existing experiments, a concrete setup for the verification of the properties of the advocated sequence is proposed.