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arXiv:1303.2756 · Physical Review A

Protecting dissipative quantum state preparation via dynamical decoupling

Zongping Gong, Wang Yao

Published Mar 11, 2013• 8 citations
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Abstract

We show that dissipative quantum state preparation processes can be protected against qubit dephasing by interlacing the state preparation control with dynamical decoupling (DD) control consisting of a sequence of short $\ensuremath{\pi}$ pulses. The inhomogeneous broadening can be suppressed to second order of the pulse interval, and the protection efficiency is nearly independent of the pulse sequence but determined by the average interval between pulses. The DD protection is numerically tested and found to be efficient against inhomogeneous dephasing on two exemplary dissipative state preparation schemes that use collective pumping to realize many-body singlets and linear cluster states, respectively. Numerical simulation also shows that the state preparation can be efficiently protected by $\ensuremath{\pi}$ pulses with completely random arrival time. Our results make possible the application of these state preparation schemes in inhomogeneously broadened systems. DD protection of state preparation against dynamical noises is also discussed using the example of Gaussian noise with a semiclasscial description.

DOI
10.1103/physreva.87.032314

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We show that dissipative quantum state preparation processes can be protected against qubit dephasing by interlacing the state preparation control with dynamical decoupling (DD) control consisting of a sequence of short \ensuremathπ\ensuremath{\pi}\ensuremathπ pulses. The inhomogeneous broadening can be suppressed to second order of the pulse interval, and the protection efficiency is nearly independent of the pulse sequence but determined by the average interval between pulses. The DD protection is numerically tested and found to be efficient against inhomogeneous dephasing on two exemplary dissipative state preparation schemes that use collective pumping to realize many-body singlets and linear cluster states, respectively. Numerical simulation also shows that the state preparation can be efficiently protected by \ensuremathπ\ensuremath{\pi}\ensuremathπ pulses with completely random arrival time. Our results make possible the application of these state preparation schemes in inhomogeneously broadened systems. DD protection of state preparation against dynamical noises is also discussed using the example of Gaussian noise with a semiclasscial description.
Aperiodic dynamical decoupling (DD) sequences of π pulses are of great interest to decoherence control and have been recently extended from single-qubit to two-qubit systems. If the environmental noise power spectrum is made available, then one may further optimize aperiodic DD sequences to reach higher efficiency of decoherence suppression than known universal schemes. This possibility is investigated in this work for the protection of two-qubit states, using an exactly solvable pure dephasing model including both local and nonlocal noise. The performance of optimized DD sequences in protecting two-qubit states is compared with that achieved by nested Uhrig's DD (nested-UDD) sequences, for several different types of noise spectrum. Except for the cases with noise spectrum decaying slowly in the high-frequency regime, optimized DD sequences with tens of control pulses can perform orders of magnitude better than that of nested-UDD. A two-qubit system with highly unbalanced local noise is also examined to shed more light on a recent experiment. Possible experiments that may be motivated by this work are discussed.
Dynamical decoupling (DD) emerges as a promising tool to suppress decoherence of quantum systems by eliminating the system-environment coupling. We investigate its power in combating pure dephasing of a qubit under random classical noise. Interestingly, the decoherence rate can be viewed as the interplay between noise spectrum and a controllable filter function. More specifically, the filter function is determined by the DD sequence we employed. Here we take Uhrig DD (UDD) as a benchmark sequence to illustrate the filtering process. We find that UDD sequence works as a perfect dynamical filter for low-frequency noise. For spectrum with hard cutoff, UDD increases the performance order by order with linearly increased number of pulses. However, for noise spectrum with soft cutoff, the required pulse number grows exponentially.
Dynamical decoupling (DD) is a well-established technique for protecting quantum systems from environmental noise. DD effectively mitigates decoherence in superconducting quantum computing systems, where precise implementation plays a crucial role in optimizing its performance. This study investigates how DD implementation timing and sequence design critically affect spectator-induced dephasing from adjacent qubits. We find that excited states of adjacent qubits dramatically degrade operational qubit coherence. We demonstrate that DD sequences applied to adjacent qubits effectively suppress this dephasing. This protection persists even when adjacent qubits remain in superposition states during the sequence. Through systematic characterization of Carr-Purcell-Meiboom-Gill (CPMG) sequences, we show that implementation timing strongly impacts protection effectiveness. While optimal timing achieves substantial coherence enhancement, improper sequence delays can severely degrade protection. Our results highlight the importance of precise timing control for implementing DD in optimizing multi-qubit quantum circuits.
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.
Active protection of quantum states is an essential prerequisite for the implementation of quantum computing. Dynamical decoupling (DD) is a promising approach that applies sequences of control pulses to the system in order to reduce the adverse effect of system-environment interactions. Since every hardware device has finite precision, the errors of the DD control pulses can themselves destroy the stored information rather than protect it. We experimentally compare the performance of different DD sequences in the presence of an environment that was chosen such that all relevant DD sequences can equally suppress its effect on the system. Under these conditions, the remaining decay of the qubits under DD allows us to compare very precisely the robustness of the different DD sequences with respect to imperfections of the control pulses.
Dephasing--phase randomization of a quantum superposition state--is a major obstacle for the realization of high fidelity quantum logic operations. Here, we implement a two-qubit controlled-NOT gate using dynamical decoupling (DD), despite the gate time being more than 1 order of magnitude longer than the intrinsic coherence time of the system. For realizing this universal conditional quantum gate, we have devised a concatenated DD sequence that ensures robustness against imperfections of DD pulses that otherwise may destroy quantum information or interfere with gate dynamics. We compare its performance with three other types of DD sequences. These experiments are carried out using a well-controlled prototype quantum system--trapped atomic ions coupled by an effective spin-spin interaction. The scheme for protecting conditional quantum gates demonstrated here is applicable to other physical systems, such as nitrogen vacancy centers, solid state nuclear magnetic resonance, and circuit quantum electrodynamics.