We address the problem of decoupling the interactions in a spin network governed by a pair-interaction Hamiltonian. Combinatorial schemes for decoupling and for manipulating the couplings of Hamiltonians have been developed, which use selective pulses. In this paper, we consider an additional requirement on these pulse sequences: as few different control operations as possible should be used. This requirement is motivated by the fact that to find an optimal implementation of each individual selective pulse will be expensive since it requires to solve a pulse shaping problem. Hence, it is desirable to use as few different selective pulses as possible. As a first result, we show that for d-dimensional systems, where d⩾2, the ability to implement only two control operations is sufficient to turn off the time evolution. Next, we address the case of a bipartite system with local control and show that four different control operations are sufficient. Finally, turning to networks consisting of several d-dimensional nodes, we show that decoupling can be achieved if one is able to control a number of different control operations, which is logarithmic in the number of nodes. We give an explicit family of efficient decoupling schemes with logarithmic number of different pulses based on the classic Hamming codes. We also provide a table of the best known decoupling schemes for small networks of qubits.We address the problem of decoupling the interactions in a spin network governed by a pair-interaction Hamiltonian. Combinatorial schemes for decoupling and for manipulating the couplings of Hamiltonians have been developed, which use selective pulses. In this paper, we consider an additional requirement on these pulse sequences: as few different control operations as possible should be used. This requirement is motivated by the fact that to find an optimal implementation of each individual selective pulse will be expensive since it requires to solve a pulse shaping problem. Hence, it is desirable to use as few different selective pulses as possible. As a first result, we show that for d-dimensional systems, where d⩾2, the ability to implement only two control operations is sufficient to turn off the time evolution. Next, we address the case of a bipartite system with local control and show that four different control operations are sufficient. Finally, turning to networks consisting of several d-dimensional nodes, we show that decoupling can be achieved if one is able to control a number of different control operations, which is logarithmic in the number of nodes. We give an explicit family of efficient decoupling schemes with logarithmic number of different pulses based on the classic Hamming codes. We also provide a table of the best known decoupling schemes for small networks of qubits.

Journal of Mathematical PhysicsApr 1, 20084 citations

A geometrical approach to dynamical decoupling with smooth pulses

Junkai Zeng, Xiu–Hao Deng, Edwin Barnes

Bulletin of the American Physical SocietyMar 17, 20170 citations

Efficient coherent control by sequences of pulses of finite duration

Götz Silvester Uhrig, Stefano Pasini

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.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.

arXiv:0906.3605New Journal of PhysicsApr 1, 201040 citations

High-order dynamical decoupling

Zhenyu Wang, Ren‐Bao Liu

Cambridge University Press eBooksSep 5, 20130 citations

Coherent control of a local phonon in trapped ions using dynamical decoupling

Ryutaro Ohira, Shota Kume, Kenji Toyoda

In this article, we present a dynamical decoupling (DD) technique to coherently control the dynamics of a single local phonon in trapped ions. A $2\ensuremath{\pi}$ rotation at a motional sideband transition flips the sign of the relevant local-phonon state, resulting in cancellation of the phonon dynamics. In this work, we implement DD using resonant blue-sideband pulses to control the hopping of a single local phonon between two ${^{40}\mathrm{Ca}}^{+}$ ions in a linear Paul trap. Our proposed DD technique can be used to engineer coupling between local-phonon modes.In this article, we present a dynamical decoupling (DD) technique to coherently control the dynamics of a single local phonon in trapped ions. A $2\ensuremath{\pi}$ rotation at a motional sideband transition flips the sign of the relevant local-phonon state, resulting in cancellation of the phonon dynamics. In this work, we implement DD using resonant blue-sideband pulses to control the hopping of a single local phonon between two ${^{40}\mathrm{Ca}}^{+}$ ions in a linear Paul trap. Our proposed DD technique can be used to engineer coupling between local-phonon modes.

arXiv:2112.14082Physical Review AOct 4, 20224 citations

{^{40}\mathrm{Ca}}^{+}

ions in a linear Paul trap. Our proposed DD technique can be used to engineer coupling between local-phonon modes.