Dynamical Decoupling Schemes Research Articles

Universal Dynamical Decoupling of a Single Solid-State Spin from a Spin Bath

Controlling the interaction of a single quantum system with its environment is a fundamental challenge in quantum science and technology. We strongly suppressed the coupling of a single spin in diamond with the surrounding spin bath by using double-axis dynamical decoupling. The coherence was preserved for arbitrary quantum states, as verified by quantum process tomography. The resulting coherence time enhancement followed a general scaling with the number of decoupling pulses. No limit was observed for the decoupling action up to 136 pulses, for which the coherence time was enhanced more than 25 times compared to that obtained with spin echo. These results uncover a new regime for experimental quantum science and allow us to overcome a major hurdle for implementing quantum information protocols.

Near-Optimal Dynamical Decoupling of a Qubit

We present a near-optimal quantum dynamical decoupling scheme that eliminates general decoherence of a qubit to order n using O(n2) pulses, an exponential decrease in pulses over all previous decoupling methods. Numerical simulations of a qubit coupled to a spin bath demonstrate the superior performance of the new pulse sequences.

Erratum: Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences [Phys. Rev. A75, 062310 (2007)

Erratum: Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences [Phys. Rev. A<b>75</b>, 062310 (2007)

Wavefunction considerations for the central spin decoherence problem in a nuclear spin bath

Decoherence of a localized electron spin in a solid state material (the ``central spin'' problem) at low temperature is believed to be dominated by interactions with nuclear spins in the lattice. This decoherence is partially suppressed through the application of a large magnetic field that splits the energy levels of the electron spin and prevents depolarization. However, the dephasing decoherence resulting from a dynamical nuclear spin bath cannot be removed in this way. Fluctuations of the nuclear field lead to an uncertainty of the electron's precessional frequency in a process known as spectral diffusion. This paper considers the effect of the electron's wavefunction shape on spectral diffusion and provides wavefunction dependent decoherence time formulas for a free induction decay as well as spin echoes and concatenated dynamical decoupling schemes for enhancing coherence. We also discuss a dephasing of a qubit encoded in singlet-triplet states of a double quantum dot. A central theoretical result of this work is the development of a continuum approximation for the spectral diffusion problem which we have applied to GaAs and InAs materials specifically.

Dynamical decoupling schemes derived from Hamilton cycles

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.

Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences

Dynamical decoupling can be used to preserve arbitrary quantum states despite undesired interactions with the environment, using control Hamiltonians affecting the system only. We present a system-independent analysis of dynamical decoupling based on leading order decoupling error estimates, valid for bounded-strength environments. Using as a key tool a renormalization transformation of the effective system-bath coupling Hamiltonian, we delineate the reliability domain of dynamical decoupling used for quantum state preservation, in a general setting for a single qubit. We specifically analyze and compare two deterministic dynamical decoupling schemes -- periodic and concatenated -- and distinguish between two limiting cases of fast versus slow environments. We prove that concatenated decoupling outperforms periodic decoupling over a wide range of parameters. These results are obtained for both ``ideal'' (zero-width) and realistic (finite-width) pulses This work extends and generalizes our earlier work, Phys. Rev. Lett. 95, 180501 (2005).

Non-Markovian Quantum Error Deterrence by Dynamical Decoupling in a General Environment

A dynamical decoupling(DD) scheme for the prevention of errors in the non-Markovian (usually corresponding to low temperature, short time, and strong coupling) regimes suitable for qubits constructed out of a multilevel structure is studied. We use the effective spin-boson model (ESBM) introduced recently [K. Shiokawa and B. L. Hu, Phys. Rev. A70, 062106 (2004)] as a low temperature limit of the quantum Brownian oscillator model, where one can obtain exact solutions for a general environment with colored noises. In our decoupling scheme, a train of pairs of strong pulses are used to evolve the interaction Hamiltonian instantaneously. Using this scheme we show that the dynamical decoupling method can suppress 1/f noise with slower and hence more accessible pulses than previously studied, but it still fails to decouple super-Ohmic types of environments.

Controlling Quantum Systems by Embedded Dynamical Decoupling Schemes

A dynamical decoupling method is presented which is based on embedding a deterministic decoupling scheme into a stochastic one. This way it is possible to combine the advantages of both methods and to increase the suppression of undesired perturbations of quantum systems significantly even for long interaction times. As a first application the stabilization of a quantum memory is discussed which is perturbed by one- and two-qubit interactions.

Laser threshold and nonlinear Landau fluctuation theory of phase transitions

The threshold region for a single mode laser is treated by Landau's theory of order parameter fluctuations. Taking into account a kinetic energy in the Landau functional, approximate equations of motion for the laser field are derived which include coupling of phase and amplitude. From these it is easy to get the correlation functions and linewidths for intensity and field as well as the transient behaviour of intensity throughout the nonlinear transition region. In addition, a dynamical decoupling scheme of noise theory is applied to calculate the same quantities. Although these methods are very simple the results agree fairly well with those of the much more involved Fokker-Planck theory.