Expansion of Vibration-Based Sphere-Pack Technology to Binary Mixture Including Irregular Particles

Abstract

Control scenarios have been identified where the use of randomized design may substantially improve the performance of dynamical decoupling methods (Santos and Viola 2006 Phys. Rev. Lett. 97 150501). Here, by focusing on the suppression of internal unwanted interactions in closed quantum systems, we review and further elaborate on the advantages of randomization at long evolution times. By way of illustration, special emphasis is devoted to isolated Heisenberg chains of coupled spin-1/2 particles. In particular, for nearestneighbor interactions, two types of decoupling cycles are contrasted: inefficient averaging, whereby the number of control actions increases exponentially with the system size, and efficient averaging associated to a fixed-size control group. The latter allows for analytical and numerical studies of efficient decoupling schemes created by exploiting and merging together randomization and deterministic strategies, such as symmetrization, concatenation and cyclic permutations. Notably, sequences capable of removing interactions up to third order in the achievable control timescale are explicitly constructed, and a numerical algorithm to search for optimal decoupling sequences is proposed. The consequences of faulty controls in deterministic versus randomized schemes are also analyzed. so to effectively project out components with unintended symmetry. Since then, DD has become the subject of intense theoretical and experimental investigations. On the theoretical side, some notable advances include: the construction of bounded-strength Eulerian [10] and concatenated DD (CDD) protocols [11,12], as well as efficient combinatorial schemes for multipartite systems [13]-[16]; the identification of optimized control sequences capable to ensure exact high-order cancellation of pure dephasing in a single qubit [17, 18]; proposed applications within specific (notably, solid-state) scalable quantum computing architectures [19]; quantitative investigations of DD schemes for compensating specific decoherence mechanisms, such as magnetic state decoherence in atomic systems [20], 1/ f noise in superconducting devices [21]-[25], and hyperfine-as well as phonon-induced decoherence in quantum dots [26]-[31]; control procedures for combining DD with universal quantum computation [32, 33]. Within experimental QIP, DD techniques have been successfully applied to decoherence control in a single-photon polarization interferometer [34]; have found extensive applications in liquid-state NMR QIP [35], also in conjunction with error-correcting codes [36]; have inspired charge-based [37] and flux-based [38] echo experiments in superconducting qubits; and are being scrutinized for further applications in solid-state systems such as nuclear quadrupole qubits [39] and fullerene qubits [40].Even if, in the limit where no control constraint is present and under appropriate mathematical assumptions, DD techniques may guarantee the exact elimination of all the undesired coupling, a main limitation is the fact that, in general, such...