Phenomenological Study of Decoherence in Solid-State Spin Qubits due to Nuclear Spin Diffusion

We present a study of the prospects for coherence preservation in solid-state spin qubits using dynamical decoupling protocols. Recent experiments have provided the first demonstrations of multipulse dynamical decoupling sequences in this qubit system, but quantitative analyses of potential coherence improvements have been hampered by a lack of concrete knowledge of the relevant noise processes. We present simulations of qubit coherence under the application of arbitrary dynamical decoupling pulse sequences based on an experimentally validated semiclassical model. This phenomenological approach bundles the details of underlying noise processes into a single experimentally relevant noise power spectral density. Our results show that the dominant features of experimental measurements in a two-electron singlet-triplet spin qubit can be replicated using a $1/\omega^{2}$ noise power spectrum associated with nuclear-spin-flips in the host material. Beginning with this validation we address the effects of nuclear programming, high-frequency nuclear-spin dynamics, and other high-frequency classical noise sources, with conjectures supported by physical arguments and microscopic calculations where relevant. Our results provide expected performance bounds and identify diagnostic metrics that can be measured experimentally in order to better elucidate the underlying nuclear spin dynamics.Comment: Updated References. Related articles at: http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm

Toward Spin Squeezing with Trapped Ions

Building robust instruments capable of making interferometric measurements with precision beyond the standard quantum limit remains an important goal in many metrology laboratories. We describe here the basic concepts underlying spin squeezing experiments that allow one to surpass this limit. In priniciple it is possible to reach the so-called Heisenberg limit, which constitutes an improvement in precision by a factor $\sqrt{N}$, where $N$ is the number of particles on which the measurement is carried out. In particular, we focus on recent progress toward implementing spin squeezing with a cloud of beryllium ions in a Penning ion trap, via the geometric phase gate used more commonly for performing two-qubit entangling operations in quantum computing experiments.Comment: 18 pages, 9 figures, Contribution to Quantum Africa 2010 conference proceeding

High-order noise filtering in nontrivial quantum logic gates

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of non-commuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.Comment: Revised and expanded to include filter function terms beyond first order in the Magnus expansion. Related manuscripts available from http://www.physics.usyd.edu.au/~mbiercu