14 research outputs found
Electron Spin Dephasing due to Hyperfine Interactions with a Nuclear Spin Bath
We investigate pure dephasing decoherence (free induction decay and spin
echo) of a spin qubit interacting with a nuclear spin bath. While for infinite
magnetic field B the only decoherence mechanism is spectral diffusion due to
dipolar flip-flops of nuclear spins, with decreasing B the hyperfine-mediated
interactions between the nuclear spins become important. We give a theory of
decoherence due to these interactions which takes advantage of their long-range
nature. For a thermal uncorrelated bath we show that our theory is applicable
down to B~10 mT, allowing for comparison with recent experiments in GaAs
quantum dots.Comment: Published version, new title suggested by the PRL edito
Verifying Quantum Phase Estimation (QPE) using Prove-It
The general-purpose interactive theorem-proving assistant called Prove-It was
used to verify the Quantum Phase Estimation (QPE) algorithm, specifically
claims about its outcome probabilities. Prove-It is unique in its ability to
express sophisticated mathematical statements, including statements about
quantum circuits, integrated firmly within its formal theorem-proving
framework. We demonstrate our ability to follow a textbook proof to produce a
formally certified proof, highlighting useful automation features to fill in
obvious steps and make formal proving nearly as straightforward as informal
theorem proving. Finally, we make comparisons with formal theorem-proving in
other systems where similar claims about QPE have been proven.Comment: 28 pages, 18 figures, 5 tables. Prove-It theorem-proving results
available at http://pyproveit.org/ and Prove-It code available at
https://github.com/PyProveIt/Prove-I
Quantum simulation of multiple-exciton generation in a nanocrystal by a single photon
We have shown theoretically that efficient multiple exciton generation (MEG)
by a single photon can be observed in small nanocrystals (NCs). Our quantum
simulations that include hundreds of thousands of exciton and multi-exciton
states demonstrate that the complex time-dependent dynamics of these states in
a closed electronic system yields a saturated MEG effect on a picosecond
timescale. Including phonon relaxation confirms that efficient MEG requires the
exciton--biexciton coupling time to be faster than exciton relaxation time
Optimized pulses for the control of uncertain qubits
Constructing high-fidelity control fields that are robust to control, system,
and/or surrounding environment uncertainties is a crucial objective for quantum
information processing. Using the two-state Landau-Zener model for illustrative
simulations of a controlled qubit, we generate optimal controls for \pi/2- and
\pi-pulses, and investigate their inherent robustness to uncertainty in the
magnitude of the drift Hamiltonian. Next, we construct a quantum-control
protocol to improve system-drift robustness by combining environment-decoupling
pulse criteria and optimal control theory for unitary operations. By
perturbatively expanding the unitary time-evolution operator for an open
quantum system, previous analysis of environment-decoupling control pulses has
calculated explicit control-field criteria to suppress environment-induced
errors up to (but not including) third order from \pi/2- and \pi-pulses. We
systematically integrate this criteria with optimal control theory,
incorporating an estimate of the uncertain parameter, to produce improvements
in gate fidelity and robustness, demonstrated via a numerical example based on
double quantum dot qubits. For the qubit model used in this work, post facto
analysis of the resulting controls suggests that realistic control-field
fluctuations and noise may contribute just as significantly to gate errors as
system and environment fluctuations.Comment: 38 pages, 15 figures, RevTeX 4.1, minor modifications to the previous
versio