We develop a systematic method of performing corrected gate operations on an array of exchange-coupled singlet-triplet qubits in the presence of both fluctuating nuclear Overhauser field gradients and charge noise. The single-qubit control sequences
we present have a simple form, are relatively short, and form the building blocks of a corrected CNOT gate when also implemented on the inter-qubit exchange link. This is a key step towards enabling large-scale quantum computation in a semiconductor-based architecture by facilitating error reduction below the quantum error correction threshold for both single-qubit and multi-qubit gate operations.
We propose a realization of the one-dimensional random dimer model and certain N-leg generalizations using cold atoms in an optical lattice. We show that these models exhibit multiple delocalization energies that depend strongly on the symmetry prope
rties of the corresponding Hamiltonian and we provide analytical and numerical results for the localization length as a function of energy. We demonstrate that the N-leg systems possess similarities with their 1D ancestors but are demonstrably distinct. The existence of critical delocalization energies leads to dips in the momentum distribution which serve as a clear signal of the localization-delocalization transition. These momentum distributions are different for models with different group symmetries and are identical for those with the same symmetry.
Charged impurities in semiconductor quantum dots comprise one of the main obstacles to achieving scalable fabrication and manipulation of singlet-triplet spin qubits. We theoretically show that using dots that contain several electrons each can help
to overcome this problem through the screening of the rough and noisy impurity potential by the excess electrons. We demonstrate how the desired screening properties turn on as the number of electrons is increased, and we characterize the properties of a double quantum dot singlet-triplet qubit for small odd numbers of electrons per dot. We show that the sensitivity of the multi-electron qubit to charge noise may be an order of magnitude smaller than that of the two-electron qubit.
We propose an implementation of the two-qubit gate in a quantum dot spin qubit system which is immune to charge noise problems. Our proposed implementation, if it could be realized in a physical system, would have the advantage of being robust agains
t uncertainties and fluctuations in the tunnel coupling and barrier gate voltage pulse area. The key idea is to introduce an auxiliary dot and use an analog to the stimulated Raman adiabatic passage pulse sequence in three-level atomic systems, often referred to in the context of electron transport in quantum dot systems as Coherent Tunneling by Adiabatic Passage. Spin-dependent tunneling opens the possibility of performing two-qubit gate operations by this method.
We show that ultracold two-component fermionic dipolar gases in an optical lattice with strong two-body on-site loss can be used to realize a tunable effective spin-one model. Fermion number conservation provides an unusual constraint that $sum_i (S^
z_i)^2$ is conserved, leading to a novel topological liquid phase in one dimension which can be thought of as the gapless analog of the Haldane gapped phase of a spin-one Heisenberg chain. The properties of this phase are calculated numerically via the infinite time-evolving block decimation method and analytically via a mapping to a one-mode Luttinger liquid with hidden spin information.
The compressibility, zero sound dispersion, and effective mass of a gas of fermionic dipolar molecules is calculated at finite temperature for one-, two-, and three-dimensional uniform systems, and in a multilayer quasi-two-dimensional system. The co
mpressibility is nonmonotonic in the reduced temperature, $T/T_F$, exhibiting a maximum at finite temperature. This effect might be visible in a quasi-low-dimensional experiment, providing a clear signature of the onset of many-body quantum degeneracy effects. The collective mode dispersion and effective mass show similar nontrivial temperature and density dependence. In a quasi-low-dimensional system, the zero sound mode may propagate at experimentally attainable temperatures.
To test effective Hamiltonians for strongly interacting fermions in an optical lattice, we numerically find the energy spectrum for two fermions interacting across a Feshbach resonance in a double well potential. From the spectrum, we determine the r
ange of detunings for which the system can be described by an effective lattice model, and how the model parameters are related to the experimental parameters. We find that for a range of strong interactions the system is well described by an effective $t-J$ model, and the effective superexchange term, $J$, can be smoothly tuned through zero on either side of unitarity. Right at and around unitarity, an effective one-band general Hubbard model is appropriate, with a finite and small on-site energy, due to a lattice-induced anharmonic coupling between atoms at the scattering threshold and a weakly bound Feshbach molecule in an excited center of mass state.
When two atoms interact in the presence of an anharmonic potential, such as an optical lattice, the center of mass motion cannot be separated from the relative motion. In addition to generating a confinement-induced resonance (or shifting the positio
n of an existing Feshbach resonance), the external potential changes the resonance picture qualitatively by introducing new resonances where molecular excited center of mass states cross the scattering threshold. We demonstrate the existence of these resonances, give their quantitative characterization in an optical superlattice, and propose an experimental scheme to detect them through controlled sweeping of the magnetic field.
We derive an effective low-dimensional Hamiltonian for strongly interacting ultracold atoms in a transverse trapping potential near a wide Feshbach resonance. The Hamiltonian includes crucial information about transverse excitations in an effective m
odel with renormalized interaction between atoms and composite dressed molecules. We fix all the parameters in the Hamiltonian for both one- and two-dimensional cases.
We present a solution of the three-fermion problem in a harmonic potential across a Feshbach resonance. We compare the spectrum with that of the two-body problem and show that it is energetically unfavorable for the three fermions to occupy one latti
ce site rather than two. We also demonstrate the existence of an energy level crossing in the ground state with a symmetry change of its wave function, suggesting the possibility of a phase transition for the corresponding many-body case.
