48 research outputs found
Anisotropic Stark Effect and Electric-Field Noise Suppression for Phosphorus Donor Qubits in Silicon
We report the use of novel, capacitively terminated coplanar waveguide (CPW)
resonators to measure the quadratic Stark shift of phosphorus donor qubits in
Si. We confirm that valley repopulation leads to an anisotropic spin-orbit
Stark shift depending on electric and magnetic field orientations relative to
the Si crystal. By measuring the linear Stark effect, we estimate the effective
electric field due to strain in our samples. We show that in the presence of
this strain, electric-field sources of decoherence can be non-negligible. Using
our measured values for the Stark shift, we predict magnetic fields for which
the spin-orbit Stark effect cancels the hyperfine Stark effect, suppressing
decoherence from electric-field noise. We discuss the limitations of these
noise-suppression points due to random distributions of strain and propose a
method for overcoming them
Electron Spin Resonance at the Level of 10000 Spins Using Low Impedance Superconducting Resonators
We report on electron spin resonance (ESR) measurements of phosphorus donors
localized in a 200 square micron area below the inductive wire of a lumped
element superconducting resonator. By combining quantum limited parametric
amplification with a low impedance microwave resonator design we are able to
detect around 20000 spins with a signal-to-noise ratio (SNR) of 1 in a single
shot. The 150 Hz coupling strength between the resonator field and individual
spins is significantly larger than the 1 - 10 Hz coupling rates obtained with
typical coplanar waveguide resonator designs. Due to the larger coupling rate,
we find that spin relaxation is dominated by radiative decay into the resonator
and dependent upon the spin-resonator detuning, as predicted by Purcell
Addressing spin transitions on 209Bi donors in silicon using circularly-polarized microwaves
Over the past decade donor spin qubits in isotopically enriched Si
have been intensely studied due to their exceptionally long coherence times.
More recently bismuth donor electron spins have become popular because Bi has a
large nuclear spin which gives rise to clock transitions (first-order
insensitive to magnetic field noise). At every clock transition there are two
nearly degenerate transitions between four distinct states which can be used as
a pair of qubits. Here it is experimentally demonstrated that these transitions
are excited by microwaves of opposite helicity such that they can be
selectively driven by varying microwave polarization. This work uses a
combination of a superconducting coplanar waveguide (CPW) microresonator and a
dielectric resonator to flexibly generate arbitrary elliptical polarizations
while retaining the high sensitivity of the CPW
High fidelity state preparation, quantum control, and readout of an isotopically enriched silicon spin qubit
Quantum systems must be prepared, controlled, and measured with high fidelity
in order to perform complex quantum algorithms. Control fidelities have greatly
improved in silicon spin qubits, but state preparation and readout fidelities
have generally been poor. By operating with low electron temperatures and
employing high-bandwidth cryogenic amplifiers, we demonstrate single qubit
readout visibilities >99%, exceeding the threshold for quantum error
correction. In the same device, we achieve average single qubit control
fidelities >99.95%. Our results show that silicon spin qubits can be operated
with high overall operation fidelity
A Geometric Variational Approach to Bayesian Inference
We propose a novel Riemannian geometric framework for variational inference
in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold
of probability density functions. Under the square-root density representation,
the manifold can be identified with the positive orthant of the unit
hypersphere in L2, and the Fisher-Rao metric reduces to the standard L2 metric.
Exploiting such a Riemannian structure, we formulate the task of approximating
the posterior distribution as a variational problem on the hypersphere based on
the alpha-divergence. This provides a tighter lower bound on the marginal
distribution when compared to, and a corresponding upper bound unavailable
with, approaches based on the Kullback-Leibler divergence. We propose a novel
gradient-based algorithm for the variational problem based on Frechet
derivative operators motivated by the geometry of the Hilbert sphere, and
examine its properties. Through simulations and real-data applications, we
demonstrate the utility of the proposed geometric framework and algorithm on
several Bayesian models