16 research outputs found
What if Critical Race Theory Were Just a Legal Theory? A Christian Critique
The national debate over Critical Race Theory (CRT) continues to grow and deepen. Some Christians seemingly find CRT legitimate, useful, and nonthreatening to Christian theological commitments. This view is incorrect. CRT is in fundamental conflict with Christianity due to its misguided perspectives on law, morality, truth, and justice. Although CRT is more than âjust a legal theory,â this article examines CRTâs legal origins and outlook, showing the inevitable tension between its claims and a Christian understanding of reality. This article also calls attention to several policy proposals suggested by CRT scholars to demonstrate how they are incompatible with Christian views of divine moral law and procedural justice
Qubit coherence control in a nuclear spin bath
Coherent dynamics of localized spins in semiconductors is limited by spectral
diffusion arising from dipolar fluctuation of lattice nuclear spins. Here we
extend the semiclassical theory of spectral diffusion for nuclear spins I=1/2
to the high nuclear spins relevant to the III-V materials and show that
applying successive qubit pi-rotations at a rate approximately proportional to
the nuclear spin quantum number squared (I^2) provides an efficient method for
coherence enhancement. Hence robust coherent manipulation in the large spin
environments characteristic of the III-V compounds is possible without
resorting to nuclear spin polarization, provided that the pi-pulses can be
generated at intervals scaling as I^{-2}
The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling
Tensor hypercontraction is a method that allows the representation of a
high-rank tensor as a product of lower-rank tensors. In this paper, we show how
tensor hypercontraction can be applied to both the electron repulsion integral
(ERI) tensor and the two-particle excitation amplitudes used in the parametric
reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions
are needed in both of these approximations, our overall algorithm can be shown
to scale as O(r4), where r is the number of single-particle basis functions. We
apply our algorithm to several small molecules, hydrogen chains, and alkanes to
demonstrate its low formal scaling and practical utility. Provided we use
enough auxiliary functions, we obtain accuracy similar to that of the
traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).Comment: 11 pages, 1 figur
The Initial and Final States of Electron and Energy Transfer Processes: Diabatization as Motivated by System-Solvent Interactions
For a system which undergoes electron or energy transfer in a polar solvent, we define the diabatic states to be the initial and final states of the system, before and after the nonequilibrium transfer process. We consider two models for the system-solvent interactions: A solvent which is linearly polarized in space and a solvent which responds linearly to the system. From these models, we derive two new schemes for obtaining diabatic states from ab initio calculations of the isolated system in the absence of solvent. These algorithms resemble standard approaches for orbital localization, namely, the Boys and EdmistonâRuedenberg (ER) formalisms. We show that Boys localization is appropriate for describing electron transfer [ Subotnik et al., J. Chem. Phys. 129, 244101 (2008) ] while ER describes both electron and energy transfer. Neither the Boys nor the ER methods require definitions of donor or acceptor fragments and both are computationally inexpensive. We investigate one chemical example, the case of oligomethylphenyl-3, and we provide attachment/detachment plots whereby the ER diabatic states are seen to have localized electron-hole pairs
Effects of Noisy Oracle on Search Algorithm Complexity
Grover's algorithm provides a quadratic speed-up over classical algorithms
for unstructured database or library searches. This paper examines the
robustness of Grover's search algorithm to a random phase error in the oracle
and analyzes the complexity of the search process as a function of the scaling
of the oracle error with database or library size. Both the discrete- and
continuous-time implementations of the search algorithm are investigated. It is
shown that unless the oracle phase error scales as O(N^(-1/4)), neither the
discrete- nor the continuous-time implementation of Grover's algorithm is
scalably robust to this error in the absence of error correction.Comment: 16 pages, 4 figures, submitted to Phys. Rev.
Spatial search using the discrete time quantum walk
We study the quantum walk search algorithm of Shenvi et al. (Phys Rev A 67:052307, 2003) on data structures of one to two spatial dimensions, on which the algorithm is thought to be less efficient than in three or more spatial dimensions. Our aim is to understand why the quantum algorithm is dimension dependent whereas the best classical algorithm is not, and to show in more detail how the efficiency of the quantum algorithm varies with spatial dimension or accessibility of the data. Our numerical results agree with the expected scaling in 2D of O(âN log N}) , and show how the prefactors display significant dependence on both the degree and symmetry of the graph. Specifically, we see, as expected, the prefactor of the time complexity dropping as the degree (connectivity) of the structure is increased