We present a review of our recent results for the comparative evaluation of the induced exchange interaction
and quantum noise mediated by the bosonic environment in two-qubit systems. We report new calculations
for P-donor-electron spins in Si-Ge type materials. Challenges and open problems are discussed.
We survey results on the decay of multiqubit entanglement due to internal interactions between qubits. Dipole-dipole interaction induces decoherence of strongly entangled nuclear spins. The dynamics of spin clusters can be described as quantum decoherence due to an effective composite bath consisting of fully correlated and uncorrelated parts. The rate of decoherence scales up as a square root of the number of entangled spins, resulting in linear scaling of a measure of quantum noise. Our theory is consistent with a recent experiment.
We review our recent work establishing by an explicit many-body
calculation for an open quantum-mechanical system of two qubits
subject to independent noise modelled by bosonic baths, a newly identified
connection between two important quantities in the studies of
entanglement and decoherence. We demonstrate that the decay of
entanglement is governed by the product of the suppression factors
describing decoherence of the subsystems (qubits). This result is
a detailed model calculation proving an important and
intuitively natural physical property that separated open quantum
systems can evolve coherently, quantum mechanically on time scales
larger than the times for which they remain entangled.
Our result also suggests avenues for future work. Specifically, for
multiqubit systems, it is expected that similar arguments should
apply "by induction." This will stimulate research to develop
appropriate quantitative measures of entanglement, and attempts to
quantify entanglement and decoherence in a unified way. We
considered one "physically meaningful" measure of two-qubit
entanglement, the concurrence. In future research, it would be of
interest to obtain similar results for other measures of
entanglement as well.
We compare approaches to evaluation of decoherence at low temperatures in two-state quantum systems weakly coupled to the environment. By analyzing an exactly solvable model, we demonstrate that a non-Markovian approximation scheme yields good quality estimates of the reduced density matrix for time scales appropriate for evaluation of quantum computing designs.
Methods for quantifying environmentally induced decoherence
in quantum systems are investigated. We formulate criteria for measuring the degree of decoherence and consider several representative examples, including a spin interacting with the modes of a bosonic, e.g., phonon, bath. We formulate an approach based on the operator norm measuring the deviation of the actual density matrix from the ideal one which would describe the system without environmental interactions.
We introduce a new approximation scheme for evaluation of onset of decoherence at low temperatures in quantum systems interacting with environment. The approximation is argued to apply at short and intermediate times. It provides an approach complementary to Markovian approximations and appropriate for evaluation of quantum computing schemes.
We review results of a recently developed model of a microscopic quantum system interacting with the macroscopic world components which are modeled by collections of bosonic modes. The interaction is via a general operator (Lambda) of the system, coupled to the creation and annihilation operators of the environment modes. We assume that in the process of a nearly instantaneous quantum measurement, the function of the environment involves two distinct parts: the pointer and the bath. Interaction of the system with the bath leads to decoherence such that the system and the pointer both evolve into a statistical mixture state described by the density matrix such that the system is in one of the eigenstates of (Lambda) with the correct quantum mechanical probability, whereas the expectation values of pointer operators retain amplified information on that eigenstate. We argue that this process represents the initial step of a quantum measurement.
We argue that the analog nature of quantum computing makes the usual design approach of constructing complicated logical operations from many simple gates inappropriate. Instead, we propose to design multi-spin quantum gates in which the input and output two-state systems (spins) are not necessarily identical. We outline the design criteria for such devices and then review recent results for single-unit Hamiltonians that accomplish the NOT and XOR functions.
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