Leonid Fedichkin

Error rate of a charge qubit coupled to an acoustic phonon reservoir

We analyze decoherence of an electron in a double-dot due to the interaction with acoustic phonons. For large tunneling rates between the quantum dots, the main contribution to decoherence comes from the phonon emission relaxation processes, while for small tunneling rates, the virtual-phonon, dephasing processes dominate. Our results show that in common semiconductors, such as Si and GaAs, the latter mechanism determines the upper limit for the double-dot charge qubit performance measure.

Continuous-time quantum walks on a cycle graph

We present an analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with a nearby quantum point contact. We derive an analytical expression of the probability distribution along the cycle. An upper-bound estimate to the mixing time is shown.

Measures of Decoherence

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.

Additivity of decoherence measures for multiqubit quantum systems

We introduce new measures of decoherence appropriate for evaluation of quantum computing designs. Environment-induced deviation of a quantum systems evolution from controlled dynamics is quantified by a single numerical measure. This measure is defined as a maximal norm of the density matrix deviation. We establish the property of additivity: in the regime of the onset of decoherence, the sum of the individual qubit error measures provides an estimate of the error for a several-qubit system. This property is illustrated by exact calculations for a spin-boson model.

Nonunitary quantum walks on hypercycles

We present analytical treatment of quantum walks on multidimensional hypercycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.

Collective decoherence of nuclear spin clusters

The problem of dipole–dipole decoherence of nuclear spins is considered for strongly entangled spin clusters. We consider the pure dephasing part of the dipole–dipole interaction which can be classically interpreted as a random field fluctuating along the quantization axes. Due to the long (but finite) range nature of dipole–dipole interaction this field is expected to be partially correlated at the sites of different spins in the cluster. Consequently our results show that the dynamics of the entangled spin cluster can be described as the decoherence due to interaction with a composite bath consisting of fully correlated and uncorrelated parts. The correlated term causes the slower decay of coherence at larger times. The decoherence rate scales up as a square root of the number of spins, giving the linear scaling of the resulting error. Our theory is consistent with recent experiments reported on decoherence of correlated spin clusters.

Study of temperature dependence of electron-phonon relaxation and dephasing in semiconductor double-dot nanostructures

This paper examines mechanisms of relaxation and dephasing of electrons in double-dot nanostructures due to interaction with acoustic phonon modes. The effect of temperature of phonon bath on decay on electron quantum evolution is obtained. Our results set the temperature ranges outside of which the quantum dynamics of electrons will be significantly suppressed.

Quantitative Treatment of Decoherence

We review several approaches to define and quantify decoherence. We find that a measure based on a norm of deviation of the density matrix is appropriate for quantifying decoherence for quantum registers. For a semiconductor double quantum-dot charge qubit, evaluation of this measure is presented. For a general class of decoherence processes, including those occurring in semiconductor qubits, we establish that this measure is additive: It scales linearly with the number of qubits in the quantum register.

Robustness of Multiqubit Entanglement

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.

Interaction-induced decoherence of solid state quantum computer

Uncontrollable interaction between qubits can completely destroy coherent state of quantum computer. We study such decoherence processes by numerical simulation of quantum computer operation performer adder algorithm. A polynomial procedure of avoiding such decoherence was also simulated.