Monte Carlo Method for a Quantum Measurement Process by a Single-Electron Transistor

We derive the quantum trajectory or stochastic (conditional) master equation for a single superconducting Cooper-pair box (SCB) charge qubit measured by a single-electron transistor (SET) detector. This stochastic master equation describes the random evolution of the measured SCB qubit density matrix which both conditions and is conditioned on a particular realization of the measured electron tunneling events through the SET junctions. Hence it can be regarded as a Monte Carlo method that allows us to simulate the continuous quantum measurement process. We show that the master equation for the "partially" reduced density matrix [Y. Makhlin et.al., Phys. Rev. Lett. 85, 4578 (2000)] can be obtained when a "partial" average is taken on the stochastic master equation over the fine grained measurement records of the tunneling events in the SET. Finally, we present some Monte Carlo simulation results for the SCB/SET measurement process. We also analyze the probability distribution P(m,t) of finding m electrons that have tunneled into the drain of the SET in time t to demonstrate the connection between the quantum trajectory approach and the "partially" reduced density matrix approach.Comment: 7 pages, to appear in Phys. Rev.

Quantum Hall Effect in Quasi-One-Dimensional Conductors: The Roles of Moving FISDW, Finite Temperature, and Edge States

This paper reviews recent developments in the theory of the quantum Hall effect (QHE) in the magnetic-field-induced spin-density-wave (FISDW) state of the quasi-one-dimensional organic conductors (TMTSF)$_2$X. The origin and the basic features of the FISDW are reviewed. The QHE in the pinned FISDW state is derived in several simple, transparent ways, including the edge states formulation of the problem. The temperature dependence of the Hall conductivity is found to be the same as the temperature dependence of the Fr\"ohlich current. It is shown that, when the FISDW is free to move, it produces an additional contribution to the Hall conductivity that nullifies the total Hall effect. The paper is written on mathematically simple level, emphasizes physical meaning over sophisticated mathematical technique, and uses inductive, rather than deductive, reasoning.Comment: Minor typos have been corrected, and a reference to the published version has been added. 22 pages, LaTeX 2.09, 3 eps figures inserted via psfi

Gates for the Kane Quantum Computer in the Presence of Dephasing

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a CNOT gate is $8.3 \times 10^{-5}$. We also compute the fidelities of Z, X, Swap, and Controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.Comment: 9 pages, 9 figure

Optimal control of fast and high-fidelity quantum gates with electron and nuclear spins of a nitrogen-vacancy center in diamond

A negatively charged nitrogen vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at or below the thresholds required for fault-tolerant quantum computation (FTQC). Using quantum optimal control theory based on the Krotov method, we show here that fast and high-fidelity single-qubit and two-qubit gates in the universal quantum gate set for FTQC, taking into account the effects of the leakage state, nearby noise qubits and distant bath spins, can be achieved with errors less than those required by the threshold theorem of FTQC.Comment: 12 pages,6 figures; Accepted by Phys. Rev. A. Some typos in References corrected and Ref.[88] update