## Decoherence and readout of solid-state qubits

Recent experiments with Josephson-junction circuits demonstrated long-lived coherent oscillations. They had acquired a resolution sufficient for detailed studies of the dephasing times and decay laws, stressing the need for the theory analysis of the dissipative dynamics of qubits subject to relevant noise sources. In solid-state systems decoherence is potentially strong due the host of microscopic modes. In Josephson qubits the noise is dominated by material-dependent sources, such as background-charge fluctuations or variations of critical currents and magnetic fields, with power spectrum peaked at low frequencies, often proportional to 1/f. A further relevant contribution is the electromagnetic noise of the control circuit, typically Ohmic at low frequencies. The 1/f noise appears difficult to suppress and, since the dephasing is dominated by low-frequency noise, it is particularly destructive. On the other hand, Vion et al showed that the effect of this noise can be substantially reduced by tuning the linear longitudinal qubit-noise coupling to zero. The same strategy, suppressing the linear qubit-detector coupling, was used to minimize the effect of the quantum detector in the off-state. The coherence time achieved in this way was 2 orders of magnitude longer than in earlier experiments.

Motivated by these experiments with Josephson-junction circuits, we analyse the influence of various noise sources on the dynamics of two-level systems at optimal operation points where the linear coupling to low-frequency fluctuations is suppressed. We studied the decoherence due to nonlinear (quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic noise power spectra. An Ohmic noise coupling linearly to the qubit lead sto a decoherence rate which scales proportional to the temperature T, for quadratic coupling this low changes into a T3 dependence. For 1/f noise and Gaussian noise the decay is proportional to exp (-const t2). Our analysis shows, however, that non-Gaussian effects are strong and lead to a power law decay. For further details we refer to our publication: Dephasing at optimal points, Y. Makhlin and A. Shnirman, Phys. Rev. Lett. 92, 178301 (2004).

For quantum information technology it is necessary to investigate properties of real physical systems used as quantum detectors. Certain quantum algorithms require an efficient (single-shot) read out the final state of a qubit. This can be done by either strongly coupled threshold detectors, or by "measurement in stages" strategy. For weakly coupled detectors the only way to perform single-shot measurements is to be in the quantum-non-demolition (QND) regime, i.e., by measuring an observable, which commutes with the Hamiltonian and is, thus, conserved.

In our work we concentrated on continuous weak non-QND measurements (monitoring) of the coherent oscillations of a qubit (two-level system, spin-1/2). This regime is realized, e.g., for the transverse coupling between the spin and the meter, e.g., when the effective magnetic field acting on the spin is along the x-axis while the component along the z-axis is being measured. In this case one observes the stationary state properties of the system, after the information about the initial state of the qubit is lost. Thus, this regime is not useful for quantum computation. Yet, studying the properties of the meter in the stationary monitoring regime, one can obtain information necessary in order to employ the meter in the QND regime. Another motivation for our study comes from the recent activity in the STM single spin detection. For further details we refer to our publication: Output spectrum of a measuring device at arbitrary voltage and temperature, A. Shnirman, D. Mozyrsky and I. Martin, Europhys. Lett. 67, 840 (2004).

Motivated by these experiments with Josephson-junction circuits, we analyse the influence of various noise sources on the dynamics of two-level systems at optimal operation points where the linear coupling to low-frequency fluctuations is suppressed. We studied the decoherence due to nonlinear (quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic noise power spectra. An Ohmic noise coupling linearly to the qubit lead sto a decoherence rate which scales proportional to the temperature T, for quadratic coupling this low changes into a T3 dependence. For 1/f noise and Gaussian noise the decay is proportional to exp (-const t2). Our analysis shows, however, that non-Gaussian effects are strong and lead to a power law decay. For further details we refer to our publication: Dephasing at optimal points, Y. Makhlin and A. Shnirman, Phys. Rev. Lett. 92, 178301 (2004).

For quantum information technology it is necessary to investigate properties of real physical systems used as quantum detectors. Certain quantum algorithms require an efficient (single-shot) read out the final state of a qubit. This can be done by either strongly coupled threshold detectors, or by "measurement in stages" strategy. For weakly coupled detectors the only way to perform single-shot measurements is to be in the quantum-non-demolition (QND) regime, i.e., by measuring an observable, which commutes with the Hamiltonian and is, thus, conserved.

In our work we concentrated on continuous weak non-QND measurements (monitoring) of the coherent oscillations of a qubit (two-level system, spin-1/2). This regime is realized, e.g., for the transverse coupling between the spin and the meter, e.g., when the effective magnetic field acting on the spin is along the x-axis while the component along the z-axis is being measured. In this case one observes the stationary state properties of the system, after the information about the initial state of the qubit is lost. Thus, this regime is not useful for quantum computation. Yet, studying the properties of the meter in the stationary monitoring regime, one can obtain information necessary in order to employ the meter in the QND regime. Another motivation for our study comes from the recent activity in the STM single spin detection. For further details we refer to our publication: Output spectrum of a measuring device at arbitrary voltage and temperature, A. Shnirman, D. Mozyrsky and I. Martin, Europhys. Lett. 67, 840 (2004).