Decoherence sources

Before reviewing existing examples, a very brief explanation on the mechanisms of decoherence for molecular spin qubits is necessary more details are available elsewhere [67]. Broadly speaking, the three decoherence sources for these systems are spin bath decoherence, oscillator bath decoherence and pairwise dipolar decoherence, and can be regulated by a combination of temperature, magnetic field and chemical design of the system [70]. The spin bath mainly consists of nuclear spins, but in general it also includes any localized excitations that can couple to the... 

Quantum-state decay to a continuum or changes in its population via coupling to a thermal bath is known as amplitude noise (AN). It characterizes decoherence processes in many quantum systems, for example, spontaneous emission of photons by excited atoms [35], vibrational and collisional relaxation of trapped ions [36] and the relaxation of current-biased Josephson junctions [37], Another source of decoherence in the same systems is proper dephasing or phase noise (PN) [38], which does not affect the populations of quantum states but randomizes their energies or phases. 

A novel interplay between entanglement as a QIP resource and entanglement as the source of decoherence was detailed [116]. Two entangled qubits were analyzed, each coupled to a bath via common modes. The non-Markovian timescale was considered, as well as dynamical modulations. It was shown how the entanglement of the qubits could vanish after a finite time (entanglement sudden death, ESD), but later restored by non-Markovian modulation-induced oscillations of the system-bath coherence. 

Although the term electron-phonon coupling is used here, the discussion applies equally to coupling with an electro-magnetic source. In any event, in order to retain the coherence of the electrons at the given T, the system has to be sufficiently small. At the same time, the strength of the acoustic source is assumed to be such that the additional decoherence it causes is not detrimental. The precise parameter windows in which this can be achieved will be sensitive to acoustic mismatch, details of the sample geometries, etc. 

Taking the phonon source out of equilibrium at a certain frequency range may lead to enhancement in Ipc. On a speculative level, one may visualize shining the electrons with a high intensity beam of non-equilibrium phonons with a narrow frequency range around, say, w0. Icc, resulting from resonant transitions, will be significantly affected only when u>o is close to the differences e — Cj or c( — C(. The effect on the Debye-Waller factor will be small for a narrow-band beam. In this way, Icc will initially increase with the intensity of this radiation, until decoherence effects will take over and Ipc will disappear. 

Both effects were shown to be the main source of decoherence at very low temperature. At higher temperatures, phonons are another source of decoherence. 

An alternate source of decoherence is in the nature of the laser used to irradiate the system. Specifically, if the laser has random components, then it inputs a degree of randomness into the system, reducing the phase information content and hence decohering the system.. t... 

We would like to attract the attention of the reader to the case when the environment is a source of anomalous diffusion. Paz et al. [116] studied the decoherence process generated by a supra-ohmic bath, but they did not find any problem with the adoption of the decoherence theory. It is convenient to devote some attention to the case when the fluctuation E, is a source of Levy diffusion [59]. If the fluctuation E, is an uncorrelated Levy process, the characteristic function again decays exponentially, and the only significant change is that the... 

It is important to point out that even at 77 = 0 the observed value V = 0.942 0.006 is far from its ideal value of V = 0. One important source of error is the finite retrieval efficiency, which is limited by two factors. Due to the atomic memory decoherence rate 7C, the finite retrieval time Tr always results in a finite loss probability p 7c Tr. For the correlation measurements we use a relatively weak retrieve laser ( 2 mW) to reduce the number of background photons and to avoid APD dead-time effects. The resulting anti-Stokes pulse width is on the order of the measured decoherence time, so the atomic excitation decays before it is fully retrieved. Moreover, even as 7C —> 0 the retrieval efficiency is limited by the finite optical depth q of the ensemble, which yields an error scaling as p 1/ y/rj. The measured maximum retrieval efficiency at 77 = 0 corresponds to about 0.3. In addition to finite retrieval efficiency, many other factors reduce correlations, including losses in the detection system, background photons, APD afterpulsing effects, and imperfect spatial mode-matching. 

The conductance, from source to drain, is determined by the corresponding transmission probability T d Neglecting decoherence processes, with tran-mission (reflection) amplitude U (rt) of the ith QPC fulfilling n I2 + N2 —1> the collected currents at D1 and D2 are ... 

The state represented by Eq. (15) is of the same form as that ofEq. (10). Both involve entangled superpositions and both are subject to the destructive effects of decoherence. Creation of SchrOdinger cats like Eq. (10) is particularly relevant to the ion-based quantum computer because the primary source of decoherence will probably be due to decoherence of the n=0,l) motional states during the logic operations. 

QCs will be exposed to a variety of errors. It is generally believed that the most important source of errors is the coupling of the QC to its environment (Chuang et al. 1995, Unruh 1995, Palma et al. 1996). This coupling will destroy quantum superpositions required for quantum computations and is usually referred to as decoherence (Zurek 1991). 

The proximity of the donor to an oxide interface and nearby electrostatic gates did not introduce additional decoherence. Some coherence measurements are shown in Fig. 5, and the same group have even more recently reported electron Tz times of around 1 ms (with a spin echo) and 0.56 s (with dynamic decoupling), as well as a Tz time for the nucleus with a neutral donor of 1.5 ms for one device and 20 ms for another (both with a spin echo). Ionizing the donor provided a nuclear Tz time of 1.75 s (spin echo) and 35.6 s (with dynamic decoupling). These times are shorter than those measured in bulk Si samples for electrons and nuclei,which was attributed to Johnson-Nyquist thermal noise due to the microwave source. High fidelity control pulses were achieved, reaching 97% for the electron and 99.99% for the nuclear spin. 

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