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• W2739954527 abstract "On the noise that causes the phase decoherence of a qubit, we propose a method of obtaining the noise spectrum directly from experimentally available values. The method is based on a simple relation between the spectrum and a coherence time of the qubit in the presence of a multiple �-pulse sequence. The relation is found to hold for every system of a qubit interacting with classical-noise, bosonic, and spin baths. Introduction.—Implementation of quantum informa- tion processing (QIP) requires keeping alive quantum coherence of systems during the operation. In reality, however, systems are not completely isolated from their environments. Interactions with the environments act as noises to the systems and cause decoherence. It is therefore one of the challenging issues in QIP to manip- ulate a system appropriately in the environment noise and/or to reduce the noise level by weakening the system- environment coupling. Several strategies for this issue have been developed, including quantum error correction (1-3), quantum estimation (4, 5), and dynamical decou- pling (DD) (6-17). In DD, application of multiple �-pulses cancels out the noise, and effectively suppresses the system-environment coupling (6). This basic idea of DD comes from the con- cepts in pulsed NMR (18). In fact, NMR experiments have demonstrated suppression of decoherence by using familiar techniques of pulsed NMR, such as alternating- phase-Carr-Purcell (APCP) and Carr-Purcell-Meiboom- Gill (CPMG) sequences (19, 20). Since then there have been many theoretical (7-14) and experimental (15-17) studies on DD in various kinds of spin- and charge-related qubit systems other than NMR. In these studies com- parison among several methods of DD is of main inter- est, which suggests that optimization of DD requires the properties of noise. In any strategies (even apart from DD), knowledge of the noise properties is helpful, because the strategies can be improved based on the knowledge. It is therefore im- portant to specify the noise properties of the environ- ment. For longitudinal decoherence (energy relaxation) noise, it is well-known that the noise spectrum is obtained from the longitudinal relaxation time (which is called T1 in NMR) (18, 21, 22), and it is proposed that a qubit (two-level system) is utilized as a noise spectrum analyzer (23). In contrast, measurement method for transverse de- coherence (pure dephasing) noise is not established, al- though some methods have recently been proposed (also by using a qubit) (10, 24). In the method in Ref. (10), the moments of the spectrum are obtained by using the Uhrig pulse sequence (8). In the method in Ref. (24), the spectrum at the Rabi frequency is obtained by using a nearly-continuous and on-resonant control field. In this Letter we propose a method of measuring the dephasing noise spectrum. In this method we use a sim- ple sequence of equidistant �-pulses (such as the APCP and CPMG sequences). Using a relation between the noise spectrum and a coherence time under a sequence of sufficiently large number of pulses, we can evaluate the spectrum at frequency �/2� directly from experimentally obtained values of the coherence time, where 2� is the in- terval between pulses. We show that this relation holds in classical-noise, spin-boson, and spin-spin bath models. Model and noise spectrum.—Throughout this Letter we investigate a model of a single spin-1/2 (qubit) inter- acting with its environmental degrees of freedom (bath). The Hamiltonian of the total system is given by" @default.
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• W2739954527 date "2011-05-09" @default.
• W2739954527 modified "2023-10-17" @default.
• W2739954527 title "Measurement of noise spectrum by multiple pulse sequence" @default.
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