We describe how to use the fidelity decay as a tool to characterize the errors affecting a quantum information processor through a noise generator Gτ . For weak noise, the initial decay rate of the fidelity proves to be a simple way to measure the magnitude of the different terms in Gτ . When the generator has only terms associated with few-body couplings, our proposal is scalable. We present the explicit protocol for estimating the magnitude of the noise generators when the noise consists of only one and two-body terms, and describe a method for measuring the parameters of more general noise models. The protocol focuses on obtaining the magnitude with which these terms affect the system during a time step of length τ ; measurement of this information has critical implications for assesing the scalability of fault-tolerant quantum computation in any physical setup.
We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an N 2 -dimensional quantum environment and random classical fields. This model offers the advantage that it may be implemented on small quantum information processors in order to explore the intermediate regime between semiclassical and fully quantum models. We consider in particular σzσz system-environment couplings which induce coherence (phase) damping, though the model is directly extendable to other coupling Hamiltonians. Effective, irreversible phase-damping of the system is obtained by applying an additional stochastic Hamiltonian on the environment alone, periodically redressing it and thereby irreversibliy randomizing the system phase information that has leaked into the environment as a result of the coupling. This model is exactly solvable in the case of phase-damping, and we use this solution to describe the model's behavior in some limiting cases. In the limit of small stochastic phase kicks the system's coherence decays exponentially at a rate which increases linearly with the kick frequency. In the case of strong kicks we observe an effective decoupling of the system from the environment. We present a detailed implementation of the method on an nuclear magnetic resonance quantum information processor.
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