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arXiv:quant-ph/0506085 · Physical Review Letters

Characterization of Complex Quantum Dynamics with a Scalable NMR Information Processor

Colm A. Ryan, Joseph Emerson, David Poulin, C. Negrevergne, Raymond Laflamme

Published Dec 15, 2005• 39 citations
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Abstract

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system or measuring the decoherence rate from engineered environments.

DOI
10.1103/physrevlett.95.250502

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We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system or measuring the decoherence rate from engineered environments.
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Among the most important parameters for the usefulness of quantum computers are the size of the quantum register and the decoherence time for the quantum information. The decoherence time is expected to get shorter with the number of correlated qubits, but experimental data are only available for small numbers of qubits. Solid-state nuclear magnetic resonance allows one to correlate large numbers of qubits (several hundred) and measure their decoherence rates. We use a modified magnetic dipole-dipole interaction to correlate the proton spins in a solid sample and observe the decay of the resulting highly correlated states. By systematically varying the number of correlated spins, we measure the increase of the decoherence rate with the size of the quantum register.
We describe how to use the fidelity decay as a tool to characterize the errors affecting a quantum information processor through a noise generator ${G}_{\ensuremath{\tau}}$. 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 ${G}_{\ensuremath{\tau}}$. 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 $\ensuremath{\tau}$; measurement of this information has critical implications for assessing the scalability of fault-tolerant quantum computation in any physical setup.
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One of the major experimental achievements in the past decades is the ability to control quantum systems to high levels of precision. To quantify the level of control we need to characterize the dynamical evolution. Full characterization via quantum process tomography is impractical and often unnecessary. For most practical purposes, it is enough to estimate more general quantities such as the average fidelity. Here we use a unitary 2-design and twirling protocol for efficiently estimating the average fidelity of Clifford gates, to certify a 7-qubit entangling gate in a nuclear magnetic resonance quantum processor. Compared with more than 10^{8} experiments required by full process tomography, we conducted 1656 experiments to satisfy a statistical confidence level of 99%. The average fidelity of this Clifford gate in experiment is 55.1%, and rises to at least 87.5% if the signal's decay due to decoherence is taken into account. The entire protocol of certifying Clifford gates is efficient and scalable, and can easily be extended to any general quantum information processor with minor modifications.