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AIP conference proceedings

Simulation of non-resonant quantum control protocols for a single qubit

Sara Cruz y Cruz, Julieta Medina, Miguel García Rocha, Ricardo Lopez Fernandez, Luis F. Rojas Ochoa, Gabino Torres Vega

Published Jan 1, 2010• 1 citation
Publisher

Abstract

The resonant control techniques are susceptible of assisting error accumulation in quantum control protocols consisting of large sequences of external fields. It is shown that for some algorithms the information about the final state of the system may be partially or completely lost. Non trivial operations in the non resonant regime are also discussed.

DOI
10.1063/1.3507425

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The resonant control techniques are susceptible of assisting error accumulation in quantum control protocols consisting of large sequences of external fields. It is shown that for some algorithms the information about the final state of the system may be partially or completely lost. Non trivial operations in the non resonant regime are also discussed.
In this paper the stability of specific quantum control protocols is analyzed through a simu­lation. Two-level quantum systems driven by resonant external fields are studied. The focus of attention are those protocols requiring long sequences of external pulses. It is proven that these techniques are prone to cumulative error. Inspired by the methodology of the treatment of noise in signal processing, noise effects of practical implementations of single qubit quantum algorithms are also considered. The numerical results are consistent when compared to experimental data previously reported.
The successful operation of quantum computers relies on protecting qubits from decoherence and noise, which - if uncorrectet - will lead to erroneous results. Because these errors accumulate during an algorithm, correcting them becomes a key requirement for large-scale and fault-tolerant quantum information processors. Besides computational errors, which can be addressed by quantum error correction [2] – [8] , the carrier of the information can also be completely lost or the information can leak out of the computational space [9] – [13] .
In building a quantum-information processor (QIP), the challenge is to coherently control a large quantum system well enough to perform an arbitrary quantum algorithm and to be able to correct errors induced by decoherence. Nuclear magnetic resonance (NMR) QIPs offer an excellent testbed on which to develop and benchmark tools and techniques to control quantum systems. Two main issues to consider when designing control methods are accuracy and efficiency, for which two complementary approaches have been developed so far to control qubit registers with liquid-state NMR methods. The first applies optimal control theory to numerically optimize the control fields to implement unitary operations on low-dimensional systems with high fidelity. The second technique is based on the efficient optimization of a sequence of imperfect control elements so that implementation of a full quantum algorithm is possible while minimizing error accumulation. This paper summarizes our work in implementing both of these methods. Furthermore, we show that taken together, they form a basis to design quantum control methods for a block-architecture QIP so that large system size is not a barrier to implementing optimal control techniques.