Overview of Quantum Error Prevention and Leakage Elimination

Abstract

Quantum error prevention strategies will be required to produce a scalable quantum computing device and are of central importance in this regard. Progress in this area has been quite rapid in the past few years. In order to provide an overview of the achievements in this area, we discuss the three major classes of error prevention strategies, the abilities of these methods and the shortcomings. We then discuss the combinations of these strategies which have recently been proposed in the literature. Finally we present recent results in reducing errors on encoded subspaces using decoupling controls. We show how to generally remove mixing of an encoded subspace with external states (termed leakage errors) using decoupling controls. Such controls are known as ``leakage elimination operations'' or ``LEOs.''

8 pages, no figures, submitted to the proceedings of the Physics of Quantum Electronics, 2004

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• Protection of entanglement from sudden death using continuous dynamical decoupling
• Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: ${}^{174}$Yb${}^{+}$ and ${}^{171}$Yb${}^{+}$
• Handling Leakage with Subsystem Codes
• Single-bit Feedback and Quantum Dynamical Decoupling
• Robust and Reliable Transfer of a Quantum State Through a Spin Chain
• Dynamical control of quantum state transfer within hybrid open systems
• Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems
• Entanglement-Preserving Limit Cycles from Sequential Quantum Measurements and Feedback
• Affine Maps of the Polarization Vector for Quantum Systems of Arbitrary Dimension
• Dynamics of one-dimensional tight-binding models with arbitrary time-dependent external homogeneous fields
• Compatible Transformations for a Qudit Decoherence-free/Noiseless Encoding
• Continuously decoupling a Hadamard quantum gate from independent classes of errors
• Methods for Producing Decoherence-Free States and Noiseless Subsystems Using Photonic Qutrits
• Shielding quantum discord through continuous dynamical decoupling
• Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations
• Perfect Function Transfer in two- and three- dimensions without initialization
• Dynamics of a tight-binding ring threaded by time-periodic magnetic flux
• General Depolarized Pure States: Identification and Properties
• Casimir Invariants for Systems Undergoing Collective Motion
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
• Combating errors in propagation of orbital angular momentum modes of light in turbulent media
• Decoherence-Free Communication over Multiaccess Quantum Channels
• Error-immune quantum communication