Universal Leakage Elimination

Abstract

``Leakage'' errors are particularly serious errors which couple states within a code subspace to states outside of that subspace thus destroying the error protection benefit afforded by an encoded state. We generalize an earlier method for producing leakage elimination decoupling operations and examine the effects of the leakage eliminating operations on decoherence-free or noiseless subsystems which encode one logical, or protected qubit into three or four qubits. We find that by eliminating the large class of leakage errors, under some circumstances, we can create the conditions for a decoherence free evolution. In other cases we identify a combination decoherence-free and quantum error correcting code which could eliminate errors in solid-state qubits with anisotropic exchange interaction Hamiltonians and enable universal quantum computing with only these interactions.

14 pages, no figures, new version has references updated/fixed

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• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
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• Nonperturbative Leakage Elimination Operators and Control of a Three-Level System
• Principles of Control for Decoherence-Free Subsystems
• Dynamically corrected gates for an exchange-only qubit
• Level Reduction and the Quantum Threshold Theorem
• Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: ${}^{174}$Yb${}^{+}$ and ${}^{171}$Yb${}^{+}$
• Quantum computation with ultracold atoms in a driven optical lattice
• Experimental recovery of a qubit from partial collapse
• Handling Leakage with Subsystem Codes
• Elastic Spin Relaxation Processes in Semiconductor Quantum Dots
• Subspace Confinement: How good is your qubit?
• Decoherence of an exchange qubit by hyperfine interaction
• Robust and Reliable Transfer of a Quantum State Through a Spin Chain
• Intrinsic leakage of the Josephson flux qubit and breakdown of the two-level approximation for strong driving
• Dynamical control of quantum state transfer within hybrid open systems
• Pulse sequences for suppressing leakage in single-qubit gate operations
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• Almost exact state transfer in a spin chain via pulse control
• An adiabatic Leakage Elimination Operator in experimental framework
• Device Architecture for Coupling Spin Qubits Via an Intermediate Quantum State
• Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems
• Benchmarking quantum gates and circuits
• Experimentally Realizable C-NOT Gate in a Flux Qubit/Resonator System
• Compatible Transformations for a Qudit Decoherence-free/Noiseless Encoding
• Quantum communication, reference frames and gauge theory
• Dynamically Generated Decoherence-Free Subspaces and Subsystems on Superconducting Qubits
• Decoherence-free quantum information in the presence of dynamical evolution
• Single-step controlled-NOT logic from any exchange interaction
• Relative information encoded in the degree of entanglement to discriminate bipartite states
• Error metric for non-trace-preserving quantum operations
• The Spin Density Matrix I: General Theory and Exact Master Equations
• Nonperturbative leakage elimination for a logical qubit encoded in a mechanical oscillator
• Dynamics and Control of Two Coupled Quantum Oscillators: An Analytical Approach
• Fields of quantum reference frames based on different representations of rational numbers as states of qubit strings
• Experimental implementation of leakage elimination operators