Quantum Error Correction in the Zeno Regime

Abstract

In order to reduce errors, error correction codes (ECCs) need to be implemented fast. They can correct the errors corresponding to the first few orders in the Taylor expansion of the Hamiltonian of the interaction with the environment. If implemented fast enough, the zeroth order error predominates and the dominant effect is of error prevention by measurement (Zeno Effect) rather than correction. In this ``Zeno Regime'', codes with less redundancy are sufficient for protection. We describe such a simple scheme, which uses two ``noiseless'' qubits to protect a large number, $n$, of information qubits from noise from the environment. The ``noisless qubits'' can be realized by treating them as logical qubits to be encoded by one of the previously introduced encoding schemes.

11 pages

References in corpus (9)

• Mixed State Entanglement and Quantum Error Correction
• Dynamical suppression of decoherence in two-state quantum systems
• Teleportation of Quantum States
• Robustness of adiabatic quantum computation
• Universal dynamical control of quantum mechanical decay: Modulation of the coupling to the continuum
• Error Prevention Scheme with Four Particles
• Combined encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing
• Quantum Computing in the Presence of Detected Spontaneous Emission
• Combined Error Correction Techniques for Quantum Computing Architectures

Cited by in corpus (15)

• Continuous quantum error correction by cooling
• Protecting, Enhancing and Reviving Entanglement
• All-Optical control of linear and nonlinear energy transfer via Zeno effect
• Perfect Zeno-like effect through imperfect measurements at a finite frequency
• Quantum Zeno effect for open quantum systems
• Experimental protection against evolution of states in a subspace via a super-Zeno scheme on an NMR quantum information processor
• Quantum Quasi-Zeno Dynamics: Transitions mediated by frequent projective measurements near the Zeno regime
• Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions
• Generation of polarization entanglement via the quantum Zeno effect
• Robustness-optimized quantum error correction
• Quantum Trajectory method for the Quantum Zeno and anti-Zeno effects
• On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications
• Quantum control for the Zeno effect with noise
• Eliminating the Second-Order Time Dependence from the Time Dependent Schrödinger Equation Using Recursive Fourier Transforms
• Error correction in short time steps during the application of quantum gates