The Non-Equilibrium Reliability of Quantum Memories

Abstract

The ability to store quantum information without recourse to constant feedback processes would yield a significant advantage for future implementations of quantum information processing. In this paper, limitations of the prototypical model, the Toric code in two dimensions, are elucidated along with a sufficient condition for overcoming these limitations. Specifically, the interplay between Hamiltonian perturbations and dynamically occurring noise is considered as a system in its ground state is brought into contact with a thermal reservoir. This proves that when utilizing the Toric code on N^2 qubits in a 2D lattice as a quantum memory, the information cannot be stored for a time O(N). In contrast, the 2D Ising model protects classical information against the described noise model for exponentially long times. The results also have implications for the robustness of braiding operations in topological quantum computation.

4 pages. v3: published version

References in corpus (8)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• Perfect state transfer in quantum spin networks
• Mirror Inversion of Quantum States in Linear Registers
• Spin Chains as Perfect Quantum State Mirrors
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Entanglement and topological entropy of the toric code at finite temperature
• State Transfer and Spin Measurement

Cited by in corpus (23)

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• Perfect Quantum Routing in Regular Spin Networks
• The Basics of Perfect Communication through Quantum Networks
• Simulations of quantum double models
• Bringing order through disorder: Localization of errors in topological quantum memories
• Unification and limitations of error suppression techniques for adiabatic quantum computing
• Error suppression and error correction in adiabatic quantum computation I: techniques and challenges
• Topological Order Following a Quantum Quench
• Localization of Toric Code Defects
• Incoherent dynamics in the toric code subject to disorder
• The Capabilities of a Perturbed Toric Code as a Quantum Memory
• Anyonic self-induced disorder in a stabilizer code: quasi-many body localization in a translational invariant model
• Topological order, entanglement, and quantum memory at finite temperature
• Multipartite entanglement of the topologically ordered state in a perturbed toric code
• Thermalization of Topological Entropy after a Quantum Quench
• Thermal States of Anyonic Systems
• Logarithmic light cone, slow entanglement growth, and quantum memory
• Bounded light cone and robust topological order out of equilibrium
• Disorder-protected topological entropy after a quantum quench