Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code

@inproceedings{Bravyi2011AnalyticAN,
  title={Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code},
  author={Sergey Bravyi and Jeongwan Haah},
  year={2011}
}
A big open question in the quantum information theory concerns feasibility of a selfcorrecting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction if the memory is put in contact with a cold enough thermal bath. In this paper we derive a rigorous lower bound on the memory time Tmem of the 3D Cubic Code model which was recently conjectured to have a self-correcting behavior. Assuming that dynamics of the… Expand

Figures from this paper

Self-correcting quantum memory with a boundary
We study the two-dimensional toric-code Hamiltonian with effective long-range interactions between its anyonic excitations induced by coupling the toric code to external fields. It has been shownExpand
The Ising ferromagnet as a self-correcting physical memory: a Monte-Carlo study
The advent of quantum computing has heralded a renewed interest in physical memories - physically realizable structures that offer reliable data storage with error correction only at the point ofExpand
Lattice quantum codes and exotic topological phases of matter
This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one ofExpand
Topological quantum error correction in the Kitaev honeycomb model
The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it isExpand
Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics thatExpand
Self-correcting quantum computers
TLDR
This work first gives a sufficient condition on the connectedness of excitations for a stabilizer code model to be a self-correcting quantum memory, then studies the two main examples of topological stabilizer codes in arbitrary dimensions and establishes their self-Correcting capabilities. Expand
Finite Temperature Quantum Memory and Haah’s Code
One of the more exciting potential applications of topological phases is in quantum computing and information science. First proposed by Kitaev,[12] it may be possible to implement the unitaryExpand
Conditional Independence in Quantum Many-Body Systems
In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed toExpand
Towards self-correcting quantum memories
TLDR
A no-go theorem is proved for a class of Hamiltonians where the interaction terms are local, of bounded strength and commute with the stabilizer group and under these conditions the energy barrier can only be increased by a multiplicative constant. Expand
Topological Code Architectures for Quantum Computation
This dissertation is concerned with quantum computation using many-body quantum systems encoded in topological codes. The interest in these topological systems has increased in recent years asExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 46 REFERENCES
Feasibility of self-correcting quantum memory and thermal stability of topological order
Abstract Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing theExpand
Self-correcting quantum memory in a thermal environment
The ability to store information is of fundamental importance to any computer, be it classical or quantum. To identify systems for quantum memories, which rely, analogously to classical memories, onExpand
Topological quantum memory
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, andExpand
Disorder-Assisted Error Correction in Majorana Chains
It was recently realized that quenched disorder may enhance the reliability of topological qubits by reducing the mobility of anyons at zero temperature. Here we compute storage times with andExpand
Toric-boson model: Toward a topological quantum memory at finite temperature
We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum informationExpand
Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes
We discuss several thermodynamic criteria that have been introduced to characterize the thermal stability of a self-correcting quantum memory. We first examine the use of symmetry-breaking fields inExpand
Autocorrelations and thermal fragility of anyonic loops in topologically quantum ordered systems
Are systems that display Topological Quantum Order (TQO), and have a gap to excitations, hardware fault-tolerant at finite temperatures? We show that in models that display low d-dimensionalExpand
Bringing order through disorder: localization of errors in topological quantum memories.
TLDR
It is demonstrated that the induced localization of Anderson localization allows the topological quantum memory to regain a finite critical anyon density and the memory to remain stable for arbitrarily long times. Expand
Thermal states of anyonic systems
Abstract A study of the thermal properties of two-dimensional topological lattice models is presented. This work is relevant to assess the usefulness of these systems as a quantum memory. For ourExpand
A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
We study properties of stabilizer codes that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge group for subsystemExpand
...
1
2
3
4
5
...