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Quantum Serial Turbo Codes
A theory of quantum serial turbo codes, a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular, its recursiveness and the presence of catastrophic error propagation is presented.
On the iterative decoding of sparse quantum codes
These results indicate that the main source of errors in the quantum coding scheme remains in the decoding, and propose heuristic methods to improve belief propagation decoding specifically targeted at these two problems.
Quantum Metropolis sampling
This paper demonstrates how to implement a quantum version of the Metropolis algorithm, a method that has basically acquired a monopoly on the simulation of interacting particles and permits sampling directly from the eigenstates of the Hamiltonian, and thus avoids the sign problem present in classical simulations.
Practical characterization of quantum devices without tomography.
It is demonstrated that fidelity can be estimated from a number of simple experiments that is independent of the system size, removing an important roadblock for the experimental study of larger quantum information processing units.
Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space.
We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it
Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer.
A quantum algorithm is presented that sets a universal upper bound D(alpha) on the thermalization time of a quantum system, where D is the system's Hilbert space dimension and alpha < or = 1/2 is proportional to the Helmholtz free energy density.
Stabilizer formalism for operator quantum error correction.
  • D. Poulin
  • Computer Science
    Physical review letters
  • 18 August 2005
This Letter identifies a gauge symmetry in Shor's 9-qubit code that allows us to remove 3 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties, which opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.
Fast decoders for topological quantum codes.
A family of algorithms is presented, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects, which achieves a higher depolarizing error threshold.
Information-preserving structures: A general framework for quantum zero-error information
An operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly preserved by quantum dynamics, and proves that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected.
Objective properties from subjective quantum states: environment as a witness.
It is shown that only preferred pointer states of the system can leave a redundant and therefore easily detectable imprint on the environment.