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Stabilizer Codes and Quantum Error Correction
TLDR
An overview of the field of quantum error correction and the formalism of stabilizer codes is given and a number of known codes are discussed, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation are discussed.
Improved Simulation of Stabilizer Circuits
TLDR
The Gottesman-Knill theorem, which says that a stabilizer circuit, a quantum circuit consisting solely of controlled-NOT, Hadamard, and phase gates can be simulated efficiently on a classical computer, is improved in several directions.
Encoding a qubit in an oscillator
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes
The Heisenberg Representation of Quantum Computers
Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features
Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
TLDR
It is shown that single quantum bit operations, Bell-basis measurements and certain entangled quantum states such as Greenberger–Horne–Zeilinger (GHZ) states are sufficient to construct a universal quantum computer.
Security of quantum key distribution with imperfect devices
This paper prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the source and detector are under the limited control of an adversary. This proof
HOW TO SHARE A QUANTUM SECRET
We investigate the concept of quantum secret sharing. In a (k,thinspn) threshold scheme, a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the
Quantum accuracy threshold for concatenated distance-3 codes
TLDR
A new version of the quantum threshold theorem is proved that applies to concatenation of a quantum code that corrects only one error, and this theorem is used to derive arigorous lower bound on the quantum accuracy threshold e0, the best lower bound that has been rigorously proven so far.
An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some
Theory of fault-tolerant quantum computation
In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a
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