Stabilizer Codes and Quantum Error Correction
- D. Gottesman
- Computer Science
- 28 May 1997
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
- S. Aaronson, D. Gottesman
- Computer ScienceArXiv
- 25 June 2004
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
- D. Gottesman, A. Kitaev, J. Preskill
- Physics
- 8 August 2000
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
- D. Gottesman
- Physics
- 24 June 1998
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
- D. Gottesman, I. Chuang
- Physics, Computer ScienceNature
- 2 August 1999
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
- D. Gottesman, H. Lo, N. Lütkenhaus, J. Preskill
- Computer ScienceInternational Symposium onInformation Theory…
- 11 December 2002
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
- R. Cleve, D. Gottesman, H. Lo
- Mathematics
- 12 January 1999
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
- P. Aliferis, D. Gottesman, J. Preskill
- Computer ScienceQuantum information & computation
- 28 April 2005
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.
Theory of fault-tolerant quantum computation
- D. Gottesman
- Computer Science, Physics
- 12 February 1997
It is demonstrated that fault-tolerant universal computation is possible for any stabilizer code, including the five-quantum-bit code.
An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
- D. Gottesman
- Computer Science, Physics
- 16 April 2009
The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary quantum computation provided the error rate per physical gate or time step is below some constant threshold value.
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