Error Correcting Codes For Adiabatic Quantum Computation

@article{Jordan2006ErrorCC,
  title={Error Correcting Codes For Adiabatic Quantum Computation},
  author={Stephen P. Jordan and Edward Farhi and Peter W. Shor},
  journal={Physical Review A},
  year={2006},
  volume={74},
  pages={052322}
}
Mathematics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139(Dated: February 1, 2008)Recently, there has been growing interest in using adiabatic quantum computation as an architec-ture for experimentally realizable quantum computers. One of the reasons for this is the idea thatthe energy gap should provide some inherent resistance to noise. It is now known that universalquantum computation can be achieved adiabatically using 2-local Hamiltonians. The energy gap… 
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References

SHOWING 1-10 OF 12 REFERENCES
Quantum Computation and Quantum Information
TLDR
This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Classical and Quantum Computation
Introduction Classical computation Quantum computation Solutions Elementary number theory Bibliography Index.
Quantum Computation and Quantum Information (Cambridge
  • 2000
and O
  • Regev, Proceedings of FSTTCS
  • 2004
and R
  • Seiler, arXiv:quantph/0603175
  • 2006
Physical Review A 71
  • 032330
  • 2005
and R
  • Schützhold, Physical Review A 73
  • 2006
and M
  • Sipser, arXiv:quant-ph/0001106
  • 2000
Physical Review Letters 63
  • 1989
...
...