Threshold theorem shows noisy quantum computers can still compute reliably

Why it matters

It means quantum hardware has to be good enough, not perfect. Shor recalls that it made quantum computers look technologically possible and set off a wave of research on how to build them.

Related

• Peter Shor shows quantum information can be protected from errors (Oct 1, 1995)
• Steane, Calderbank and Shor find a recipe for building quantum codes (1996)
• Alexei Kitaev proposes the toric code and topological quantum computing (Jul 9, 1997)

Sources (5)

• arXiv (Knill, Laflamme and Zurek) Threshold Accuracy for Quantum Computation
  Primary sourceOct 8, 1996

  “10/15/96: Added references to threshold results by Aharanov and Ben-Or and by Kitaev”

• arXiv (Aharonov and Ben-Or) Fault Tolerant Quantum Computation with Constant Error
  Primary sourceNov 14, 1996

  “We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than some constant threshold.”

• arXiv (Knill, Laflamme and Zurek) Resilient Quantum Computation: Error Models and Thresholds
  Primary sourceFeb 26, 1997

  “Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value.”

• arXiv (John Preskill) Quantum computing 40 years later
  Independent coverageJun 2021

  “By the end of 1996, it was understood at least in principle that quantum computing could be scaled up to large devices that solve very hard problems, assuming that errors afflicting the hardware are not too common or too strongly correlated”

• arXiv (Peter W. Shor) The Early Days of Quantum Computation
  Independent coverageAug 21, 2022

  “The discovery of the threshold theorem showed that quantum computers might be technologically possible (although still very difficult), and led to an outburst of research into ways that they might actually be built.”