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why topological quantum computers cannot work -Gil Kalai

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Published on Mar 16, 2014

Speaker: Gil Kalai (Hebrew University of Jerusalem and Yale University)

Title: Why Topological quantum computers cannot work

Abstract: This is a supplement to Gil Kalai's lectures at the Simons' Institute for the Theory of Computing on "Why quantum computers cannot work".
The lecture explains why topological quantum computers cannot work and discusses
why noisy gapped evolutions with local terms on lattices in 2D and 3D cannot present quantum computational speedup.

The argument for why topological quantum computing cannot work is based on the basic idea of
reductions: The experimental process for creating the building blocks, the anyonic qubits, can be simulated by a noisy quantum computer not involving quantum fault tolerance.
This means that there will be a substantial probability for logical errors, rather than the highly stable qubits expected by researchers.
This argument applies for several other idea for "short-cuts" towards quantum computation
like adiabatic computation, quantum annealing, and BosonSampling.

The argument for gapped systems is based on a
vicious circle between new phases of matter, (deep) quantum computing, and quantum error-correction:
new phases of matter requires deep quantum computing, deep quantum computing requires
quantum error-correction and quantum error-correction requires new phases of matter.

Some further remarks on quantum noise, quantum fault tolerance, geometry, and time are made. Those can be summarized by a slogan:
"The geometry of spacetime is enabled by the failure of quantum fault-tolerance."

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