The stabilizer code formalism is presented as a powerful group-theoretic tool for quantum error correction, enabling code construction, analysis of quantum channel capacity, bounds on codes, and fault-tolerant computation.
Strengths and weaknesses of quantum computing
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SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity with the regularized maximal geodesic length as distinguisher.
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Stabilizer Codes and Quantum Error Correction
The stabilizer code formalism is presented as a powerful group-theoretic tool for quantum error correction, enabling code construction, analysis of quantum channel capacity, bounds on codes, and fault-tolerant computation.
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Pseudorandom Dynamics in the SYK Model and Cryptographic Censorship in JT Gravity
SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity with the regularized maximal geodesic length as distinguisher.