Trapdoored Clifford Operators and Applications
Authors construct trapdoored Clifford operators that look random but implement much faster with a secret trapdoor.
The paper introduces trapdoored Clifford operator distributions that are computationally indistinguishable from uniformly random n-qubit Cliffords but faster to implement given a trapdoor. Sampling and implementation run in near-linear time under a variant of learning parity with noise, and can be optimized to polylogarithmic depth. The authors also construct trapdoored matrices over finite fields that multiply efficiently by both a matrix and its inverse. They apply the constructions to faster random-Clifford protocols and show batch Clifford circuit synthesis is at least as hard as worst-case matrix multiplication.
- Trapdoored Cliffords are indistinguishable from uniformly random Cliffords.
- Sampling and implementation run in near-linear time under an LPN variant.
- Trapdoored finite-field matrices support efficient multiplication by the inverse.
- Batch Clifford synthesis is at least as hard as matrix multiplication.
From the original article
1 min read at arxiv.orgRandom Clifford operators have numerous applications in quantum computing, including randomized benchmarking, classical shadows, and quantum authentication. However, sampling and implementing uniformly random $n$-qubit Clifford incur near-quadratic complexity due to the size of Clifford group.
By Minki Hhan · arxiv.org
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