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Optimization of Clifford circuits

Thursday December 2, 2021
3:30 pm

 Presenter:  Sergey Bravyi (IBM Quantum)
 Series:  CQuIC Seminars
 Abstract:  The Clifford group is a finite subgroup of the unitary group generated by the Hadamard, the CNOT, and the Phase gates. This group plays a prominent role in quantum error correction, randomized benchmarking protocols, and the study of entanglement. We consider the problem of finding a short quantum circuit implementing a given Clifford group element. The goal is to minimize the CNOT gate count assuming all-to-all qubit connectivity. Three methods are discussed: (1) Optimal compiler that finds a provably shortest circuit implementation for small-size circuits, (2) Symbolic peephole and template matching optimizers that can be scaled up to medium size circuits but do not guarantee optimality, and (3) Canonical decompositions that apply to arbitrary size circuits. The last method also yields an improved algorithm for generating a random uniformly distributed Clifford operator.
 Host:  Milad Marvian
 Location:  Zoom

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