Clifford hierarchy

For each fixed degree bound \(d\geq2\), is there a deterministic polynomial-time algorithm that computes the Clifford-hierarchy level of an \(n\)-qubit permutation gate from degree-at-most-\(d\) algebraic normal forms of the permutation and its inverse, or reports…

• Quantum Algorithm
• Clifford hierarchy
• Computational complexity and computability

What is the smallest number of qubits on which the third level of the Clifford hierarchy contains a gate that is not semi-Clifford?

• Quantum Algorithm
• Clifford hierarchy

Is every two-qudit gate in every level \(k\geq4\) of the Clifford hierarchy semi-Clifford when the local dimension is an odd prime?

• Quantum Algorithm
• Clifford hierarchy

What is the highest Clifford-hierarchy level that a controlled gate can reach when its target lies in a given level \(k\geq3\) and has a given Pauli periodicity, and is that level bounded independently of the number of target qubits?

• Quantum Algorithm
• Clifford hierarchy