Pith. sign in

This requires another polynomial multiplication q(x) · p(x), which uses a circuit depth of O(log n) and a size of O(n log n log logn)

Remainder computation: Compute the remainder: r(x) = c′(x) − q(x) · p(x) = c′(x) + q(x) · p(x), (33) where the second equality holds in F2[x]

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Unitary designs in nearly optimal depth

quant-ph · 2025-07-08 · conditional · novelty 8.0

An ε-approximate unitary k-design on n qubits can be implemented in depth O(log k · log log(nk/ε)) using long-range two-qubit gates, with near-optimal ancilla and randomness costs.

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  • Unitary designs in nearly optimal depth quant-ph · 2025-07-08 · conditional · none · ref 5

    An ε-approximate unitary k-design on n qubits can be implemented in depth O(log k · log log(nk/ε)) using long-range two-qubit gates, with near-optimal ancilla and randomness costs.