Quantum circuit compilation and hybrid computation using Pauli-based computation

Understand

Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables.

• Any quantum circuit written in terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiled into a PBC on $t$ qubits.
• Here we propose practical ways of implementing PBC as adaptive quantum circuits and provide code to do the required classical side-processing.
• Our schemes reduce the number of quantum gates to $O(t^2)$ (from a previous $O(t^3 / \log t)$ scaling) and space/time trade-offs are discussed which lead to a reduction of the depth from $O(t \log t)$ to $O(t)$ within our schemes, at the cost of $t$ additional auxiliary qubits.