Quantum circuit compilation and hybrid computation using Pauli-based computation

Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, nondestructive 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(t2) (from a previous O(t3/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. We compile examples of random and hidden-shift quantum circuits into adaptive PBC circuits. We also simulate hybrid quantum computation, where a classical computer effectively extends the working memory of a small quantum computer by k virtual qubits, at a cost exponential in k. Our results demonstrate the practical advantage of PBC techniques for circuit compilation and hybrid computation.