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Pauli-based computation (PBC) is driven by a sequence of adaptively chosen,non-destructive measurements of Pauli observables. Any quantum circuit writtenin terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiledinto a PBC on $t$ qubits. Here we propose practical ways of implementing PBC asadaptive quantum circuits and provide code to do the required classicalside-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 arediscussed 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 compileexamples of random and hidden-shift quantum circuits into adaptive PBCcircuits. We also simulate hybrid quantum computation, where a classicalcomputer effectively extends the working memory of a small quantum computer by$k$ virtual qubits, at a cost exponential in $k$. Our results demonstrate thepractical advantage of PBC techniques for circuit compilation and hybridcomputation.

Quantum circuit compilation and hybrid computation using Pauli-based computation