Quantum circuit compilation and hybrid computation using Pauli-based computation

TL;DR

This paper introduces efficient methods for compiling Clifford+$T$ quantum circuits into Pauli-based computation, reducing gate complexity and enabling hybrid quantum-classical computation with practical advantages.

Contribution

It presents new algorithms for implementing PBC with reduced gate count and depth, and demonstrates hybrid quantum computation extending quantum memory via classical simulation.

Findings

Reduced quantum gate complexity to O(t^2) from O(t^3 / log t)

Achieved depth reduction from O(t log t) to O(t) with additional qubits

Showed practical advantages in circuit compilation and hybrid computation

Abstract

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. 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.