Reducing circuit depth with qubitwise diagonalization

TL;DR

This paper introduces an efficient algorithm for diagonalizing multiple Pauli operators simultaneously, significantly reducing quantum circuit depth and gate count, especially beneficial for hardware with limited qubit connectivity.

Contribution

The proposed algorithm achieves $O(n \, log r)$ circuit depth for diagonalizing n-qubit operators generated by r Pauli operators, improving over previous methods.

Findings

Performs well on randomly generated Hamiltonians

Produces low-depth circuits for molecular Hamiltonians

Maintains low two-qubit gate counts

Abstract

A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves simultaneous diagonalization of Pauli operators generating unitary evolution operators or observables of interest. We propose an algorithm yielding quantum circuits with depths $O(n \log r)$ diagonalizing $n$-qubit operators generated by $r$ Pauli operators. Moreover, as our algorithm iteratively diagonalizes all operators on at least one qubit per step, it is well suited to maintain low circuit depth even on hardware with limited qubit connectivity. We observe that our algorithm performs favorably in producing quantum circuits diagonalizing randomly generated Hamiltonians as well as molecular Hamiltonians with short depths and low two-qubit gate counts.