Decision Diagrams for Quantum Measurements with Shallow Circuits

TL;DR

This paper introduces decision diagram-based estimators for quantum measurements using shallow circuits, improving estimation precision for certain quantum chemistry Hamiltonians over previous methods.

Contribution

It presents a novel estimator framework using decision diagrams for quantum observable estimation with shallow circuits, generalizing existing randomised measurement techniques.

Findings

Estimators outperform previous protocols on some quantum chemistry Hamiltonians.

Decision diagrams enable optimized sampling strategies.

Numerical results show increased measurement precision.

Abstract

We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on randomised measurements, which use decision diagrams to sample from probability distributions on measurement bases. This approach generalises previously known uniform and locally-biased randomised estimators. The decision diagrams are constructed given target quantum operators and can be optimised considering different strategies. We show numerically that the estimators introduced here can produce more precise estimates on some quantum chemistry Hamiltonians, compared to previously known randomised protocols and Pauli grouping methods.