# Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers

## TL;DR

This paper introduces a measurement strategy for quantum chemistry on near-term quantum computers that significantly reduces measurement time and improves noise resilience through low rank tensor factorization and postselection techniques.

## Contribution

A novel low rank tensor factorization method that reduces measurement complexity and enhances noise resilience in variational quantum algorithms for molecular systems.

## Key findings

- Measurement times reduced by three orders of magnitude.
- Elimination of sampling challenges with non-local operators.
- Effective error mitigation via postselection.

## Abstract

Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of these techniques to larger molecules might be infeasible. We present a measurement strategy based on a low rank factorization of the two-electron integral tensor. Our approach provides a cubic reduction in term groupings over prior state-of-the-art and enables measurement times three orders of magnitude smaller than those suggested by commonly referenced bounds for the largest systems we consider. Although our technique requires execution of a linear-depth circuit prior to measurement, this is compensated for by eliminating challenges associated with sampling non-local Jordan-Wigner transformed operators in the presence of measurement error, while enabling a powerful form of error mitigation based on efficient postselection. We numerically characterize these benefits with noisy quantum circuit simulations for ground state energies of strongly correlated electronic systems.