Noise mitigation of quantum observables via learning from Hamiltonian symmetry decays

TL;DR

The paper introduces GUESS, a quantum error mitigation method leveraging Hamiltonian symmetries to enhance the accuracy of noisy quantum expectation value estimations, demonstrating superior performance on large-scale circuits.

Contribution

It proposes a novel symmetry-based error mitigation technique called GUESS, which learns extrapolation coefficients and enforces symmetries to improve quantum observable estimates.

Findings

Achieves ~10% relative error on 100-qubit systems with up to 8000 CZ gates.

Outperforms baseline Zero Noise Extrapolation in accuracy and variance reduction.

Enables statistical post-selection using symmetry observable outcomes.

Abstract

We present a new quantum error mitigation technique (QEM), called GUiding Extrapolations from Symmetry decayS (GUESS), which exploits Hamiltonian symmetries to improve accuracy of noisy quantum computations. This method is explicitly designed for quantum algorithms that estimate expectation values of observables and consists in learning the extrapolation coefficients from a symmetry observable of the system to then estimate the value of a target observable. Furthermore, we propose a Hamiltonian impurity technique to enforce symmetries allowing the mitigation of local observables of interest. We employ the IBM Heron r2 quantum processing unit '\texttt{ibm\_basquecountry}' to simulate the time evolution of average magnetization and nearest-neighbor correlator observables for transverse field Ising and $XZ$ Heisenberg models in 1D with open boundary conditions. We benchmark the accuracy of our method against baseline Zero Noise Extrapolation (ZNE) and tensor network simulations for systems of $100$ qubits. Remarkably, GUESS achieves a relative error around $10\%$ for circuits containing up to $8000$ CZ gates, while showcasing lower variance than ZNE on average across $20$ observables and requiring only twice the number of shots per observable compared to baseline ZNE. Furthermore, we demonstrate that GUESS enables statistical post-selection based on the outcomes of the symmetry observable, which provides critical information about the quality of the target qubits by means of its mean and variance. These results indicate that GUESS is a powerful QEM technique capable of mitigating utility-scale circuit outcomes, delivering high accuracy and reduced variance for large-scale circuits with minimal quantum overhead.